Working 2D-mpi for enhanced solver

2023-10-09 16:56:43 +02:00
parent fcff353999
commit 86f7677f34
31 changed files with 39012 additions and 171322 deletions
--- a/BasicSolver/2D-mpi-v3/Makefile
+++ b/BasicSolver/2D-mpi-v3/Makefile
@@ -39,7 +39,7 @@ $(BUILD_DIR)/%.s:  %.c

 .PHONY: clean distclean tags info asm format

-clean:
+clean: vis
 	$(info ===>  CLEAN)
 	@rm -rf $(BUILD_DIR)
 	@rm -f tags
@@ -54,6 +54,11 @@ info:

 asm:  $(BUILD_DIR) $(ASM)

+vis:
+	$(info ===>  REMOVING VIZUALISATION FILES)	
+	@rm -f vtk_files/particle*.vtk
+	@rm -f vis_files/particle*.dat
+
 tags:
 	$(info ===>  GENERATE TAGS)
 	$(Q)ctags -R
--- a/BasicSolver/2D-mpi-v3/backstep.par
+++ b/BasicSolver/2D-mpi-v3/backstep.par
@@ -0,0 +1,72 @@
+#==============================================================================
+#                            Laminar Canal Flow
+#==============================================================================
+
+# Problem specific Data:
+# ---------------------
+
+name backstep             # name of flow setup
+
+bcTop      1			#  flags for boundary conditions
+bcBottom   1			#  1 = no-slip      3 = outflow
+bcLeft     3			#  2 = free-slip    4 = periodic
+bcRight    3			#
+
+gx    0.0      # Body forces (e.g. gravity)
+gy    0.0      #
+
+re    36500.0	   # Reynolds number
+
+u_init    1.0      # initial value for velocity in x-direction
+v_init    0.0      # initial value for velocity in y-direction
+p_init    1.0      # initial value for pressure
+
+# Geometry Data:
+# -------------
+
+xlength    7.0     # domain size in x-direction
+ylength    1.5	   # domain size in y-direction
+imax       210      # number of interior cells in x-direction
+jmax       45	   # number of interior cells in y-direction
+
+# Time Data:
+# ---------
+
+te      60.0   # final time
+dt      0.02    # time stepsize
+tau     0.5     # safety factor for time stepsize control (<0 constant delt)
+
+# Pressure Iteration Data:
+# -----------------------
+
+itermax  500       # maximal number of pressure iteration in one time step
+eps      0.0001   # stopping tolerance for pressure iteration
+rho      0.52
+omg      1.8       # relaxation parameter for SOR iteration
+gamma    0.9       # upwind differencing factor gamma
+
+# Particle Tracing Data:
+# -----------------------
+
+numberOfParticles   200
+startTime           0
+injectTimePeriod    1.0
+writeTimePeriod     0.5
+
+x1                  0.0
+y1                  0.5
+x2                  0.0
+y2                  1.5
+
+# Obstacle Geometry Data:
+# -----------------------
+# Shape 0 disable, 1 Rectangle/Square, 2 Circle
+
+shape               1 
+xCenter             0.0
+yCenter             0.0
+xRectLength         2.0
+yRectLength         1.0
+circleRadius        1.0
+
+#===============================================================================
--- a/BasicSolver/2D-mpi-v3/canal.par
+++ b/BasicSolver/2D-mpi-v3/canal.par
@@ -12,50 +12,61 @@ bcBottom   1			#  1 = no-slip      3 = outflow
 bcLeft     3			#  2 = free-slip    4 = periodic
 bcRight    3			#

-gx     0.0      # Body forces (e.g. gravity)
-gy     0.0      #
+gx    0.0      # Body forces (e.g. gravity)
+gy    0.0      #

-re            100.0	   # Reynolds number
+re    100.0	   # Reynolds number

-u_init        1.0      # initial value for velocity in x-direction
-v_init        0.0      # initial value for velocity in y-direction
-p_init        0.0      # initial value for pressure
+u_init    1.0      # initial value for velocity in x-direction
+v_init    0.0      # initial value for velocity in y-direction
+p_init    1.0      # initial value for pressure

 # Geometry Data:
 # -------------

-xlength       30.0     # domain size in x-direction
-ylength       4.0	   # domain size in y-direction
-imax          200      # number of interior cells in x-direction
-jmax          50	   # number of interior cells in y-direction
+xlength    30.0     # domain size in x-direction
+ylength    4.0	   # domain size in y-direction
+imax       200      # number of interior cells in x-direction
+jmax       50	   # number of interior cells in y-direction

 # Time Data:
 # ---------

-te       60.0   # final time
-dt       0.02    # time stepsize
-tau      0.5     # safety factor for time stepsize control (<0 constant delt)
+te      60.0   # final time
+dt      0.02    # time stepsize
+tau     0.5     # safety factor for time stepsize control (<0 constant delt)

 # Pressure Iteration Data:
 # -----------------------

-itermax       500       # maximal number of pressure iteration in one time step
-eps           0.00001   # stopping tolerance for pressure iteration
-rho           0.52  	#
-omg           1.8       # relaxation parameter for SOR iteration
-gamma         0.9       # upwind differencing factor gamma
-
+itermax  500       # maximal number of pressure iteration in one time step
+eps      0.0001   # stopping tolerance for pressure iteration
+rho      0.52
+omg      1.8       # relaxation parameter for SOR iteration
+gamma    0.9       # upwind differencing factor gamma

 # Particle Tracing Data:
 # -----------------------

-numberOfParticles   30
-startTime           10
+numberOfParticles   60
+startTime           500
 injectTimePeriod    2.0
-writeTimePeriod     2.0
+writeTimePeriod     0.5

 x1                  1.0
 y1                  0.0
 x2                  1.0
 y2                  4.0
+
+# Obstacle Geometry Data:
+# -----------------------
+# Shape 0 disable, 1 Rectangle/Square, 2 Circle
+
+shape               1 
+xCenter             10.0
+yCenter             2
+xRectLength         6.0
+yRectLength         1.0
+circleRadius        1.0
+
 #===============================================================================
--- a/BasicSolver/2D-mpi-v3/karman.par
+++ b/BasicSolver/2D-mpi-v3/karman.par
@@ -0,0 +1,72 @@
+#==============================================================================
+#                            Laminar Canal Flow
+#==============================================================================
+
+# Problem specific Data:
+# ---------------------
+
+name karman             # name of flow setup
+
+bcTop      1			#  flags for boundary conditions
+bcBottom   1			#  1 = no-slip      3 = outflow
+bcLeft     3			#  2 = free-slip    4 = periodic
+bcRight    3			#
+
+gx    0.0      # Body forces (e.g. gravity)
+gy    0.0      #
+
+re    5050.0	   # Reynolds number
+
+u_init    1.0      # initial value for velocity in x-direction
+v_init    0.0      # initial value for velocity in y-direction
+p_init    0.0      # initial value for pressure
+
+# Geometry Data:
+# -------------
+
+xlength    30.0     # domain size in x-direction
+ylength    8.0	   # domain size in y-direction
+imax       400      # number of interior cells in x-direction
+jmax       200	   # number of interior cells in y-direction
+
+# Time Data:
+# ---------
+
+te      150.0   # final time
+dt      0.02    # time stepsize
+tau     0.5     # safety factor for time stepsize control (<0 constant delt)
+
+# Pressure Iteration Data:
+# -----------------------
+
+itermax  200       # maximal number of pressure iteration in one time step
+eps      0.001   # stopping tolerance for pressure iteration
+rho      0.52
+omg      1.75      # relaxation parameter for SOR iteration
+gamma    0.9       # upwind differencing factor gamma
+
+# Particle Tracing Data:
+# -----------------------
+
+numberOfParticles   200
+startTime           50
+injectTimePeriod    1.0
+writeTimePeriod     0.5
+
+x1                  0.0
+y1                  3.8
+x2                  0.0
+y2                  4.1
+
+# Obstacle Geometry Data:
+# -----------------------
+# Shape 0 disable, 1 Rectangle/Square, 2 Circle
+
+shape               2 
+xCenter             5.0
+yCenter             4.0
+xRectLength         2.0
+yRectLength         1.0
+circleRadius        1.0
+
+#===============================================================================
--- a/BasicSolver/2D-mpi-v3/pressure.dat
+++ b/BasicSolver/2D-mpi-v3/pressure.dat
--- a/BasicSolver/2D-mpi-v3/src/main.c
+++ b/BasicSolver/2D-mpi-v3/src/main.c
@@ -11,18 +11,14 @@
 #include <unistd.h>

 #include "parameter.h"
-#include "progress.h"
-#include "solver.h"
-#include "timing.h"
 #include "particletracing.h"
-#include "vtkWriter.h"
-
+#include "progress.h"
+#include "timing.h"
 #include <mpi.h>

-
 enum VARIANT { SOR = 1, RB, RBA };

-int main (int argc, char** argv)
+int main(int argc, char** argv)
 {
    int rank;
    int variant = RB;
@@ -32,7 +28,6 @@ int main (int argc, char** argv)
    Solver solver;
    ParticleTracer particletracer;

-
    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    initParameter(&params);
@@ -43,15 +38,13 @@ int main (int argc, char** argv)
    }

    readParameter(&params, argv[1]);
-    if (argc == 3) 
-    {
+    if (argc == 3) {
        variant = atoi(argv[2]);
    }

    initSolver(&solver, &params);
    initParticleTracer(&particletracer, &params, &solver);
-    if (rank == 0) 
-    {
+    if (rank == 0) {
        printParameter(&params);
    }

@@ -62,29 +55,27 @@ int main (int argc, char** argv)
    double te  = solver.te;
    double t   = 0.0;

-    int (*solver_generic[])() = {solve, solveRB, solveRBA};
-
+    int (*solver_generic[])() = { solve, solveRB, solveRBA };

    S = getTimeStamp();

-    while (t <= te) 
-    {
+    while (t <= te) {
        if (tau > 0.0) {
            computeTimestep(&solver);
        }

        setBoundaryConditions(&solver);
        setSpecialBoundaryCondition(&solver);
+        setObjectBoundaryCondition(&solver);
        computeFG(&solver);
        computeRHS(&solver);
        solver_generic[variant - 1](&solver);
        adaptUV(&solver);

-        //trace(&particletracer, solver.u, solver.v, t);
+        trace(&particletracer, solver.u, solver.v, solver.s, t);

        t += solver.dt;

-
 #ifdef VERBOSE
        if (rank == 0) {
            printf("TIME %f , TIMESTEP %f\n", t, solver.dt);
@@ -102,7 +93,6 @@ int main (int argc, char** argv)
    collectResult(&solver);
    freeParticles(&particletracer);

-
    MPI_Finalize();
    return EXIT_SUCCESS;
 }
--- a/BasicSolver/2D-mpi-v3/src/parameter.c
+++ b/BasicSolver/2D-mpi-v3/src/parameter.c
@@ -25,7 +25,6 @@ void initParameter(Parameter* param)
    param->gamma   = 0.9;
    param->tau     = 0.5;
    param->rho     = 0.99;
-
 }

 void readParameter(Parameter* param, const char* filename)
@@ -82,7 +81,6 @@ void readParameter(Parameter* param, const char* filename)
            PARSE_REAL(p_init);
            PARSE_REAL(rho);

-
            /* Added new particle tracing parameters */
            PARSE_INT(numberOfParticles);
            PARSE_REAL(startTime);
@@ -92,6 +90,14 @@ void readParameter(Parameter* param, const char* filename)
            PARSE_REAL(y1);
            PARSE_REAL(x2);
            PARSE_REAL(y2);
+
+            /* Added obstacle geometry parameters */
+            PARSE_INT(shape);
+            PARSE_REAL(xCenter);
+            PARSE_REAL(yCenter);
+            PARSE_REAL(xRectLength);
+            PARSE_REAL(yRectLength);
+            PARSE_REAL(circleRadius);
        }
    }

--- a/BasicSolver/2D-mpi-v3/src/parameter.h
+++ b/BasicSolver/2D-mpi-v3/src/parameter.h
@@ -23,6 +23,9 @@ typedef struct {
    double startTime, injectTimePeriod, writeTimePeriod;

    double x1, y1, x2, y2;
+
+    int shape;
+    double xCenter, yCenter, xRectLength, yRectLength, circleRadius;
 } Parameter;

 void initParameter(Parameter*);
--- a/BasicSolver/2D-mpi-v3/src/particletracing.c
+++ b/BasicSolver/2D-mpi-v3/src/particletracing.c
@@ -10,18 +10,19 @@
 #include <stdlib.h>
 #include <string.h>

-#include "vtkWriter.h"
+#include "particletracing.h"

-#define U(i, j)   u[(j) * (imaxLocal + 2) + (i)]
-#define V(i, j)   v[(j) * (imaxLocal + 2) + (i)]
+#define U(i, j) u[(j) * (imaxLocal + 2) + (i)]
+#define V(i, j) v[(j) * (imaxLocal + 2) + (i)]
+#define S(i, j) s[(j) * (imaxLocal + 2) + (i)]

 static int ts = 0;

 #define IDIM 0
 #define JDIM 1

-#define XOFFSET 0
-#define YOFFSET 1
+#define XOFFSET    0
+#define YOFFSET    1
 #define XOFFSETEND 2
 #define YOFFSETEND 3

@@ -29,32 +30,7 @@ static double sum(int* sizes, int size)
 {
    double sum = 0;

-    for (int i = 0; i < size; ++i) 
-    {
-        sum += sizes[i];
-    }
-
-    return sum;
-}
-
-static double sumX(double* sizes, int size, int offset, int coord, int init)
-{
-    double sum = 0;
-
-    for (int i = init; i < size && coord > 0; i+=offset, --coord) 
-    {
-        sum += sizes[i];
-    }
-
-    return sum;
-}
-
-static double sumY(double* sizes, int size, int offset, int coord, int init)
-{
-    double sum = 0;
-
-    for (int i = init * offset; i < size && coord > 0; ++i, --coord) 
-    {
+    for (int i = 0; i < size; ++i) {
        sum += sizes[i];
    }

@@ -70,7 +46,7 @@ void printUV(ParticleTracer* particletracer, double* u, double* v)
            printf(
                "\n### RANK %d #######################################################\n",
                particletracer->rank);
-                printf("\nGrid U : \n");
+            printf("\nGrid U : \n");
            for (int j = 0; j < particletracer->jmaxLocal + 2; j++) {
                printf("%02d: ", j);
                for (int i = 0; i < particletracer->imaxLocal + 2; i++) {
@@ -95,33 +71,37 @@ void printUV(ParticleTracer* particletracer, double* u, double* v)

 void printParticles(ParticleTracer* particletracer)
 {
-    for(int i = 0; i < particletracer->totalParticles; ++i)
-    {   
-        printf("Rank : %d Particle position X : %.2f, Y : %.2f, flag : %d, total pt : %d, pointer : %d, xOffset : %.2f, yOffset : %.2f, xOffsetEnd : %.2f, yOffsetEnd : %.2f\n", 
+    for (int i = 0; i < particletracer->totalParticles; ++i) {
+        printf("Rank : %d Particle position X : %.2f, Y : %.2f, flag : %d, total pt : "
+               "%d, pointer : %d, xOffset : %.2f, yOffset : %.2f, xOffsetEnd : %.2f, "
+               "yOffsetEnd : %.2f\n",
            particletracer->rank,
            particletracer->particlePool[i].x,
            particletracer->particlePool[i].y,
            particletracer->particlePool[i].flag,
            particletracer->totalParticles,
            particletracer->pointer,
-            particletracer->xOffset, particletracer->yOffset, 
-            particletracer->xOffsetEnd, particletracer->yOffsetEnd);
+            particletracer->xOffset,
+            particletracer->yOffset,
+            particletracer->xOffsetEnd,
+            particletracer->yOffsetEnd);
    }
 }
 void injectParticles(ParticleTracer* particletracer)
 {
    double x, y;
-    for(int i = 0; i < particletracer->numberOfParticles; ++i)
-    {
+    for (int i = 0; i < particletracer->numberOfParticles; ++i) {
        x = particletracer->linSpaceLine[i].x;
        y = particletracer->linSpaceLine[i].y;
-        if(x >= particletracer->xOffset && y >= particletracer->yOffset && x <= particletracer->xOffsetEnd && y <= particletracer->yOffsetEnd )
-        {
+        if (x >= particletracer->xOffset && y >= particletracer->yOffset &&
+            x <= particletracer->xOffsetEnd && y <= particletracer->yOffsetEnd) {
            // printf("\nRank : %d\n", particletracer->rank);
-            // printf("\t%.2f >= %.2f && %.2f >= %.2f && %.2f <= %.2f && %.2f <= %.2f\n",x , particletracer->xOffset ,y , particletracer->yOffset, x , particletracer->xOffsetEnd ,y , particletracer->yOffsetEnd);
+            // printf("\t%.2f >= %.2f && %.2f >= %.2f && %.2f <= %.2f && %.2f <= %.2f\n",x
+            // , particletracer->xOffset ,y , particletracer->yOffset, x ,
+            // particletracer->xOffsetEnd ,y , particletracer->yOffsetEnd);

-            particletracer->particlePool[particletracer->pointer].x = x;
-            particletracer->particlePool[particletracer->pointer].y = y;
+            particletracer->particlePool[particletracer->pointer].x    = x;
+            particletracer->particlePool[particletracer->pointer].y    = y;
            particletracer->particlePool[particletracer->pointer].flag = true;
            ++(particletracer->pointer);
            ++(particletracer->totalParticles);
@@ -129,27 +109,29 @@ void injectParticles(ParticleTracer* particletracer)
    }
 }

-void advanceParticles(ParticleTracer* particletracer, double* restrict u, double* restrict v, double time)
+void advanceParticles(ParticleTracer* particletracer,
+    double* restrict u,
+    double* restrict v,
+    int* restrict s,
+    double time)
 {
-    int imax       = particletracer->imax;
-    int jmax       = particletracer->jmax;
-    int imaxLocal  = particletracer->imaxLocal;
-    int jmaxLocal  = particletracer->jmaxLocal;
+    int imax      = particletracer->imax;
+    int jmax      = particletracer->jmax;
+    int imaxLocal = particletracer->imaxLocal;
+    int jmaxLocal = particletracer->jmaxLocal;

-    double dx      = particletracer->dx;
-    double dy      = particletracer->dy;
+    double dx = particletracer->dx;
+    double dy = particletracer->dy;

    double xlength = particletracer->xlength;
    double ylength = particletracer->ylength;

-    Particle buff[particletracer->size][30];
+    Particle buff[particletracer->size][100];

-    for(int i = 0; i < particletracer->size; ++i)
-    {   
-        for(int j = 0; j < 30; ++j)
-        { 
-            buff[i][j].x = 0.0;
-            buff[i][j].y = 0.0;
+    for (int i = 0; i < particletracer->size; ++i) {
+        for (int j = 0; j < 100; ++j) {
+            buff[i][j].x    = 0.0;
+            buff[i][j].y    = 0.0;
            buff[i][j].flag = false;
        }
    }
@@ -157,16 +139,13 @@ void advanceParticles(ParticleTracer* particletracer, double* restrict u, double

    memset(particleBufIndex, 0, sizeof(particleBufIndex));

-
-    for(int i = 0; i < particletracer->totalParticles; ++i)
-    {
-        if(particletracer->particlePool[i].flag == true)
-        {
+    for (int i = 0; i < particletracer->totalParticles; ++i) {
+        if (particletracer->particlePool[i].flag == true) {
            double xTemp = particletracer->particlePool[i].x;
            double yTemp = particletracer->particlePool[i].y;

-            double x   = xTemp - particletracer->xOffset;
-            double y   = yTemp - particletracer->yOffset;
+            double x = xTemp - particletracer->xOffset;
+            double y = yTemp - particletracer->yOffset;

            int iCoord = (int)(x / dx) + 1;
            int jCoord = (int)((y + 0.5 * dy) / dy) + 1;
@@ -177,10 +156,10 @@ void advanceParticles(ParticleTracer* particletracer, double* restrict u, double
            double y2 = ((double)jCoord - 0.5) * dy;

            double u_n = (1.0 / (dx * dy)) *
-                    ((x2 - x) * (y2 - y) * U(iCoord - 1, jCoord - 1) +
-                        (x - x1) * (y2 - y) * U(iCoord, jCoord - 1) +
-                        (x2 - x) * (y - y1) * U(iCoord - 1, jCoord) +
-                        (x - x1) * (y - y1) * U(iCoord, jCoord));
+                         ((x2 - x) * (y2 - y) * U(iCoord - 1, jCoord - 1) +
+                             (x - x1) * (y2 - y) * U(iCoord, jCoord - 1) +
+                             (x2 - x) * (y - y1) * U(iCoord - 1, jCoord) +
+                             (x - x1) * (y - y1) * U(iCoord, jCoord));

            double new_x = (x + particletracer->xOffset) + particletracer->dt * u_n;
            particletracer->particlePool[i].x = new_x;
@@ -194,68 +173,92 @@ void advanceParticles(ParticleTracer* particletracer, double* restrict u, double
            y2 = (double)jCoord * dy;

            double v_n = (1.0 / (dx * dy)) *
-                        ((x2 - x) * (y2 - y) * V(iCoord - 1, jCoord - 1) +
-                            (x - x1) * (y2 - y) * V(iCoord, jCoord - 1) +
-                            (x2 - x) * (y - y1) * V(iCoord - 1, jCoord) +
-                            (x - x1) * (y - y1) * V(iCoord, jCoord));
+                         ((x2 - x) * (y2 - y) * V(iCoord - 1, jCoord - 1) +
+                             (x - x1) * (y2 - y) * V(iCoord, jCoord - 1) +
+                             (x2 - x) * (y - y1) * V(iCoord - 1, jCoord) +
+                             (x - x1) * (y - y1) * V(iCoord, jCoord));

            double new_y = (y + particletracer->yOffset) + particletracer->dt * v_n;
            particletracer->particlePool[i].y = new_y;

            // printf("Rank : %d\n", particletracer->rank);
-            // printf("\tOld X : %.2f, translated X : %.2f, xOffset : %.2f, New X : %.2f, iCoord : %d\n\tOld Y : %.2f, translated X : %.2f, yOffset : %.2f, New Y : %.2f, jCoord : %d\n\n",xTemp, x, particletracer->xOffset, new_x, iCoord, yTemp, y, particletracer->yOffset , new_y, jCoord);
-            // printf("\tU(iCoord - 1, jCoord - 1) : %.2f, U(iCoord, jCoord - 1) : %.2f, U(iCoord - 1, jCoord) : %.2f, U(iCoord, jCoord) : %.2f\n", U(iCoord - 1, jCoord - 1), U(iCoord, jCoord - 1), U(iCoord - 1, jCoord), U(iCoord, jCoord));
-            // printf("\tV(iCoord - 1, jCoord - 1) : %.2f, V(iCoord, jCoord - 1) : %.2f, V(iCoord - 1, jCoord) : %.2f, V(iCoord, jCoord) : %.2f\n\n", V(iCoord - 1, jCoord - 1), V(iCoord, jCoord - 1), V(iCoord - 1, jCoord), V(iCoord, jCoord));
-            //printf("\t U N : %.2f, V N : %.2f\n\n", u_n, v_n);
+            // printf("\tOld X : %.2f, translated X : %.2f, xOffset : %.2f, New X : %.2f,
+            // iCoord : %d\n\tOld Y : %.2f, translated X : %.2f, yOffset : %.2f, New Y :
+            // %.2f, jCoord : %d\n\n",xTemp, x, particletracer->xOffset, new_x, iCoord,
+            // yTemp, y, particletracer->yOffset , new_y, jCoord); printf("\tU(iCoord - 1,
+            // jCoord - 1) : %.2f, U(iCoord, jCoord - 1) : %.2f, U(iCoord - 1, jCoord) :
+            // %.2f, U(iCoord, jCoord) : %.2f\n", U(iCoord - 1, jCoord - 1), U(iCoord,
+            // jCoord - 1), U(iCoord - 1, jCoord), U(iCoord, jCoord)); printf("\tV(iCoord
+            // - 1, jCoord - 1) : %.2f, V(iCoord, jCoord - 1) : %.2f, V(iCoord - 1,
+            // jCoord) : %.2f, V(iCoord, jCoord) : %.2f\n\n", V(iCoord - 1, jCoord - 1),
+            // V(iCoord, jCoord - 1), V(iCoord - 1, jCoord), V(iCoord, jCoord));
+            // printf("\t U N : %.2f, V N : %.2f\n\n", u_n, v_n);

-            if (((new_x < particletracer->xOffset) || (new_x >= particletracer->xOffsetEnd) ||
-                 (new_y < particletracer->yOffset) || (new_y >= particletracer->yOffsetEnd)))
-            {
-                //New logic to transfer particles to neighbouring ranks or discard the particle.
+            if (((new_x < particletracer->xOffset) ||
+                    (new_x >= particletracer->xOffsetEnd) ||
+                    (new_y < particletracer->yOffset) ||
+                    (new_y >= particletracer->yOffsetEnd))) {
+                // New logic to transfer particles to neighbouring ranks or discard the
+                // particle.

-                for(int i = 0; i < particletracer->size; ++i)
-                {
-                    if((new_x >= particletracer->offset[i + particletracer->size * XOFFSET]) && 
-                       (new_x <= particletracer->offset[i + particletracer->size * XOFFSETEND]) && 
-                       (new_y >= particletracer->offset[i + particletracer->size * YOFFSET]) && 
-                       (new_y <= particletracer->offset[i + particletracer->size * YOFFSETEND]) &&
-                       i != particletracer->rank)
-                    {
-                        buff[i][particleBufIndex[i]].x = new_x;
-                        buff[i][particleBufIndex[i]].y = new_y;
+                for (int i = 0; i < particletracer->size; ++i) {
+                    if ((new_x >=
+                            particletracer->offset[i + particletracer->size * XOFFSET]) &&
+                        (new_x <= particletracer
+                                      ->offset[i + particletracer->size * XOFFSETEND]) &&
+                        (new_y >=
+                            particletracer->offset[i + particletracer->size * YOFFSET]) &&
+                        (new_y <= particletracer
+                                      ->offset[i + particletracer->size * YOFFSETEND]) &&
+                        i != particletracer->rank) {
+                        buff[i][particleBufIndex[i]].x    = new_x;
+                        buff[i][particleBufIndex[i]].y    = new_y;
                        buff[i][particleBufIndex[i]].flag = true;
                        ++particleBufIndex[i];
                    }
                }
                particletracer->particlePool[i].flag = false;
            }
+
+            int i_new = new_x / dx, j_new = new_y / dy;
+            int iOffset = particletracer->xOffset / dx,
+                jOffset = particletracer->yOffset / dy;
+
+            if (S(i_new - iOffset, j_new - jOffset) != NONE) {
+                particletracer->particlePool[i].flag = false;
+            }
        }
    }

-    for(int i = 0; i < particletracer->size; ++i)
-    {   
-        if(i != particletracer->rank)
-        {
-            MPI_Send(buff[i], 30, particletracer->mpi_particle, i, 0, particletracer->comm);
+    for (int i = 0; i < particletracer->size; ++i) {
+        if (i != particletracer->rank) {
+            MPI_Send(buff[i],
+                100,
+                particletracer->mpi_particle,
+                i,
+                0,
+                particletracer->comm);
        }
    }
-    for(int i = 0; i < particletracer->size; ++i)
-    {   
-        if(i != particletracer->rank)
-        {
-            MPI_Recv(buff[i], 30, particletracer->mpi_particle, i, 0, particletracer->comm, MPI_STATUS_IGNORE);
+    for (int i = 0; i < particletracer->size; ++i) {
+        if (i != particletracer->rank) {
+            MPI_Recv(buff[i],
+                100,
+                particletracer->mpi_particle,
+                i,
+                0,
+                particletracer->comm,
+                MPI_STATUS_IGNORE);
        }
    }
-    for(int i = 0; i < particletracer->size; ++i)
-    {   
-        if(i != particletracer->rank)
-        {
-            for(int j = 0; j < 30; ++j)
-            {
-                if(buff[i][j].flag == true)
-                {
-                    particletracer->particlePool[particletracer->pointer].x = buff[i][j].x;
-                    particletracer->particlePool[particletracer->pointer].y = buff[i][j].y;
+    for (int i = 0; i < particletracer->size; ++i) {
+        if (i != particletracer->rank) {
+            for (int j = 0; j < 100; ++j) {
+                if (buff[i][j].flag == true) {
+                    particletracer->particlePool[particletracer->pointer].x = buff[i][j]
+                                                                                  .x;
+                    particletracer->particlePool[particletracer->pointer].y = buff[i][j]
+                                                                                  .y;
                    particletracer->particlePool[particletracer->pointer].flag = true;
                    ++(particletracer->pointer);
                    ++(particletracer->totalParticles);
@@ -276,87 +279,98 @@ void writeParticles(ParticleTracer* particletracer)
 {
    int collectedBuffIndex[particletracer->size];

-    MPI_Gather(&particletracer->totalParticles, 1, MPI_INT, collectedBuffIndex, 1, MPI_INT, 0, particletracer->comm);
+    MPI_Gather(&particletracer->totalParticles,
+        1,
+        MPI_INT,
+        collectedBuffIndex,
+        1,
+        MPI_INT,
+        0,
+        particletracer->comm);

-    if(particletracer->rank != 0)
-    {
+    if (particletracer->rank != 0) {
        Particle buff[particletracer->totalParticles];
-        for(int i = 0; i < particletracer->totalParticles; ++i)
-        {   
-            buff[i].x = particletracer->particlePool[i].x;
-            buff[i].y = particletracer->particlePool[i].y;
-            buff[i].flag =  particletracer->particlePool[i].flag;
-            //printf("Rank : %d sending to rank 0 X : %.2f, Y : %.2f with totalpt : %d\n", particletracer->rank, buff[i].x, buff[i].y, particletracer->totalParticles);
+        for (int i = 0; i < particletracer->totalParticles; ++i) {
+            buff[i].x    = particletracer->particlePool[i].x;
+            buff[i].y    = particletracer->particlePool[i].y;
+            buff[i].flag = particletracer->particlePool[i].flag;
+            // printf("Rank : %d sending to rank 0 X : %.2f, Y : %.2f with totalpt :
+            // %d\n", particletracer->rank, buff[i].x, buff[i].y,
+            // particletracer->totalParticles);
        }
-        MPI_Send(buff, particletracer->totalParticles, particletracer->mpi_particle, 0, 1, particletracer->comm);
+        MPI_Send(buff,
+            particletracer->totalParticles,
+            particletracer->mpi_particle,
+            0,
+            1,
+            particletracer->comm);
    }
-    if(particletracer->rank == 0)
-    {
+    if (particletracer->rank == 0) {
        char filename[50];
        FILE* fp;

-        snprintf(filename, 50, "vtk_files/particles_%d.vtk", ts);
+        snprintf(filename, 50, "vis_files/particles_%d.dat", ts);
        fp = fopen(filename, "w");

        if (fp == NULL) {
            printf("Error!\n");
            exit(EXIT_FAILURE);
        }
-        fprintf(fp, "# vtk DataFile Version 3.0\n");
-        fprintf(fp, "PAMPI cfd solver particle tracing file\n");
-        fprintf(fp, "ASCII\n");
+        // fprintf(fp, "# vtk DataFile Version 3.0\n");
+        // fprintf(fp, "PAMPI cfd solver particle tracing file\n");
+        // fprintf(fp, "ASCII\n");

-
-        fprintf(fp, "DATASET UNSTRUCTURED_GRID\n");
-        fprintf(fp, "FIELD FieldData 2\n");
-        fprintf(fp, "TIME 1 1 double\n");
-        fprintf(fp, "%d\n", ts);
-        fprintf(fp, "CYCLE 1 1 int\n");
-        fprintf(fp, "1\n");
+        // fprintf(fp, "DATASET UNSTRUCTURED_GRID\n");
+        // fprintf(fp, "FIELD FieldData 2\n");
+        // fprintf(fp, "TIME 1 1 double\n");
+        // fprintf(fp, "%d\n", ts);
+        // fprintf(fp, "CYCLE 1 1 int\n");
+        // fprintf(fp, "1\n");

        int overallTotalParticles = sum(collectedBuffIndex, particletracer->size);

-        fprintf(fp, "POINTS %d float\n", overallTotalParticles);
+        // fprintf(fp, "POINTS %d float\n", overallTotalParticles);

-        printf("Total particles : %d\n", overallTotalParticles);
+        // printf("Total particles : %d\n", overallTotalParticles);

-        for (int i = 1; i < particletracer->size; ++i)
-        {
+        for (int i = 1; i < particletracer->size; ++i) {
            Particle recvBuff[collectedBuffIndex[i]];
-            MPI_Recv(&recvBuff, collectedBuffIndex[i], particletracer->mpi_particle, i, 1, particletracer->comm, MPI_STATUS_IGNORE);
+            MPI_Recv(&recvBuff,
+                collectedBuffIndex[i],
+                particletracer->mpi_particle,
+                i,
+                1,
+                particletracer->comm,
+                MPI_STATUS_IGNORE);

-            for (int j = 0; j < collectedBuffIndex[i]; ++j)
-            {
+            for (int j = 0; j < collectedBuffIndex[i]; ++j) {
                double x = recvBuff[j].x;
                double y = recvBuff[j].y;
-                fprintf(fp, "%f %f 0\n", x, y);
-                //printf("Rank : 0 receiving from rank %d X : %.2f, Y : %.2f with totalpt : %d\n", i, x, y, particletracer->totalParticles);
-
+                fprintf(fp, "%f %f\n", x, y);
+                // printf("Rank : 0 receiving from rank %d X : %.2f, Y : %.2f with totalpt
+                // : %d\n", i, x, y, particletracer->totalParticles);
            }
-        
        }
-        for (int i = 0; i < particletracer->totalParticles; ++i)
-        {
+
+        for (int i = 0; i < particletracer->totalParticles; ++i) {
            double x = particletracer->particlePool[i].x;
            double y = particletracer->particlePool[i].y;
-            fprintf(fp, "%f %f 0\n", x, y);
+            fprintf(fp, "%f %f\n", x, y);
        }

-    fprintf(fp, "CELLS %d %d\n", overallTotalParticles, 2 * overallTotalParticles);
+        // fprintf(fp, "CELLS %d %d\n", overallTotalParticles, 2 * overallTotalParticles);

+        // for (int i = 0; i < overallTotalParticles; ++i)
+        // {
+        //     fprintf(fp, "1 %d\n", i);
+        // }

-    for (int i = 0; i < overallTotalParticles; ++i)
-    {
-        fprintf(fp, "1 %d\n", i);
-    }
+        // fprintf(fp, "CELL_TYPES %d\n", overallTotalParticles);

-    fprintf(fp, "CELL_TYPES %d\n", overallTotalParticles);
-
-
-    for (int i = 0; i < overallTotalParticles; ++i)
-    {
-        fprintf(fp, "1\n");
-    }
+        // for (int i = 0; i < overallTotalParticles; ++i)
+        // {
+        //     fprintf(fp, "1\n");
+        // }

        fclose(fp);
    }
@@ -376,52 +390,53 @@ void initParticleTracer(ParticleTracer* particletracer, Parameter* params, Solve
    particletracer->injectTimePeriod  = params->injectTimePeriod;
    particletracer->writeTimePeriod   = params->writeTimePeriod;

-    particletracer->dt                = params->dt;
-    particletracer->dx                = params->xlength / params->imax;
-    particletracer->dy                = params->ylength / params->jmax;
+    particletracer->dt = params->dt;
+    particletracer->dx = params->xlength / params->imax;
+    particletracer->dy = params->ylength / params->jmax;

-    particletracer->xlength           = params->xlength;
-    particletracer->ylength           = params->ylength;
+    particletracer->xlength = params->xlength;
+    particletracer->ylength = params->ylength;

-    particletracer->x1                = params->x1;
-    particletracer->y1                = params->y1;
-    particletracer->x2                = params->x2;
-    particletracer->y2                = params->y2;
+    particletracer->x1 = params->x1;
+    particletracer->y1 = params->y1;
+    particletracer->x2 = params->x2;
+    particletracer->y2 = params->y2;

-    particletracer->lastInjectTime    = params->startTime;
-    particletracer->lastUpdateTime    = params->startTime;
-    particletracer->lastWriteTime     = params->startTime;
+    particletracer->lastInjectTime = params->startTime;
+    particletracer->lastUpdateTime = params->startTime;
+    particletracer->lastWriteTime  = params->startTime;

-    particletracer->pointer           = 0;
-    particletracer->totalParticles    = 0;
+    particletracer->pointer        = 0;
+    particletracer->totalParticles = 0;

-    particletracer->imax              = params->imax;
-    particletracer->jmax              = params->jmax;
+    particletracer->imax = params->imax;
+    particletracer->jmax = params->jmax;

-    particletracer->imaxLocal         = solver->imaxLocal;
-    particletracer->jmaxLocal         = solver->jmaxLocal;
+    particletracer->imaxLocal = solver->imaxLocal;
+    particletracer->jmaxLocal = solver->jmaxLocal;

-    particletracer->estimatedNumParticles = (particletracer->imaxLocal * particletracer->jmaxLocal);
+    particletracer->estimatedNumParticles = (particletracer->imaxLocal *
+                                             particletracer->jmaxLocal);

-    particletracer->particlePool      = malloc(sizeof(Particle) * particletracer->estimatedNumParticles);
+    particletracer->particlePool = malloc(
+        sizeof(Particle) * particletracer->estimatedNumParticles);

-    for(int i = 0; i < particletracer->estimatedNumParticles; ++i)
-    {   
-        particletracer->particlePool[i].x = 0.0;
-        particletracer->particlePool[i].y = 0.0;
+    for (int i = 0; i < particletracer->estimatedNumParticles; ++i) {
+        particletracer->particlePool[i].x    = 0.0;
+        particletracer->particlePool[i].y    = 0.0;
        particletracer->particlePool[i].flag = false;
    }

-    particletracer->linSpaceLine      = malloc(sizeof(Particle) * particletracer->numberOfParticles);
+    particletracer->linSpaceLine = malloc(
+        sizeof(Particle) * particletracer->numberOfParticles);

    /* duplicating communication from solver */
    MPI_Comm_dup(solver->comm, &particletracer->comm);

-    particletracer->rank              = solver->rank;
-    particletracer->size              = solver->size;
-
-    particletracer->offset            = (double *)malloc(sizeof(double) * 4 * particletracer->size);
+    particletracer->rank = solver->rank;
+    particletracer->size = solver->size;

+    particletracer->offset = (double*)malloc(sizeof(double) * 4 * particletracer->size);

    memcpy(particletracer->dims, solver->dims, sizeof(solver->dims));

@@ -431,62 +446,81 @@ void initParticleTracer(ParticleTracer* particletracer, Parameter* params, Solve

    memcpy(particletracer->jNeighbours, solver->jNeighbours, sizeof(solver->jNeighbours));

-
-    particletracer->xLocal           = particletracer->imaxLocal * particletracer->dx;
-    particletracer->yLocal           = particletracer->jmaxLocal * particletracer->dy;
-
-
-    double xLocal[particletracer->size];
-    double yLocal[particletracer->size];
+    particletracer->xLocal = particletracer->imaxLocal * particletracer->dx;
+    particletracer->yLocal = particletracer->jmaxLocal * particletracer->dy;

    double offset[4][particletracer->size];

-    MPI_Allgather(&particletracer->xLocal, 1, MPI_DOUBLE, xLocal, 1, MPI_DOUBLE, particletracer->comm);
-    MPI_Allgather(&particletracer->yLocal, 1, MPI_DOUBLE, yLocal, 1, MPI_DOUBLE, particletracer->comm);
+    particletracer->xOffset    = solver->xOffset;
+    particletracer->yOffset    = solver->yOffset;
+    particletracer->xOffsetEnd = particletracer->xOffset + particletracer->xLocal;
+    particletracer->yOffsetEnd = particletracer->yOffset + particletracer->yLocal;

-    particletracer->xOffset     = sumX(xLocal, particletracer->size, particletracer->dims[JDIM], particletracer->coords[IDIM], particletracer->coords[JDIM]);
-    particletracer->yOffset     = sumY(yLocal, particletracer->size, particletracer->dims[JDIM], particletracer->coords[JDIM], particletracer->coords[IDIM]);
-    particletracer->xOffsetEnd  = particletracer->xOffset + particletracer->xLocal;
-    particletracer->yOffsetEnd  = particletracer->yOffset + particletracer->yLocal;
+    printf("Rank : %d, xOffset : %.2f, yOffset : %.2f, xOffsetEnd : %.2f, yOffsetEnd : "
+           "%.2f\n",
+        particletracer->rank,
+        particletracer->xOffset,
+        particletracer->yOffset,
+        particletracer->xOffsetEnd,
+        particletracer->yOffsetEnd);

-    printf("Rank : %d, xOffset : %.2f, yOffset : %.2f, xOffsetEnd : %.2f, yOffsetEnd : %.2f\n", particletracer->rank, particletracer->xOffset, particletracer->yOffset, particletracer->xOffsetEnd, particletracer->yOffsetEnd);
-
-    MPI_Allgather(&particletracer->xOffset, 1, MPI_DOUBLE, offset[0], 1, MPI_DOUBLE, particletracer->comm);
-    MPI_Allgather(&particletracer->yOffset, 1, MPI_DOUBLE, offset[1], 1, MPI_DOUBLE, particletracer->comm);
-    MPI_Allgather(&particletracer->xOffsetEnd, 1, MPI_DOUBLE, offset[2], 1, MPI_DOUBLE, particletracer->comm);
-    MPI_Allgather(&particletracer->yOffsetEnd, 1, MPI_DOUBLE, offset[3], 1, MPI_DOUBLE, particletracer->comm);
+    MPI_Allgather(&particletracer->xOffset,
+        1,
+        MPI_DOUBLE,
+        offset[0],
+        1,
+        MPI_DOUBLE,
+        particletracer->comm);
+    MPI_Allgather(&particletracer->yOffset,
+        1,
+        MPI_DOUBLE,
+        offset[1],
+        1,
+        MPI_DOUBLE,
+        particletracer->comm);
+    MPI_Allgather(&particletracer->xOffsetEnd,
+        1,
+        MPI_DOUBLE,
+        offset[2],
+        1,
+        MPI_DOUBLE,
+        particletracer->comm);
+    MPI_Allgather(&particletracer->yOffsetEnd,
+        1,
+        MPI_DOUBLE,
+        offset[3],
+        1,
+        MPI_DOUBLE,
+        particletracer->comm);

    memcpy(particletracer->offset, offset, sizeof(offset));

-    
    // if(particletracer->rank == 0)
    // {
    //     for(int i = 0;i < particletracer->size; ++i)
    //     {
-    //         printf("Rank : %d and its xOffset : %.2f, yOffset : %.2f, xLocal : %.2f, yLocal : %.2f, xOffsetEnd : %.2f, yOffsetEnd : %.2f\n", 
-    //         i, particletracer->offset[i + particletracer->size * XOFFSET],
-    //         particletracer->offset[i + particletracer->size * YOFFSET],  xLocal[i], yLocal[i], 
-    //         particletracer->offset[i + particletracer->size * XOFFSETEND], 
-    //         particletracer->offset[i + particletracer->size * YOFFSETEND]);
+    //         printf("Rank : %d and its xOffset : %.2f, yOffset : %.2f, xOffsetEnd :
+    //         %.2f, yOffsetEnd : %.2f\n", i, particletracer->offset[i +
+    //         particletracer->size * XOFFSET], particletracer->offset[i +
+    //         particletracer->size * YOFFSET], particletracer->offset[i +
+    //         particletracer->size * XOFFSETEND], particletracer->offset[i +
+    //         particletracer->size * YOFFSETEND]);
    //     }
    // }

-    
-
-    for (int i = 0; i < particletracer->numberOfParticles; ++i) 
-    {
-        double spacing                       = (double)i / (double)(particletracer->numberOfParticles - 1);
-        particletracer->linSpaceLine[i].x    = spacing * particletracer->x1 + (1.0 - spacing) * particletracer->x2;
-        particletracer->linSpaceLine[i].y    = spacing * particletracer->y1 + (1.0 - spacing) * particletracer->y2;
+    for (int i = 0; i < particletracer->numberOfParticles; ++i) {
+        double spacing = (double)i / (double)(particletracer->numberOfParticles - 1);
+        particletracer->linSpaceLine[i].x = spacing * particletracer->x1 +
+                                            (1.0 - spacing) * particletracer->x2;
+        particletracer->linSpaceLine[i].y = spacing * particletracer->y1 +
+                                            (1.0 - spacing) * particletracer->y2;
        particletracer->linSpaceLine[i].flag = true;

-        //if(particletracer->rank == 1) printf("\nRank : %d, with linspace X : %.2f and linspace Y : %.2f\n", particletracer->rank, particletracer->linSpaceLine[i].x , particletracer->linSpaceLine[i].y);
+        // if(particletracer->rank == 1) printf("\nRank : %d, with linspace X : %.2f and
+        // linspace Y : %.2f\n", particletracer->rank, particletracer->linSpaceLine[i].x ,
+        // particletracer->linSpaceLine[i].y);
    }

-    
-
-
-
    // Create the mpi_particle datatype
    MPI_Datatype mpi_particle;
    int lengths[3] = { 1, 1, 1 };
@@ -503,41 +537,65 @@ void initParticleTracer(ParticleTracer* particletracer, Parameter* params, Solve
    displacements[2] = MPI_Aint_diff(displacements[2], base_address);

    MPI_Datatype types[3] = { MPI_DOUBLE, MPI_DOUBLE, MPI_C_BOOL };
-    MPI_Type_create_struct(3, lengths, displacements, types, &particletracer->mpi_particle);
+    MPI_Type_create_struct(3,
+        lengths,
+        displacements,
+        types,
+        &particletracer->mpi_particle);
    MPI_Type_commit(&particletracer->mpi_particle);
-
 }

 void printParticleTracerParameters(ParticleTracer* particletracer)
 {
    printf("Particle Tracing data:\n");
    printf("Rank : %d\n", particletracer->rank);
-    printf("\tNumber of particles : %d being injected for every period of %.2f\n", particletracer->numberOfParticles, particletracer->injectTimePeriod);
+    printf("\tNumber of particles : %d being injected for every period of %.2f\n",
+        particletracer->numberOfParticles,
+        particletracer->injectTimePeriod);
    printf("\tstartTime : %.2f\n", particletracer->startTime);
-    printf("\t(Line along which the particles are to be injected) \n\tx1 : %.2f, y1 : %.2f, x2 : %.2f, y2 : %.2f\n", particletracer->x1, particletracer->y1, particletracer->x2, particletracer->y2);
-    printf("\tPointer : %d, TotalParticles : %d\n", particletracer->pointer, particletracer->totalParticles);
-    printf("\tdt : %.2f, dx : %.2f, dy : %.2f\n", particletracer->dt, particletracer->dx, particletracer->dy);
-    printf("\tcoord[0] : %d, coord[1] : %d\n", particletracer->coords[IDIM], particletracer->coords[JDIM]);
-    printf("\txOffset : %.2f, yOffset : %.2f\n", particletracer->xOffset, particletracer->yOffset);
-    printf("\txOffsetEnd : %.2f, yOffsetEnd : %.2f\n", particletracer->xOffsetEnd, particletracer->yOffsetEnd);
-    printf("\txLocal : %.2f, yLocal : %.2f\n", particletracer->xLocal, particletracer->yLocal);
+    printf("\t(Line along which the particles are to be injected) \n\tx1 : %.2f, y1 : "
+           "%.2f, x2 : %.2f, y2 : %.2f\n",
+        particletracer->x1,
+        particletracer->y1,
+        particletracer->x2,
+        particletracer->y2);
+    printf("\tPointer : %d, TotalParticles : %d\n",
+        particletracer->pointer,
+        particletracer->totalParticles);
+    printf("\tdt : %.2f, dx : %.2f, dy : %.2f\n",
+        particletracer->dt,
+        particletracer->dx,
+        particletracer->dy);
+    printf("\tcoord[0] : %d, coord[1] : %d\n",
+        particletracer->coords[IDIM],
+        particletracer->coords[JDIM]);
+    printf("\txOffset : %.2f, yOffset : %.2f\n",
+        particletracer->xOffset,
+        particletracer->yOffset);
+    printf("\txOffsetEnd : %.2f, yOffsetEnd : %.2f\n",
+        particletracer->xOffsetEnd,
+        particletracer->yOffsetEnd);
+    printf("\txLocal : %.2f, yLocal : %.2f\n",
+        particletracer->xLocal,
+        particletracer->yLocal);
 }

-void trace(ParticleTracer* particletracer, double* restrict u, double* restrict v, double time)
+void trace(ParticleTracer* particletracer,
+    double* restrict u,
+    double* restrict v,
+    int* restrict s,
+    double time)
 {
-    if (time >= particletracer->startTime)
-    {
-        if( (time - particletracer->lastInjectTime) >= particletracer->injectTimePeriod)
-        {
+    if (time >= particletracer->startTime) {
+        if ((time - particletracer->lastInjectTime) >= particletracer->injectTimePeriod) {
            injectParticles(particletracer);
            particletracer->lastInjectTime = time;
        }
-        if( (time - particletracer->lastWriteTime) >= particletracer->writeTimePeriod)
-        {
+        if ((time - particletracer->lastWriteTime) >= particletracer->writeTimePeriod) {
            writeParticles(particletracer);
            particletracer->lastWriteTime = time;
        }
-        advanceParticles(particletracer, u, v, time);
+        advanceParticles(particletracer, u, v, s, time);
        compress(particletracer);
        particletracer->lastUpdateTime = time;
    }
@@ -548,18 +606,15 @@ void compress(ParticleTracer* particletracer)
    Particle* memPool = particletracer->particlePool;
    Particle tempPool[particletracer->totalParticles];

-    for(int i = 0; i < particletracer->totalParticles; ++i)
-    {   
-        tempPool[i].x = 0.0;
-        tempPool[i].y = 0.0;
+    for (int i = 0; i < particletracer->totalParticles; ++i) {
+        tempPool[i].x    = 0.0;
+        tempPool[i].y    = 0.0;
        tempPool[i].flag = false;
    }
    int totalParticles = 0;

-    for(int i=0; i < particletracer->totalParticles; ++i)
-    {
-        if(memPool[i].flag == true)
-        {
+    for (int i = 0; i < particletracer->totalParticles; ++i) {
+        if (memPool[i].flag == true) {
            tempPool[totalParticles].x    = memPool[i].x;
            tempPool[totalParticles].y    = memPool[i].y;
            tempPool[totalParticles].flag = memPool[i].flag;
--- a/BasicSolver/2D-mpi-v3/src/particletracing.h
+++ b/BasicSolver/2D-mpi-v3/src/particletracing.h
@@ -8,23 +8,25 @@
 #define __PARTICLETRACING_H_
 #include "allocate.h"
 #include "parameter.h"
+
 #include "solver.h"
-#include "particletracing.h"
-#include <stdbool.h>
+
 #include <mpi.h>
+#include <stdbool.h>

 #define NDIMS 2

 typedef enum COORD { X = 0, Y, NCOORD } COORD;
-typedef struct
-{
+
+typedef struct {
    double x, y;
    bool flag;
 } Particle;

 typedef struct {
    int numberOfParticles, totalParticles;
-    double startTime, injectTimePeriod, writeTimePeriod, lastInjectTime, lastUpdateTime, lastWriteTime;
+    double startTime, injectTimePeriod, writeTimePeriod, lastInjectTime, lastUpdateTime,
+        lastWriteTime;

    int estimatedNumParticles;

@@ -51,13 +53,13 @@ typedef struct {

 } ParticleTracer;

-void initParticleTracer(ParticleTracer*, Parameter*, Solver* );
-void injectParticles(ParticleTracer*);
-void advanceParticles(ParticleTracer*, double* , double*, double);
-void freeParticles(ParticleTracer*);
-void writeParticles(ParticleTracer*);
-void printParticleTracerParameters(ParticleTracer*);
-void printParticles(ParticleTracer*);
-void trace(ParticleTracer*, double* , double* , double );
-void compress(ParticleTracer* );
+extern void initParticleTracer(ParticleTracer*, Parameter*, Solver*);
+extern void injectParticles(ParticleTracer*);
+extern void advanceParticles(ParticleTracer*, double*, double*, int*, double);
+extern void freeParticles(ParticleTracer*);
+extern void writeParticles(ParticleTracer*);
+extern void printParticleTracerParameters(ParticleTracer*);
+extern void printParticles(ParticleTracer*);
+extern void trace(ParticleTracer*, double*, double*, int*, double);
+extern void compress(ParticleTracer*);
 #endif
--- a/BasicSolver/2D-mpi-v3/src/solver.c
+++ b/BasicSolver/2D-mpi-v3/src/solver.c
@@ -14,23 +14,42 @@
 #include "allocate.h"
 #include "parameter.h"
 #include "solver.h"
+
 #include "util.h"

-#define P(i, j)   p[(j) * (imaxLocal + 2) + (i)]
-#define F(i, j)   f[(j) * (imaxLocal + 2) + (i)]
-#define G(i, j)   g[(j) * (imaxLocal + 2) + (i)]
-#define U(i, j)   u[(j) * (imaxLocal + 2) + (i)]
-#define V(i, j)   v[(j) * (imaxLocal + 2) + (i)]
+#define P(i, j) p[(j) * (imaxLocal + 2) + (i)]
+#define F(i, j) f[(j) * (imaxLocal + 2) + (i)]
+#define G(i, j) g[(j) * (imaxLocal + 2) + (i)]
+#define U(i, j) u[(j) * (imaxLocal + 2) + (i)]
+#define V(i, j) v[(j) * (imaxLocal + 2) + (i)]
+#define S(i, j) s[(j) * (imaxLocal + 2) + (i)]
+
 #define RHS(i, j) rhs[(j) * (imaxLocal + 2) + (i)]

 #define IDIM 0
 #define JDIM 1

+static double sumOffset(double* sizes, int init, int offset, int coord)
+{
+    double sum = 0;
+
+    for (int i = init - offset; coord > 0; i -= offset, --coord) {
+        sum += sizes[i];
+    }
+
+    return sum;
+}
+
 static int sizeOfRank(int rank, int size, int N)
 {
    return N / size + ((N % size > rank) ? 1 : 0);
 }

+static double distance(double i, double j, double iCenter, double jCenter)
+{
+    return sqrt(pow(iCenter - i, 2) + pow(jCenter - j, 2) * 1.0);
+}
+
 void print(Solver* solver, double* grid)
 {
    int imaxLocal = solver->imaxLocal;
@@ -43,7 +62,29 @@ void print(Solver* solver, double* grid)
            for (int j = 0; j < solver->jmaxLocal + 2; j++) {
                printf("%02d: ", j);
                for (int i = 0; i < solver->imaxLocal + 2; i++) {
-                    printf("%12.8f  ", grid[j * (imaxLocal + 2) + i]);
+                    printf("%2.2f  ", grid[j * (imaxLocal + 2) + i]);
+                }
+                printf("\n");
+            }
+            fflush(stdout);
+        }
+        MPI_Barrier(MPI_COMM_WORLD);
+    }
+}
+
+void printInt(Solver* solver, int* grid)
+{
+    int imaxLocal = solver->imaxLocal;
+
+    for (int i = 0; i < solver->size; i++) {
+        if (i == solver->rank) {
+            printf(
+                "### RANK %d #######################################################\n",
+                solver->rank);
+            for (int j = 0; j < solver->jmaxLocal + 2; j++) {
+                printf("%02d: ", j);
+                for (int i = 0; i < solver->imaxLocal + 2; i++) {
+                    printf("%2d  ", grid[j * (imaxLocal + 2) + i]);
                }
                printf("\n");
            }
@@ -68,6 +109,21 @@ static void exchange(Solver* solver, double* grid)
        solver->comm);
 }

+static void exchangeInt(Solver* solver, int* grid)
+{
+    int counts[4] = { 1, 1, 1, 1 };
+
+    MPI_Neighbor_alltoallw(grid,
+        counts,
+        solver->sdisplsInt,
+        solver->bufferIntTypes,
+        grid,
+        counts,
+        solver->rdisplsInt,
+        solver->bufferIntTypes,
+        solver->comm);
+}
+
 static void shift(Solver* solver)
 {
    MPI_Request requests[4] = { MPI_REQUEST_NULL,
@@ -315,7 +371,6 @@ void initSolver(Solver* solver, Parameter* params)
    solver->gamma    = params->gamma;
    solver->rho      = params->rho;

-
    /* setup communication */
    MPI_Comm_rank(MPI_COMM_WORLD, &(solver->rank));
    MPI_Comm_size(MPI_COMM_WORLD, &(solver->size));
@@ -350,26 +405,56 @@ void initSolver(Solver* solver, Parameter* params)
        &iBufferType);
    MPI_Type_commit(&iBufferType);

+    MPI_Datatype jBufferIntType;
+    MPI_Type_contiguous(solver->imaxLocal, MPI_INT, &jBufferIntType);
+    MPI_Type_commit(&jBufferIntType);
+
+    MPI_Datatype iBufferIntType;
+    MPI_Type_vector(solver->jmaxLocal,
+        1,
+        solver->imaxLocal + 2,
+        MPI_INT,
+        &iBufferIntType);
+    MPI_Type_commit(&iBufferIntType);
+
    // in the order of the dimensions i->0, j->1
    // first negative direction, then positive direction
-    size_t dblsize         = sizeof(double);
-    int imaxLocal          = solver->imaxLocal;
-    int jmaxLocal          = solver->jmaxLocal;
+    size_t dblsize = sizeof(double);
+    size_t intsize = sizeof(int);
+
+    int imaxLocal = solver->imaxLocal;
+    int jmaxLocal = solver->jmaxLocal;
+
    solver->bufferTypes[0] = iBufferType; // left
    solver->bufferTypes[1] = iBufferType; // right
    solver->bufferTypes[2] = jBufferType; // bottom
    solver->bufferTypes[3] = jBufferType; // top

+    solver->bufferIntTypes[0] = iBufferIntType; // left
+    solver->bufferIntTypes[1] = iBufferIntType; // right
+    solver->bufferIntTypes[2] = jBufferIntType; // bottom
+    solver->bufferIntTypes[3] = jBufferIntType; // top
+
    solver->sdispls[0] = ((imaxLocal + 2) + 1) * dblsize;               // send left
    solver->sdispls[1] = ((imaxLocal + 2) + imaxLocal) * dblsize;       // send right
    solver->sdispls[2] = ((imaxLocal + 2) + 1) * dblsize;               // send bottom
    solver->sdispls[3] = ((jmaxLocal) * (imaxLocal + 2) + 1) * dblsize; // send top

+    solver->sdisplsInt[0] = ((imaxLocal + 2) + 1) * intsize;               // send left
+    solver->sdisplsInt[1] = ((imaxLocal + 2) + imaxLocal) * intsize;       // send right
+    solver->sdisplsInt[2] = ((imaxLocal + 2) + 1) * intsize;               // send bottom
+    solver->sdisplsInt[3] = ((jmaxLocal) * (imaxLocal + 2) + 1) * intsize; // send top
+
    solver->rdispls[0] = (imaxLocal + 2) * dblsize;                         // recv left
    solver->rdispls[1] = ((imaxLocal + 2) + (imaxLocal + 1)) * dblsize;     // recv right
    solver->rdispls[2] = 1 * dblsize;                                       // recv bottom
    solver->rdispls[3] = ((jmaxLocal + 1) * (imaxLocal + 2) + 1) * dblsize; // recv top

+    solver->rdisplsInt[0] = (imaxLocal + 2) * intsize;                     // recv left
+    solver->rdisplsInt[1] = ((imaxLocal + 2) + (imaxLocal + 1)) * intsize; // recv right
+    solver->rdisplsInt[2] = 1 * intsize;                                   // recv bottom
+    solver->rdisplsInt[3] = ((jmaxLocal + 1) * (imaxLocal + 2) + 1) * intsize; // recv top
+
    /* allocate arrays */
    size_t bytesize = (imaxLocal + 2) * (jmaxLocal + 2) * sizeof(double);
    solver->u       = allocate(64, bytesize);
@@ -378,6 +463,7 @@ void initSolver(Solver* solver, Parameter* params)
    solver->rhs     = allocate(64, bytesize);
    solver->f       = allocate(64, bytesize);
    solver->g       = allocate(64, bytesize);
+    solver->s       = allocate(64, bytesize);

    for (int i = 0; i < (imaxLocal + 2) * (jmaxLocal + 2); i++) {
        solver->u[i]   = params->u_init;
@@ -386,12 +472,119 @@ void initSolver(Solver* solver, Parameter* params)
        solver->rhs[i] = 0.0;
        solver->f[i]   = 0.0;
        solver->g[i]   = 0.0;
+        solver->s[i]   = NONE;
    }

    double dx          = solver->dx;
    double dy          = solver->dy;
    double inv_sqr_sum = 1.0 / (dx * dx) + 1.0 / (dy * dy);
    solver->dtBound    = 0.5 * solver->re * 1.0 / inv_sqr_sum;
+
+    solver->xLocal = solver->imaxLocal * solver->dx;
+    solver->yLocal = solver->jmaxLocal * solver->dy;
+
+    double xLocal[solver->size];
+    double yLocal[solver->size];
+
+    MPI_Allgather(&solver->xLocal, 1, MPI_DOUBLE, xLocal, 1, MPI_DOUBLE, solver->comm);
+    MPI_Allgather(&solver->yLocal, 1, MPI_DOUBLE, yLocal, 1, MPI_DOUBLE, solver->comm);
+
+    solver->xOffset = sumOffset(xLocal, solver->rank, solver->dims[1], solver->coords[0]);
+    solver->yOffset = sumOffset(yLocal, solver->rank, 1, solver->coords[1]);
+    solver->xOffsetEnd = solver->xOffset + solver->xLocal;
+    solver->yOffsetEnd = solver->yOffset + solver->yLocal;
+
+    printf("Rank : %d, xOffset : %.2f, yOffset : %.2f, xOffsetEnd : %.2f, yOffsetEnd : "
+           "%.2f\n",
+        solver->rank,
+        solver->xOffset,
+        solver->yOffset,
+        solver->xOffsetEnd,
+        solver->yOffsetEnd);
+
+    int* s      = solver->s;
+    int iOffset = 0, jOffset = 0;
+
+    double xCenter = 0, yCenter = 0, radius = 0;
+    double x1 = 0, x2 = 0, y1 = 0, y2 = 0;
+
+    switch (params->shape) {
+    case NOSHAPE:
+        break;
+    case RECT:
+        x1 = params->xCenter - params->xRectLength / 2;
+        x2 = params->xCenter + params->xRectLength / 2;
+        y1 = params->yCenter - params->yRectLength / 2;
+        y2 = params->yCenter + params->yRectLength / 2;
+
+        iOffset = solver->xOffset / dx;
+        jOffset = solver->yOffset / dy;
+
+        for (int j = 1; j < jmaxLocal + 1; ++j) {
+            for (int i = 1; i < imaxLocal + 1; ++i) {
+                if ((x1 <= ((i + iOffset) * dx)) && (((i + iOffset) * dx) <= x2) &&
+                    (y1 <= ((j + jOffset) * dy)) && (((j + jOffset) * dy) <= y2)) {
+                    S(i, j) = LOCAL;
+                }
+            }
+        }
+
+        break;
+    case CIRCLE:
+        xCenter = params->xCenter;
+        yCenter = params->yCenter;
+        radius  = params->circleRadius;
+
+        iOffset = solver->xOffset / dx;
+        jOffset = solver->yOffset / dy;
+
+        for (int j = 1; j < jmaxLocal + 1; j++) {
+            for (int i = 1; i < imaxLocal + 1; i++) {
+                if (distance(((i + iOffset) * dx),
+                        ((j + jOffset) * dy),
+                        xCenter,
+                        yCenter) <= radius) {
+                    S(i, j) = LOCAL;
+                }
+            }
+        }
+
+        break;
+    default:
+        break;
+    }
+
+    exchangeInt(solver, s);
+
+    for (int j = 1; j < jmaxLocal + 1; j++) {
+        for (int i = 1; i < imaxLocal + 1; i++) {
+
+            if (S(i, j - 1) == NONE && S(i, j + 1) == LOCAL && S(i, j) == LOCAL)
+                S(i, j) = BOTTOM; // BOTTOM
+            if (S(i - 1, j) == NONE && S(i + 1, j) == LOCAL && S(i, j) == LOCAL)
+                S(i, j) = LEFT; // LEFT
+            if (S(i + 1, j) == NONE && S(i - 1, j) == LOCAL && S(i, j) == LOCAL)
+                S(i, j) = RIGHT; // RIGHT
+            if (S(i, j + 1) == NONE && S(i, j - 1) == LOCAL && S(i, j) == LOCAL)
+                S(i, j) = TOP; // TOP
+            if (S(i - 1, j - 1) == NONE && S(i, j - 1) == NONE && S(i - 1, j) == NONE &&
+                S(i + 1, j + 1) == LOCAL &&
+                (S(i, j) == LOCAL || S(i, j) == LEFT || S(i, j) == BOTTOM))
+                S(i, j) = BOTTOMLEFT; // BOTTOMLEFT
+            if (S(i + 1, j - 1) == NONE && S(i, j - 1) == NONE && S(i + 1, j) == NONE &&
+                S(i - 1, j + 1) == LOCAL &&
+                (S(i, j) == LOCAL || S(i, j) == RIGHT || S(i, j) == BOTTOM))
+                S(i, j) = BOTTOMRIGHT; // BOTTOMRIGHT
+            if (S(i - 1, j + 1) == NONE && S(i - 1, j) == NONE && S(i, j + 1) == NONE &&
+                S(i + 1, j - 1) == LOCAL &&
+                (S(i, j) == LOCAL || S(i, j) == LEFT || S(i, j) == TOP))
+                S(i, j) = TOPLEFT; // TOPLEFT
+            if (S(i + 1, j + 1) == NONE && S(i + 1, j) == NONE && S(i, j + 1) == NONE &&
+                S(i - 1, j - 1) == LOCAL &&
+                (S(i, j) == LOCAL || S(i, j) == RIGHT || S(i, j) == TOP))
+                S(i, j) = TOPRIGHT; // TOPRIGHT
+        }
+    }
 #ifdef VERBOSE
    printConfig(solver);
 #endif
@@ -613,7 +806,6 @@ int solveRBA(Solver* solver)

    int pass, jsw, isw;

-
    while ((res >= epssq) && (it < itermax)) {
        res = 0.0;
        jsw = 1;
@@ -634,7 +826,7 @@ int solveRBA(Solver* solver)
                }
                isw = 3 - isw;
            }
-            jsw = 3 - jsw;
+            jsw   = 3 - jsw;
            omega = (it == 0 && pass == 0 ? 1.0 / (1.0 - 0.5 * rho * rho)
                                          : 1.0 / (1.0 - 0.25 * rho * rho * omega));
        }
@@ -685,6 +877,66 @@ int solveRBA(Solver* solver)
    }
 }

+void setObjectBoundaryCondition(Solver* solver)
+{
+    int imaxLocal = solver->imaxLocal;
+    int jmaxLocal = solver->jmaxLocal;
+    double* u     = solver->u;
+    double* v     = solver->v;
+    int* s        = solver->s;
+
+    for (int j = 1; j < jmaxLocal + 1; j++) {
+        for (int i = 1; i < imaxLocal + 1; i++) {
+            switch (S(i, j)) {
+            case TOP:
+                U(i, j)     = -U(i, j + 1);
+                U(i - 1, j) = -U(i - 1, j + 1);
+                V(i, j)     = 0.0;
+                break;
+            case BOTTOM:
+                U(i, j)     = -U(i, j - 1);
+                U(i - 1, j) = -U(i - 1, j - 1);
+                V(i, j)     = 0.0;
+                break;
+            case LEFT:
+                U(i - 1, j) = 0.0;
+                V(i, j)     = -V(i - 1, j);
+                V(i, j - 1) = -V(i - 1, j - 1);
+                break;
+            case RIGHT:
+                U(i, j)     = 0.0;
+                V(i, j)     = -V(i + 1, j);
+                V(i, j - 1) = -V(i + 1, j - 1);
+                break;
+            case TOPLEFT:
+                U(i, j)     = -U(i, j + 1);
+                U(i - 1, j) = 0.0;
+                V(i, j)     = 0.0;
+                V(i, j - 1) = -V(i - 1, j - 1);
+                break;
+            case TOPRIGHT:
+                U(i, j)     = 0.0;
+                U(i - 1, j) = -U(i - 1, j + 1);
+                V(i, j)     = 0.0;
+                V(i, j - 1) = -V(i + 1, j - 1);
+                break;
+            case BOTTOMLEFT:
+                U(i, j)     = -U(i, j - 1);
+                U(i - 1, j) = 0.0;
+                V(i, j)     = -V(i - 1, j);
+                V(i, j - 1) = 0.0;
+                break;
+            case BOTTOMRIGHT:
+                U(i, j)     = 0.0;
+                U(i - 1, j) = -U(i - 1, j - 1);
+                V(i, j)     = -V(i, j + 1);
+                V(i, j - 1) = 0.0;
+                break;
+            }
+        }
+    }
+}
+
 static double maxElement(Solver* solver, double* m)
 {
    int size      = (solver->imaxLocal + 2) * (solver->jmaxLocal + 2);
@@ -833,6 +1085,7 @@ void setSpecialBoundaryCondition(Solver* solver)
    int imaxLocal = solver->imaxLocal;
    int jmaxLocal = solver->jmaxLocal;
    double* u     = solver->u;
+    int* s        = solver->s;

    if (strcmp(solver->problem, "dcavity") == 0) {
        if (solver->coords[JDIM] == (solver->dims[JDIM] - 1)) { // set top bc
@@ -844,21 +1097,31 @@ void setSpecialBoundaryCondition(Solver* solver)
        if (solver->coords[IDIM] == 0) { // set left bc
            double ylength = solver->ylength;
            double dy      = solver->dy;
-            int rest       = solver->jmax % solver->size;
-            int yc         = solver->rank * (solver->jmax / solver->size) +
-                     MIN(rest, solver->rank);
-            double ys = dy * (yc + 0.5);
+
+            int jOffset    = solver->yOffset / dy;
+            int jOffsetEnd = solver->yOffsetEnd / dy;
+
            double y;

-            /* printf("RANK %d yc: %d ys: %f\n", solver->rank, yc, ys); */
-
-            for (int j = 1; j < jmaxLocal + 1; j++) {
-                y       = ys + dy * (j - 0.5);
+            for (int j = 1, jVal = jOffset + 1; j < jmaxLocal + 1; ++jVal, j++) {
+                y       = dy * (jVal - 0.5);
                U(0, j) = y * (ylength - y) * 4.0 / (ylength * ylength);
            }
        }
+    } else if (strcmp(solver->problem, "backstep") == 0) {
+        for (int j = 1; j < jmaxLocal + 1; j++) {
+            if (S(0, j) == NONE) U(0, j) = 1.0;
+        }
+    } else if (strcmp(solver->problem, "karman") == 0) {
+        for (int j = 1; j < jmaxLocal + 1; j++) {
+            U(0, j) = 1.0;
+        }
    }
-    /* print(solver, solver->u); */
+
+    // print(solver, solver->u);
+
+    // MPI_Barrier(solver->comm);
+    // exit(0);
 }

 void computeFG(Solver* solver)
@@ -867,6 +1130,7 @@ void computeFG(Solver* solver)
    double* v        = solver->v;
    double* f        = solver->f;
    double* g        = solver->g;
+    int* s           = solver->s;
    int imaxLocal    = solver->imaxLocal;
    int jmaxLocal    = solver->jmaxLocal;
    double gx        = solver->gx;
@@ -884,43 +1148,84 @@ void computeFG(Solver* solver)

    for (int j = 1; j < jmaxLocal + 1; j++) {
        for (int i = 1; i < imaxLocal + 1; i++) {
-            du2dx = inverseDx * 0.25 *
-                        ((U(i, j) + U(i + 1, j)) * (U(i, j) + U(i + 1, j)) -
-                            (U(i, j) + U(i - 1, j)) * (U(i, j) + U(i - 1, j))) +
-                    gamma * inverseDx * 0.25 *
-                        (fabs(U(i, j) + U(i + 1, j)) * (U(i, j) - U(i + 1, j)) +
-                            fabs(U(i, j) + U(i - 1, j)) * (U(i, j) - U(i - 1, j)));
+            if (S(i, j) == NONE) {
+                du2dx = inverseDx * 0.25 *
+                            ((U(i, j) + U(i + 1, j)) * (U(i, j) + U(i + 1, j)) -
+                                (U(i, j) + U(i - 1, j)) * (U(i, j) + U(i - 1, j))) +
+                        gamma * inverseDx * 0.25 *
+                            (fabs(U(i, j) + U(i + 1, j)) * (U(i, j) - U(i + 1, j)) +
+                                fabs(U(i, j) + U(i - 1, j)) * (U(i, j) - U(i - 1, j)));

-            duvdy = inverseDy * 0.25 *
-                        ((V(i, j) + V(i + 1, j)) * (U(i, j) + U(i, j + 1)) -
-                            (V(i, j - 1) + V(i + 1, j - 1)) * (U(i, j) + U(i, j - 1))) +
-                    gamma * inverseDy * 0.25 *
-                        (fabs(V(i, j) + V(i + 1, j)) * (U(i, j) - U(i, j + 1)) +
-                            fabs(V(i, j - 1) + V(i + 1, j - 1)) *
-                                (U(i, j) - U(i, j - 1)));
+                duvdy = inverseDy * 0.25 *
+                            ((V(i, j) + V(i + 1, j)) * (U(i, j) + U(i, j + 1)) -
+                                (V(i, j - 1) + V(i + 1, j - 1)) *
+                                    (U(i, j) + U(i, j - 1))) +
+                        gamma * inverseDy * 0.25 *
+                            (fabs(V(i, j) + V(i + 1, j)) * (U(i, j) - U(i, j + 1)) +
+                                fabs(V(i, j - 1) + V(i + 1, j - 1)) *
+                                    (U(i, j) - U(i, j - 1)));

-            du2dx2  = inverseDx * inverseDx * (U(i + 1, j) - 2.0 * U(i, j) + U(i - 1, j));
-            du2dy2  = inverseDy * inverseDy * (U(i, j + 1) - 2.0 * U(i, j) + U(i, j - 1));
-            F(i, j) = U(i, j) + dt * (inverseRe * (du2dx2 + du2dy2) - du2dx - duvdy + gx);
+                du2dx2 = inverseDx * inverseDx *
+                         (U(i + 1, j) - 2.0 * U(i, j) + U(i - 1, j));
+                du2dy2 = inverseDy * inverseDy *
+                         (U(i, j + 1) - 2.0 * U(i, j) + U(i, j - 1));
+                F(i, j) = U(i, j) +
+                          dt * (inverseRe * (du2dx2 + du2dy2) - du2dx - duvdy + gx);

-            duvdx = inverseDx * 0.25 *
-                        ((U(i, j) + U(i, j + 1)) * (V(i, j) + V(i + 1, j)) -
-                            (U(i - 1, j) + U(i - 1, j + 1)) * (V(i, j) + V(i - 1, j))) +
-                    gamma * inverseDx * 0.25 *
-                        (fabs(U(i, j) + U(i, j + 1)) * (V(i, j) - V(i + 1, j)) +
-                            fabs(U(i - 1, j) + U(i - 1, j + 1)) *
-                                (V(i, j) - V(i - 1, j)));
+                duvdx = inverseDx * 0.25 *
+                            ((U(i, j) + U(i, j + 1)) * (V(i, j) + V(i + 1, j)) -
+                                (U(i - 1, j) + U(i - 1, j + 1)) *
+                                    (V(i, j) + V(i - 1, j))) +
+                        gamma * inverseDx * 0.25 *
+                            (fabs(U(i, j) + U(i, j + 1)) * (V(i, j) - V(i + 1, j)) +
+                                fabs(U(i - 1, j) + U(i - 1, j + 1)) *
+                                    (V(i, j) - V(i - 1, j)));

-            dv2dy = inverseDy * 0.25 *
-                        ((V(i, j) + V(i, j + 1)) * (V(i, j) + V(i, j + 1)) -
-                            (V(i, j) + V(i, j - 1)) * (V(i, j) + V(i, j - 1))) +
-                    gamma * inverseDy * 0.25 *
-                        (fabs(V(i, j) + V(i, j + 1)) * (V(i, j) - V(i, j + 1)) +
-                            fabs(V(i, j) + V(i, j - 1)) * (V(i, j) - V(i, j - 1)));
+                dv2dy = inverseDy * 0.25 *
+                            ((V(i, j) + V(i, j + 1)) * (V(i, j) + V(i, j + 1)) -
+                                (V(i, j) + V(i, j - 1)) * (V(i, j) + V(i, j - 1))) +
+                        gamma * inverseDy * 0.25 *
+                            (fabs(V(i, j) + V(i, j + 1)) * (V(i, j) - V(i, j + 1)) +
+                                fabs(V(i, j) + V(i, j - 1)) * (V(i, j) - V(i, j - 1)));

-            dv2dx2  = inverseDx * inverseDx * (V(i + 1, j) - 2.0 * V(i, j) + V(i - 1, j));
-            dv2dy2  = inverseDy * inverseDy * (V(i, j + 1) - 2.0 * V(i, j) + V(i, j - 1));
-            G(i, j) = V(i, j) + dt * (inverseRe * (dv2dx2 + dv2dy2) - duvdx - dv2dy + gy);
+                dv2dx2 = inverseDx * inverseDx *
+                         (V(i + 1, j) - 2.0 * V(i, j) + V(i - 1, j));
+                dv2dy2 = inverseDy * inverseDy *
+                         (V(i, j + 1) - 2.0 * V(i, j) + V(i, j - 1));
+                G(i, j) = V(i, j) +
+                          dt * (inverseRe * (dv2dx2 + dv2dy2) - duvdx - dv2dy + gy);
+            } else {
+                switch (S(i, j)) {
+                case TOP:
+                    G(i, j) = V(i, j);
+                    break;
+                case BOTTOM:
+                    G(i, j - 1) = V(i, j - 1);
+                    break;
+                case LEFT:
+                    F(i - 1, j) = U(i - 1, j);
+                    break;
+                case RIGHT:
+                    F(i, j) = U(i, j);
+                    break;
+                case TOPLEFT:
+                    F(i - 1, j) = U(i - 1, j);
+                    G(i, j)     = V(i, j);
+                    break;
+                case TOPRIGHT:
+                    F(i, j) = U(i, j);
+                    G(i, j) = V(i, j);
+                    break;
+                case BOTTOMLEFT:
+                    F(i - 1, j) = U(i - 1, j);
+                    G(i, j - 1) = V(i, j - 1);
+                    break;
+                case BOTTOMRIGHT:
+                    F(i, j)     = U(i, j);
+                    G(i, j - 1) = V(i, j - 1);
+                    break;
+                }
+            }
        }
    }

--- a/BasicSolver/2D-mpi-v3/src/solver.h
+++ b/BasicSolver/2D-mpi-v3/src/solver.h
@@ -7,11 +7,26 @@
 #ifndef __SOLVER_H_
 #define __SOLVER_H_
 #include "parameter.h"
+
 #include <mpi.h>

 #define NDIMS 2

+enum OBJECTBOUNDARY {
+    NONE = 0,
+    TOP,
+    BOTTOM,
+    LEFT,
+    RIGHT,
+    TOPLEFT,
+    BOTTOMLEFT,
+    TOPRIGHT,
+    BOTTOMRIGHT,
+    LOCAL
+};
 enum BC { NOSLIP = 1, SLIP, OUTFLOW, PERIODIC };
+/// @brief
+enum SHAPE { NOSHAPE = 0, RECT, CIRCLE };

 typedef struct {
    /* geometry and grid information */
@@ -22,6 +37,8 @@ typedef struct {
    double *p, *rhs;
    double *f, *g;
    double *u, *v;
+    int* s;
+
    /* parameters */
    double eps, omega, rho;
    double re, tau, gamma;
@@ -38,23 +55,32 @@ typedef struct {
    MPI_Comm comm;
    MPI_Datatype bufferTypes[NDIMS * 2];
    MPI_Aint sdispls[NDIMS * 2], rdispls[NDIMS * 2];
+
+    MPI_Datatype bufferIntTypes[NDIMS * 2];
+    MPI_Aint sdisplsInt[NDIMS * 2], rdisplsInt[NDIMS * 2];
    int iNeighbours[NDIMS], jNeighbours[NDIMS];
    int coords[NDIMS], dims[NDIMS];
    int imaxLocal, jmaxLocal;
+
+    double xLocal, yLocal, xOffset, yOffset, xOffsetEnd, yOffsetEnd;
+
 } Solver;

-void initSolver(Solver*, Parameter*);
-void computeRHS(Solver*);
-int solve(Solver*);
-int solveRB(Solver*);
-int solveRBA(Solver*);
-void computeTimestep(Solver*);
-void setBoundaryConditions(Solver*);
-void setSpecialBoundaryCondition(Solver*);
-void computeFG(Solver*);
-void adaptUV(Solver*);
-void collectResult(Solver*);
-void writeResult(Solver*, double*, double*, double*);
-void debugExchange(Solver*);
-void print(Solver*, double*);
+extern void initSolver(Solver*, Parameter*);
+extern void computeRHS(Solver*);
+extern int solve(Solver*);
+extern int solveRB(Solver*);
+extern int solveRBA(Solver*);
+extern void computeTimestep(Solver*);
+extern void setBoundaryConditions(Solver*);
+extern void setSpecialBoundaryCondition(Solver*);
+extern void setObjectBoundaryCondition(Solver*);
+extern void computeFG(Solver*);
+extern void adaptUV(Solver*);
+extern void collectResult(Solver*);
+extern void writeResult(Solver*, double*, double*, double*);
+extern void debugExchange(Solver*);
+extern void print(Solver*, double*);
+extern void printInt(Solver*, int*);
+
 #endif
--- a/BasicSolver/2D-mpi-v3/src/vtkWriter.c
+++ b/BasicSolver/2D-mpi-v3/src/vtkWriter.c
@@ -1,126 +0,0 @@
-/*
- * Copyright (C) 2022 NHR@FAU, University Erlangen-Nuremberg.
- * All rights reserved. This file is part of nusif-solver.
- * Use of this source code is governed by a MIT style
- * license that can be found in the LICENSE file.
- */
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-#include "vtkWriter.h"
-
-static float floatSwap(float f)
-{
-    union {
-        float f;
-        char b[4];
-    } dat1, dat2;
-
-    dat1.f    = f;
-    dat2.b[0] = dat1.b[3];
-    dat2.b[1] = dat1.b[2];
-    dat2.b[2] = dat1.b[1];
-    dat2.b[3] = dat1.b[0];
-    return dat2.f;
-}
-
-static void writeHeader(VtkOptions* o, int ts)
-{
-    fprintf(o->fh, "# vtk DataFile Version 3.0\n");
-    fprintf(o->fh, "PAMPI cfd solver particle tracing file\n");
-    if (o->fmt == ASCII) {
-        fprintf(o->fh, "ASCII\n");
-    } else if (o->fmt == BINARY) {
-        fprintf(o->fh, "BINARY\n");
-    }
-
-    fprintf(o->fh, "DATASET UNSTRUCTURED_GRID\n");
-    fprintf(o->fh, "FIELD FieldData 2\n");
-    fprintf(o->fh, "TIME 1 1 double\n");
-    fprintf(o->fh, "%d\n", ts);
-    fprintf(o->fh, "CYCLE 1 1 int\n");
-    fprintf(o->fh, "1\n");
-}
-
-void vtkOpen(VtkOptions* o, char* problem, int ts)
-{
-    o->fh = fopen(problem, "w");
-
-    if (o->fh == NULL) {
-        printf("vtkWriter not initialize! Call vtkOpen first!\n");
-        exit(EXIT_FAILURE);
-    }
-
-    writeHeader(o, ts);
-
-    printf("Writing VTK output for %s\n", problem);
-}
-
-void vtkParticle(VtkOptions* o, char* name)
-{
-    Particle* particlePool = o->particletracer->particlePool;
-
-    if (o->fh == NULL) {
-        printf("vtkWriter not initialize! Call vtkOpen first!\n");
-        exit(EXIT_FAILURE);
-    }
-
-    fprintf(o->fh, "POINTS %d float\n", o->overallTotalParticles);
-
-
-    for (int i = 0; i < o->particletracer->size; ++i)
-    {
-        
-        double x = particlePool[i].x;
-        double y = particlePool[i].y;
-        fprintf(o->fh, "%.2f %.2f 0.0\n", x, y);
-    }
-
-    fprintf(o->fh, "CELLS %d %d\n", o->particletracer->totalParticles, 2 * o->particletracer->totalParticles);
-
-
-    for (int i = 0; i < o->particletracer->totalParticles; ++i)
-    {
-        fprintf(o->fh, "1 %d\n", i);
-    }
-
-    fprintf(o->fh, "CELL_TYPES %d\n", o->particletracer->totalParticles);
-
-
-    for (int i = 0; i < o->particletracer->totalParticles; ++i)
-    {
-        fprintf(o->fh, "1\n");
-    }
-
-    /*
-    for (int k = 0; k < kmax; k++) {
-        for (int j = 0; j < jmax; j++) {
-            for (int i = 0; i < imax; i++) {
-                if (o->fmt == ASCII) {
-                    fprintf(o->fh,
-                        "%f %f %f\n",
-                        G(vec.u, i, j, k),
-                        G(vec.v, i, j, k),
-                        G(vec.w, i, j, k));
-                } else if (o->fmt == BINARY) {
-                    fwrite((float[3]) { floatSwap(G(vec.u, i, j, k)),
-                               floatSwap(G(vec.v, i, j, k)),
-                               floatSwap(G(vec.w, i, j, k)) },
-                        sizeof(float),
-                        3,
-                        o->fh);
-                }
-            }
-        }
-    }
-    if (o->fmt == BINARY) fprintf(o->fh, "\n");
-
-    */
-}
-
-void vtkClose(VtkOptions* o)
-{
-    fclose(o->fh);
-    o->fh = NULL;
-}
--- a/BasicSolver/2D-mpi-v3/src/vtkWriter.h
+++ b/BasicSolver/2D-mpi-v3/src/vtkWriter.h
@@ -1,26 +0,0 @@
-/*
- * Copyright (C) 2022 NHR@FAU, University Erlangen-Nuremberg.
- * All rights reserved. This file is part of nusif-solver.
- * Use of this source code is governed by a MIT style
- * license that can be found in the LICENSE file.
- */
-#ifndef __VTKWRITER_H_
-#define __VTKWRITER_H_
-#include <stdio.h>
-
-#include "particletracing.h"
-#include "solver.h"
-
-typedef enum VtkFormat { ASCII = 0, BINARY } VtkFormat;
-
-typedef struct VtkOptions {
-    VtkFormat fmt;
-    FILE* fh;
-    int overallTotalParticles;
-    ParticleTracer* particletracer;
-} VtkOptions;
-
-extern void vtkOpen(VtkOptions* opts, char* filename, int ts);
-extern void vtkParticle(VtkOptions* opts, char* name);
-extern void vtkClose(VtkOptions* opts);
-#endif // __VTKWRITER_H_
--- a/BasicSolver/2D-mpi-v3/vector.plot
+++ b/BasicSolver/2D-mpi-v3/vector.plot
@@ -1,5 +1,8 @@
-set terminal png size 1800,768 enhanced font ,12
+set terminal png size 3600,768 enhanced font ,28
 set output 'velocity.png'
+set xrange[0:7]
+set yrange[0:1.5]
+set size ratio -1
 set datafile separator whitespace

 plot 'velocity.dat' using 1:2:3:4:5 with vectors filled head size 0.01,20,60 lc palette
--- a/BasicSolver/2D-mpi-v3/velocity.dat
+++ b/BasicSolver/2D-mpi-v3/velocity.dat
--- a/BasicSolver/2D-mpi-v3/velocity.png
+++ b/BasicSolver/2D-mpi-v3/velocity.png
--- a/BasicSolver/2D-mpi-v3/vis_files/animate.plot
+++ b/BasicSolver/2D-mpi-v3/vis_files/animate.plot
@@ -3,7 +3,8 @@ set term gif animate delay 50
 set output "trace.gif"
 set xrange [0:30]
 set yrange [0:4]
-do for [ts=0:200] {
+
+do for [ts=0:120] {
    plot "particles_".ts.".dat" with points pointtype 7
 }
 unset output
--- a/BasicSolver/2D-mpi-v3/vis_files/backstep_animate.plot
+++ b/BasicSolver/2D-mpi-v3/vis_files/backstep_animate.plot
@@ -0,0 +1,12 @@
+unset border; unset tics; unset key;
+set term gif animate delay 10
+set output "trace.gif"
+set xrange [0:7]
+set yrange [0:1.5]
+set object 1 rect from 0.0,0.0 to 1.0,0.5 lw 2
+
+
+do for [ts=0:300] {
+    plot "particles_".ts.".dat" with points pointtype 7
+}
+unset output
--- a/BasicSolver/2D-mpi-v3/vis_files/karman_animate.plot
+++ b/BasicSolver/2D-mpi-v3/vis_files/karman_animate.plot
@@ -0,0 +1,13 @@
+unset border; unset tics; unset key;
+set term gif animate delay 10
+set output "trace.gif"
+set xrange [0:30]
+set yrange [0:8]
+set size ratio -1
+set object 1 circle front at 5.0,4.0 size 1.0 fillcolor rgb "black" lw 2
+
+
+do for [ts=0:500] {
+    plot "particles_".ts.".dat" with points pointtype 7 pointsize 0.3
+}
+unset output
--- a/BasicSolver/2D-mpi-v3/vis_files/trace.gif
+++ b/BasicSolver/2D-mpi-v3/vis_files/trace.gif
--- a/BasicSolver/2D-mpi/pressure.dat
+++ b/BasicSolver/2D-mpi/pressure.dat
@@ -1,530 +1,423 @@
-0.07 0.04 -nan
-0.22 0.04 -nan
-0.38 0.04 -nan
-0.53 0.04 -nan
-0.67 0.04 -nan
-0.82 0.04 -nan
-0.97 0.04 -nan
-1.12 0.04 -nan
-1.27 0.04 -nan
-1.43 0.04 -nan
-1.57 0.04 -nan
-1.72 0.04 -nan
-1.88 0.04 -nan
-2.02 0.04 -nan
-2.17 0.04 -nan
-2.32 0.04 -nan
-2.48 0.04 -nan
-2.62 0.04 -nan
-2.77 0.04 -nan
-2.92 0.04 -nan
-3.07 0.04 -nan
-3.23 0.04 -nan
-3.38 0.04 -nan
-3.52 0.04 -nan
-3.67 0.04 -nan
-3.82 0.04 -nan
-3.97 0.04 -nan
-4.12 0.04 -nan
-4.27 0.04 -nan
-4.42 0.04 -nan
-4.58 0.04 -nan
-4.72 0.04 -nan
-4.88 0.04 -nan
-5.02 0.04 -nan
-5.17 0.04 -nan
-5.33 0.04 -nan
-5.47 0.04 -nan
-5.62 0.04 -nan
-5.77 0.04 -nan
-5.92 0.04 -nan
-6.08 0.04 -nan
-6.22 0.04 -nan
-6.38 0.04 -nan
-6.52 0.04 -nan
-6.67 0.04 -nan
-6.83 0.04 -nan
-6.97 0.04 -nan
-7.12 0.04 -nan
-7.27 0.04 -nan
-7.42 0.04 -nan
-7.57 0.04 -nan
-7.72 0.04 -nan
-7.88 0.04 -nan
-8.03 0.04 -nan
-8.17 0.04 -nan
-8.32 0.04 -nan
-8.47 0.04 -nan
-8.62 0.04 -nan
-8.78 0.04 -nan
-8.92 0.04 -nan
-9.07 0.04 -nan
-9.22 0.04 -nan
-9.38 0.04 -nan
-9.53 0.04 -nan
-9.67 0.04 -nan
-9.82 0.04 -nan
-9.97 0.04 -nan
-10.12 0.04 -nan
-10.28 0.04 -nan
-10.42 0.04 -nan
-10.57 0.04 -nan
-10.72 0.04 -nan
-10.88 0.04 -nan
-11.03 0.04 -nan
-11.17 0.04 -nan
-11.32 0.04 -nan
-11.47 0.04 -nan
-11.62 0.04 -nan
-11.78 0.04 -nan
-11.92 0.04 -nan
-12.07 0.04 -nan
-12.22 0.04 -nan
-12.38 0.04 -nan
-12.53 0.04 -nan
-12.67 0.04 -nan
-12.82 0.04 -nan
-12.97 0.04 -nan
-13.12 0.04 -nan
-13.28 0.04 -nan
-13.42 0.04 -nan
-13.57 0.04 -nan
-13.72 0.04 -nan
-13.88 0.04 -nan
-14.03 0.04 -nan
-14.17 0.04 -nan
-14.32 0.04 -nan
-14.47 0.04 -nan
-14.62 0.04 -nan
-14.77 0.04 -nan
-14.92 0.04 nan
-15.07 0.04 -nan
-15.22 0.04 -nan
-15.38 0.04 -nan
-15.52 0.04 -nan
-15.67 0.04 -nan
-15.82 0.04 -nan
-15.97 0.04 -nan
-16.12 0.04 -nan
-16.27 0.04 -nan
-16.43 0.04 -nan
-16.57 0.04 -nan
-16.72 0.04 -nan
-16.88 0.04 -nan
-17.02 0.04 -nan
-17.18 0.04 -nan
-17.32 0.04 -nan
-17.47 0.04 -nan
-17.62 0.04 -nan
-17.77 0.04 -nan
-17.93 0.04 -nan
-18.07 0.04 -nan
-18.22 0.04 -nan
-18.38 0.04 -nan
-18.52 0.04 -nan
-18.68 0.04 -nan
-18.82 0.04 -nan
-18.97 0.04 -nan
-19.12 0.04 -nan
-19.27 0.04 -nan
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-6.22 0.20 -nan
-6.38 0.20 -nan
-6.52 0.20 -nan
-6.67 0.20 -nan
-6.83 0.20 -nan
-6.97 0.20 -nan
-7.12 0.20 -nan
-7.27 0.20 -nan
-7.42 0.20 -nan
-7.57 0.20 -nan
-7.72 0.20 -nan
-7.88 0.20 -nan
-8.03 0.20 -nan
-8.17 0.20 -nan
-8.32 0.20 -nan
-8.47 0.20 -nan
-8.62 0.20 -nan
-8.78 0.20 -nan
-8.92 0.20 -nan
-9.07 0.20 -nan
-9.22 0.20 -nan
-9.38 0.20 -nan
-9.53 0.20 -nan
-9.67 0.20 -nan
-9.82 0.20 -nan
-9.97 0.20 -nan
-10.12 0.20 -nan
-10.28 0.20 -nan
-10.42 0.20 -nan
-10.57 0.20 -nan
-10.72 0.20 -nan
-10.88 0.20 -nan
-11.03 0.20 -nan
-11.17 0.20 -nan
-11.32 0.20 -nan
-11.47 0.20 -nan
-11.62 0.20 -nan
-11.78 0.20 -nan
-11.92 0.20 -nan
-12.07 0.20 -nan
-12.22 0.20 -nan
-12.38 0.20 -nan
-12.53 0.20 -nan
-12.67 0.20 -nan
-12.82 0.20 -nan
-12.97 0.20 -nan
-13.12 0.20 -nan
-13.28 0.20 -nan
-13.42 0.20 -nan
-13.57 0.20 -nan
-13.72 0.20 -nan
-13.88 0.20 -nan
-14.03 0.20 -nan
-14.17 0.20 -nan
-14.32 0.20 -nan
-14.47 0.20 -nan
-14.62 0.20 -nan
-14.77 0.20 -nan
-14.92 0.20 nan
-15.07 0.20 -nan
-15.22 0.20 -nan
-15.38 0.20 -nan
-15.52 0.20 -nan
-15.67 0.20 -nan
-15.82 0.20 -nan
-15.97 0.20 -nan
-16.12 0.20 -nan
-16.27 0.20 -nan
-16.43 0.20 -nan
-16.57 0.20 -nan
-16.72 0.20 -nan
-16.88 0.20 -nan
-17.02 0.20 -nan
-17.18 0.20 -nan
-17.32 0.20 -nan
-17.47 0.20 -nan
-17.62 0.20 -nan
-17.77 0.20 -nan
-17.93 0.20 -nan
-18.07 0.20 -nan
-18.22 0.20 -nan
-18.38 0.20 -nan
-18.52 0.20 -nan
-18.68 0.20 -nan
-18.82 0.20 -nan
-18.97 0.202 0.20 0.000000
+0.07 0.20 0.000000
+0.22 0.20 0.000000
+0.38 0.20 0.000000
+0.53 0.20 0.000000
+0.67 0.20 0.000000
+0.82 0.20 0.000000
+0.97 0.20 0.000000
+1.12 0.20 0.000000
+1.27 0.20 0.000000
+1.43 0.20 0.000000
+1.57 0.20 0.000000
+1.72 0.20 0.000000
+1.88 0.20 0.000000
+2.02 0.20 0.000000
+2.17 0.20 0.000000
+2.32 0.20 0.000000
+2.48 0.20 0.000000
+2.62 0.20 0.000000
+2.77 0.20 0.000000
+2.92 0.20 0.000000
 3.07 0.20 0.000000
 3.23 0.20 0.000000
 3.38 0.20 0.000000
--- a/BasicSolver/2D-seq/Makefile
+++ b/BasicSolver/2D-seq/Makefile
@@ -39,7 +39,7 @@ $(BUILD_DIR)/%.s:  %.c

 .PHONY: clean distclean tags info asm format

-clean: viz
+clean: vis
 	$(info ===>  CLEAN)
 	@rm -rf $(BUILD_DIR)
 	@rm -f tags
@@ -48,7 +48,7 @@ distclean: clean
 	$(info ===>  DIST CLEAN)
 	@rm -f $(TARGET)

-viz:
+vis:
 	$(info ===>  REMOVING VIZUALISATION FILES)	
 	@rm -f vtk_files/particle*.vtk
 	@rm -f vis_files/particle*.dat
--- a/BasicSolver/2D-seq/backstep.par
+++ b/BasicSolver/2D-seq/backstep.par
@@ -15,7 +15,7 @@ bcRight    3			#
 gx    0.0      # Body forces (e.g. gravity)
 gy    0.0      #

-re    16500.0	   # Reynolds number
+re    36500.0	   # Reynolds number

 u_init    1.0      # initial value for velocity in x-direction
 v_init    0.0      # initial value for velocity in y-direction
@@ -48,10 +48,10 @@ gamma    0.9       # upwind differencing factor gamma
 # Particle Tracing Data:
 # -----------------------

-numberOfParticles   60
-startTime           100.0
-injectTimePeriod    0.5
-writeTimePeriod     0.2
+numberOfParticles   200
+startTime           0
+injectTimePeriod    1.0
+writeTimePeriod     0.5

 x1                  0.0
 y1                  0.5
--- a/BasicSolver/2D-seq/pressure.dat
+++ b/BasicSolver/2D-seq/pressure.dat
--- a/BasicSolver/2D-seq/src/solver.c
+++ b/BasicSolver/2D-seq/src/solver.c
@@ -25,8 +25,7 @@

 static double distance(double i, double j, double iCenter, double jCenter)
 {
-    return sqrt(pow(iCenter - i, 2)
-                + pow(jCenter - j, 2) * 1.0);
+    return sqrt(pow(iCenter - i, 2) + pow(jCenter - j, 2) * 1.0);
 }

 void print(Solver* solver, double* grid)
@@ -106,7 +105,6 @@ void initSolver(Solver* solver, Parameter* params)
    solver->gamma    = params->gamma;
    solver->rho      = params->rho;

-
    int imax    = solver->imax;
    int jmax    = solver->jmax;
    size_t size = (imax + 2) * (jmax + 2) * sizeof(double);
@@ -134,75 +132,86 @@ void initSolver(Solver* solver, Parameter* params)
    solver->dtBound  = 0.5 * solver->re * 1.0 / invSqrSum;

    double xCenter = 0, yCenter = 0, radius = 0;
-    double x1=0, x2=0, y1=0, y2=0;
+    double x1 = 0, x2 = 0, y1 = 0, y2 = 0;

    int* s = solver->s;

+    switch (params->shape) {
+    case NOSHAPE:
+        break;
+    case RECT:
+        x1 = params->xCenter - params->xRectLength / 2;
+        x2 = params->xCenter + params->xRectLength / 2;
+        y1 = params->yCenter - params->yRectLength / 2;
+        y2 = params->yCenter + params->yRectLength / 2;

-    switch(params->shape)
-    {
-        case NOSHAPE:
-            break;
-        case RECT:
-            x1 = params->xCenter - params->xRectLength/2;
-            x2 = params->xCenter + params->xRectLength/2;
-            y1 = params->yCenter - params->yRectLength/2;
-            y2 = params->yCenter + params->yRectLength/2;
-
-            for (int j = 1; j < jmax + 1; j++) 
-            {
-                for (int i = 1; i < imax + 1; i++) 
-                {
-                    if((x1 <= (i*dx)) && ((i*dx) <= x2) && (y1 <= (j*dy)) && ((j*dy) <= y2))
-                    {
-                        S(i, j) = LOCAL;
-                    }
+        for (int j = 1; j < jmax + 1; j++) {
+            for (int i = 1; i < imax + 1; i++) {
+                if ((x1 <= (i * dx)) && ((i * dx) <= x2) && (y1 <= (j * dy)) &&
+                    ((j * dy) <= y2)) {
+                    S(i, j) = LOCAL;
                }
            }
+        }

-            break;
-        case CIRCLE:
-            xCenter = params->xCenter;
-            yCenter = params->yCenter;
-            radius  = params->circleRadius;
+        break;
+    case CIRCLE:
+        xCenter = params->xCenter;
+        yCenter = params->yCenter;
+        radius  = params->circleRadius;

-            for (int j = 1; j < jmax + 1; j++) 
-            {
-                for (int i = 1; i < imax + 1; i++) 
-                {
-                    if(distance((i*dx), (j*dy), xCenter, yCenter) <= radius)
-                    {
-                        S(i, j) = LOCAL;
-                    }
+        for (int j = 1; j < jmax + 1; j++) {
+            for (int i = 1; i < imax + 1; i++) {
+                if (distance((i * dx), (j * dy), xCenter, yCenter) <= radius) {
+                    S(i, j) = LOCAL;
                }
            }
+        }

-            break;
-        default:
-            break;
+        break;
+    default:
+        break;
    }

-    for (int j = 1; j < jmax + 1; j++) 
-    {
-        for (int i = 1; i < imax + 1; i++) 
-        {
-            // if( S(i+1,j+1) == NONE && S(i+1,j) == NONE && S(i,j+1) == NONE && S(i-1,j-1) == LOCAL && S(i,j) == LOCAL ) S(i,j) = BOTTOMRIGHT;
-            // else if( S(i-1,j+1) == NONE && S(i-1,j) == NONE && S(i,j+1) == NONE && S(i+1,j-1) == LOCAL && S(i,j) == LOCAL ) S(i,j) = BOTTOMLEFT;
-            // else if( S(i+1,j-1) == NONE && S(i,j-1) == NONE && S(i+1,j) == NONE && S(i-1,j+1) == LOCAL && S(i,j) == LOCAL ) S(i,j) = TOPRIGHT;
-            // else if( S(i-1,j-1) == NONE && S(i,j-1) == NONE && S(i-1,j) == NONE && S(i+1,j+1) == LOCAL && S(i,j) == LOCAL ) S(i,j) = TOPLEFT;
-            // else if( S(i+1,j) == NONE && S(i-1,j) == LOCAL && S(i,j) == LOCAL ) S(i,j) = RIGHT;
-            // else if( S(i,j+1) == NONE && S(i,j-1) == LOCAL && S(i,j) == LOCAL ) S(i,j) = BOTTOM;
-            // else if( S(i-1,j) == NONE && S(i+1,j) == LOCAL && S(i,j) == LOCAL ) S(i,j) = LEFT;
-            // else if( S(i,j-1) == NONE && S(i,j+1) == LOCAL && S(i,j) == LOCAL ) S(i,j) = TOP;
+    for (int j = 1; j < jmax + 1; j++) {
+        for (int i = 1; i < imax + 1; i++) {
+            // if( S(i+1,j+1) == NONE && S(i+1,j) == NONE && S(i,j+1) == NONE &&
+            // S(i-1,j-1) == LOCAL && S(i,j) == LOCAL ) S(i,j) = BOTTOMRIGHT; else if(
+            // S(i-1,j+1) == NONE && S(i-1,j) == NONE && S(i,j+1) == NONE && S(i+1,j-1) ==
+            // LOCAL && S(i,j) == LOCAL ) S(i,j) = BOTTOMLEFT; else if( S(i+1,j-1) == NONE
+            // && S(i,j-1) == NONE && S(i+1,j) == NONE && S(i-1,j+1) == LOCAL && S(i,j) ==
+            // LOCAL ) S(i,j) = TOPRIGHT; else if( S(i-1,j-1) == NONE && S(i,j-1) == NONE
+            // && S(i-1,j) == NONE && S(i+1,j+1) == LOCAL && S(i,j) == LOCAL ) S(i,j) =
+            // TOPLEFT; else if( S(i+1,j) == NONE && S(i-1,j) == LOCAL && S(i,j) == LOCAL
+            // ) S(i,j) = RIGHT; else if( S(i,j+1) == NONE && S(i,j-1) == LOCAL && S(i,j)
+            // == LOCAL ) S(i,j) = BOTTOM; else if( S(i-1,j) == NONE && S(i+1,j) == LOCAL
+            // && S(i,j) == LOCAL ) S(i,j) = LEFT; else if( S(i,j-1) == NONE && S(i,j+1)
+            // == LOCAL && S(i,j) == LOCAL ) S(i,j) = TOP;

-            if( S(i,j-1) == NONE && S(i,j+1) == LOCAL && S(i,j) == LOCAL ) S(i,j) = BOTTOM; //TOP
-            if( S(i-1,j) == NONE && S(i+1,j) == LOCAL && S(i,j) == LOCAL ) S(i,j) = LEFT; //LEFT
-            if( S(i+1,j) == NONE && S(i-1,j) == LOCAL && S(i,j) == LOCAL ) S(i,j) = RIGHT; //RIGHT
-            if( S(i,j+1) == NONE && S(i,j-1) == LOCAL && S(i,j) == LOCAL ) S(i,j) = TOP; //BOTTOM
-            if( S(i-1,j-1) == NONE && S(i,j-1) == NONE && S(i-1,j) == NONE && S(i+1,j+1) == LOCAL && (S(i,j) == LOCAL || S(i,j) == LEFT || S(i,j) == BOTTOM ) ) S(i,j) = BOTTOMLEFT; //TOPLEFT
-            if( S(i+1,j-1) == NONE && S(i,j-1) == NONE && S(i+1,j) == NONE && S(i-1,j+1) == LOCAL && (S(i,j) == LOCAL || S(i,j) == RIGHT || S(i,j) == BOTTOM ) ) S(i,j) = BOTTOMRIGHT; //TOPRIGHT
-            if( S(i-1,j+1) == NONE && S(i-1,j) == NONE && S(i,j+1) == NONE && S(i+1,j-1) == LOCAL && (S(i,j) == LOCAL || S(i,j) == LEFT || S(i,j) == TOP )) S(i,j) = TOPLEFT; //BOTTOMLEFT
-            if( S(i+1,j+1) == NONE && S(i+1,j) == NONE && S(i,j+1) == NONE && S(i-1,j-1) == LOCAL && (S(i,j) == LOCAL || S(i,j) == RIGHT || S(i,j) == TOP ) ) S(i,j) = TOPRIGHT; //BOTTOMRIGHT
+            if (S(i, j - 1) == NONE && S(i, j + 1) == LOCAL && S(i, j) == LOCAL)
+                S(i, j) = BOTTOM; // TOP
+            if (S(i - 1, j) == NONE && S(i + 1, j) == LOCAL && S(i, j) == LOCAL)
+                S(i, j) = LEFT; // LEFT
+            if (S(i + 1, j) == NONE && S(i - 1, j) == LOCAL && S(i, j) == LOCAL)
+                S(i, j) = RIGHT; // RIGHT
+            if (S(i, j + 1) == NONE && S(i, j - 1) == LOCAL && S(i, j) == LOCAL)
+                S(i, j) = TOP; // BOTTOM
+            if (S(i - 1, j - 1) == NONE && S(i, j - 1) == NONE && S(i - 1, j) == NONE &&
+                S(i + 1, j + 1) == LOCAL &&
+                (S(i, j) == LOCAL || S(i, j) == LEFT || S(i, j) == BOTTOM))
+                S(i, j) = BOTTOMLEFT; // TOPLEFT
+            if (S(i + 1, j - 1) == NONE && S(i, j - 1) == NONE && S(i + 1, j) == NONE &&
+                S(i - 1, j + 1) == LOCAL &&
+                (S(i, j) == LOCAL || S(i, j) == RIGHT || S(i, j) == BOTTOM))
+                S(i, j) = BOTTOMRIGHT; // TOPRIGHT
+            if (S(i - 1, j + 1) == NONE && S(i - 1, j) == NONE && S(i, j + 1) == NONE &&
+                S(i + 1, j - 1) == LOCAL &&
+                (S(i, j) == LOCAL || S(i, j) == LEFT || S(i, j) == TOP))
+                S(i, j) = TOPLEFT; // BOTTOMLEFT
+            if (S(i + 1, j + 1) == NONE && S(i + 1, j) == NONE && S(i, j + 1) == NONE &&
+                S(i - 1, j - 1) == LOCAL &&
+                (S(i, j) == LOCAL || S(i, j) == RIGHT || S(i, j) == TOP))
+                S(i, j) = TOPRIGHT; // BOTTOMRIGHT
        }
    }

@@ -223,12 +232,11 @@ void computeRHS(Solver* solver)
    double* g   = solver->g;
    int* s      = solver->s;

-    for (int j = 1; j < jmax + 1; j++) 
-    {
-        for (int i = 1; i < imax + 1; i++) 
-        {
+    for (int j = 1; j < jmax + 1; j++) {
+        for (int i = 1; i < imax + 1; i++) {
            // if(S(i,j) == NONE)
-            RHS(i, j) = idt * ((F(i, j) - F(i - 1, j)) * idx + (G(i, j) - G(i, j - 1)) * idy);
+            RHS(i, j) = idt *
+                        ((F(i, j) - F(i - 1, j)) * idx + (G(i, j) - G(i, j - 1)) * idy);
        }
    }
 }
@@ -311,7 +319,6 @@ void solveRB(Solver* solver)
        res = 0.0;
        jsw = 1;

-
        for (int i = 1; i < imax + 1; i++) {
            P(i, 0)        = P(i, 1);
            P(i, jmax + 1) = P(i, jmax);
@@ -324,23 +331,20 @@ void solveRB(Solver* solver)

        // setObjectPBoundaryCondition(solver);

-        for (pass = 0; pass < 2; pass++) 
-        {
+        for (pass = 0; pass < 2; pass++) {
            isw = jsw;

-            for (int j = 1; j < jmax + 1; j++) 
-            {
-                for (int i = isw; i < imax + 1; i += 2) 
-                {
+            for (int j = 1; j < jmax + 1; j++) {
+                for (int i = isw; i < imax + 1; i += 2) {
                    // if(S(i,j) == NONE)
                    // {
-                        double r = RHS(i, j) -
-                                ((P(i + 1, j) - 2.0 * P(i, j) + P(i - 1, j)) * idx2 +
-                                    (P(i, j + 1) - 2.0 * P(i, j) + P(i, j - 1)) * idy2);
+                    double r = RHS(i, j) -
+                               ((P(i + 1, j) - 2.0 * P(i, j) + P(i - 1, j)) * idx2 +
+                                   (P(i, j + 1) - 2.0 * P(i, j) + P(i, j - 1)) * idy2);

-                        P(i, j) -= (factor * r );
+                    P(i, j) -= (factor * r);

-                        res += (r * r);
+                    res += (r * r);
                    // }
                }
                isw = 3 - isw;
@@ -400,7 +404,7 @@ void solveRBA(Solver* solver)
                }
                isw = 3 - isw;
            }
-            jsw = 3 - jsw;
+            jsw   = 3 - jsw;
            omega = (it == 0 && pass == 0 ? 1.0 / (1.0 - 0.5 * rho * rho)
                                          : 1.0 / (1.0 - 0.25 * rho * rho * omega));
        }
@@ -589,8 +593,7 @@ void setSpecialBoundaryCondition(Solver* solver)
        for (int i = 1; i < imax; i++) {
            U(i, jmax + 1) = 2.0 - U(i, jmax);
        }
-    } 
-    else if (strcmp(solver->problem, "canal") == 0) {
+    } else if (strcmp(solver->problem, "canal") == 0) {
        double ylength = solver->ylength;
        double y;

@@ -598,18 +601,12 @@ void setSpecialBoundaryCondition(Solver* solver)
            y       = mDy * (j - 0.5);
            U(0, j) = y * (ylength - y) * 4.0 / (ylength * ylength);
        }
-    }
-    else if (strcmp(solver->problem, "backstep") == 0) 
-    {
-        for (int j = 1; j < jmax + 1; j++) 
-        {
-            if(S(0,j) == NONE) U(0, j) = 1.0;
+    } else if (strcmp(solver->problem, "backstep") == 0) {
+        for (int j = 1; j < jmax + 1; j++) {
+            if (S(0, j) == NONE) U(0, j) = 1.0;
        }
-    }
-    else if (strcmp(solver->problem, "karman") == 0) 
-    {
-        for (int j = 1; j < jmax + 1; j++) 
-        {
+    } else if (strcmp(solver->problem, "karman") == 0) {
+        for (int j = 1; j < jmax + 1; j++) {
            U(0, j) = 1.0;
        }
    }
@@ -617,62 +614,59 @@ void setSpecialBoundaryCondition(Solver* solver)

 void setObjectBoundaryCondition(Solver* solver)
 {
-    int imax   = solver->imax;
-    int jmax   = solver->jmax;
-    double* u  = solver->u;
-    double* v  = solver->v;
-    int* s     = solver->s;
+    int imax  = solver->imax;
+    int jmax  = solver->jmax;
+    double* u = solver->u;
+    double* v = solver->v;
+    int* s    = solver->s;

-    for (int j = 1; j < jmax + 1; j++) 
-    {
-        for (int i = 1; i < imax + 1; i++) 
-        {
-            switch(S(i,j))
-            {
-                case TOP:
-                    U(i,j)      = -U(i,j+1);
-                    U(i-1,j)    = -U(i-1,j+1);
-                    V(i,j)      = 0.0;
-                    break;
-                case BOTTOM:
-                    U(i,j)      = -U(i,j-1);
-                    U(i-1,j)    = -U(i-1,j-1);
-                    V(i,j)      = 0.0;
-                    break;
-                case LEFT:
-                    U(i-1,j)      = 0.0;
-                    V(i,j)      = -V(i-1,j);
-                    V(i,j-1)    = -V(i-1,j-1);
-                    break;
-                case RIGHT:
-                    U(i,j)      = 0.0;
-                    V(i,j)      = -V(i+1,j);
-                    V(i,j-1)    = -V(i+1,j-1);
-                    break;
-                case TOPLEFT:
-                    U(i,j)      = -U(i,j+1);
-                    U(i-1,j)    = 0.0;
-                    V(i,j)      = 0.0;
-                    V(i,j-1)    = -V(i-1,j-1);
-                    break;
-                case TOPRIGHT:
-                    U(i,j)      = 0.0;
-                    U(i-1,j)    = -U(i-1,j+1);
-                    V(i,j)      = 0.0;
-                    V(i,j-1)    = -V(i+1,j-1);
-                    break;
-                case BOTTOMLEFT:
-                    U(i,j)      = -U(i,j-1);
-                    U(i-1,j)    = 0.0;
-                    V(i,j)      = -V(i-1,j);
-                    V(i,j-1)    = 0.0;
-                    break;
-                case BOTTOMRIGHT:
-                    U(i,j)      = 0.0;
-                    U(i-1,j)    = -U(i-1,j-1);
-                    V(i,j)      = -V(i,j+1);
-                    V(i,j-1)    = 0.0;
-                    break;
+    for (int j = 1; j < jmax + 1; j++) {
+        for (int i = 1; i < imax + 1; i++) {
+            switch (S(i, j)) {
+            case TOP:
+                U(i, j)     = -U(i, j + 1);
+                U(i - 1, j) = -U(i - 1, j + 1);
+                V(i, j)     = 0.0;
+                break;
+            case BOTTOM:
+                U(i, j)     = -U(i, j - 1);
+                U(i - 1, j) = -U(i - 1, j - 1);
+                V(i, j)     = 0.0;
+                break;
+            case LEFT:
+                U(i - 1, j) = 0.0;
+                V(i, j)     = -V(i - 1, j);
+                V(i, j - 1) = -V(i - 1, j - 1);
+                break;
+            case RIGHT:
+                U(i, j)     = 0.0;
+                V(i, j)     = -V(i + 1, j);
+                V(i, j - 1) = -V(i + 1, j - 1);
+                break;
+            case TOPLEFT:
+                U(i, j)     = -U(i, j + 1);
+                U(i - 1, j) = 0.0;
+                V(i, j)     = 0.0;
+                V(i, j - 1) = -V(i - 1, j - 1);
+                break;
+            case TOPRIGHT:
+                U(i, j)     = 0.0;
+                U(i - 1, j) = -U(i - 1, j + 1);
+                V(i, j)     = 0.0;
+                V(i, j - 1) = -V(i + 1, j - 1);
+                break;
+            case BOTTOMLEFT:
+                U(i, j)     = -U(i, j - 1);
+                U(i - 1, j) = 0.0;
+                V(i, j)     = -V(i - 1, j);
+                V(i, j - 1) = 0.0;
+                break;
+            case BOTTOMRIGHT:
+                U(i, j)     = 0.0;
+                U(i - 1, j) = -U(i - 1, j - 1);
+                V(i, j)     = -V(i, j + 1);
+                V(i, j - 1) = 0.0;
+                break;
            }
        }
    }
@@ -680,45 +674,42 @@ void setObjectBoundaryCondition(Solver* solver)

 void setObjectPBoundaryCondition(Solver* solver)
 {
-    int imax      = solver->imax;
-    int jmax      = solver->jmax;
+    int imax = solver->imax;
+    int jmax = solver->jmax;

-    double* p     = solver->p;
-    int*    s     = solver->s;
+    double* p = solver->p;
+    int* s    = solver->s;

-    for (int j = 1; j < jmax + 1; j++) 
-    {
-        for (int i = 1; i < imax + 1; i++) 
-        {
-            switch (S(i,j))
-            {
-                case TOP:
-                    P(i,j)      = P(i,j+1);
-                    break;
-                case BOTTOM:
-                    P(i,j)      = P(i,j-1);
-                    break;
-                case LEFT:
-                    P(i,j)      = P(i-1,j);
-                    break;
-                case RIGHT:
-                    P(i,j)      = P(i,j+1);
-                    break;
-                case TOPLEFT:
-                    P(i,j)      = (P(i-1,j) + P(i,j+1))/2;
-                    break;
-                case TOPRIGHT:
-                    P(i,j)      = (P(i+1,j) + P(i,j+1))/2;
-                    break;
-                case BOTTOMLEFT:
-                    P(i,j)      = (P(i-1,j) + P(i,j-1))/2;
-                    break;
-                case BOTTOMRIGHT:
-                    P(i,j)      = (P(i+1,j) + P(i,j-1))/2;
-                    break;
+    for (int j = 1; j < jmax + 1; j++) {
+        for (int i = 1; i < imax + 1; i++) {
+            switch (S(i, j)) {
+            case TOP:
+                P(i, j) = P(i, j + 1);
+                break;
+            case BOTTOM:
+                P(i, j) = P(i, j - 1);
+                break;
+            case LEFT:
+                P(i, j) = P(i - 1, j);
+                break;
+            case RIGHT:
+                P(i, j) = P(i, j + 1);
+                break;
+            case TOPLEFT:
+                P(i, j) = (P(i - 1, j) + P(i, j + 1)) / 2;
+                break;
+            case TOPRIGHT:
+                P(i, j) = (P(i + 1, j) + P(i, j + 1)) / 2;
+                break;
+            case BOTTOMLEFT:
+                P(i, j) = (P(i - 1, j) + P(i, j - 1)) / 2;
+                break;
+            case BOTTOMRIGHT:
+                P(i, j) = (P(i + 1, j) + P(i, j - 1)) / 2;
+                break;

-                default:
-                    break;
+            default:
+                break;
            }
        }
    }
@@ -743,12 +734,9 @@ void computeFG(Solver* solver)
    double du2dx, dv2dy, duvdx, duvdy;
    double du2dx2, du2dy2, dv2dx2, dv2dy2;

-    for (int j = 1; j < jmax + 1; j++) 
-    {
-        for (int i = 1; i < imax + 1; i++) 
-        {
-            if(S(i,j) == NONE) 
-            {
+    for (int j = 1; j < jmax + 1; j++) {
+        for (int i = 1; i < imax + 1; i++) {
+            if (S(i, j) == NONE) {
                du2dx = inverseDx * 0.25 *
                            ((U(i, j) + U(i + 1, j)) * (U(i, j) + U(i + 1, j)) -
                                (U(i, j) + U(i - 1, j)) * (U(i, j) + U(i - 1, j))) +
@@ -758,19 +746,24 @@ void computeFG(Solver* solver)

                duvdy = inverseDy * 0.25 *
                            ((V(i, j) + V(i + 1, j)) * (U(i, j) + U(i, j + 1)) -
-                                (V(i, j - 1) + V(i + 1, j - 1)) * (U(i, j) + U(i, j - 1))) +
+                                (V(i, j - 1) + V(i + 1, j - 1)) *
+                                    (U(i, j) + U(i, j - 1))) +
                        gamma * inverseDy * 0.25 *
                            (fabs(V(i, j) + V(i + 1, j)) * (U(i, j) - U(i, j + 1)) +
                                fabs(V(i, j - 1) + V(i + 1, j - 1)) *
                                    (U(i, j) - U(i, j - 1)));

-                du2dx2  = inverseDx * inverseDx * (U(i + 1, j) - 2.0 * U(i, j) + U(i - 1, j));
-                du2dy2  = inverseDy * inverseDy * (U(i, j + 1) - 2.0 * U(i, j) + U(i, j - 1));
-                F(i, j) = U(i, j) + dt * (inverseRe * (du2dx2 + du2dy2) - du2dx - duvdy + gx);
+                du2dx2 = inverseDx * inverseDx *
+                         (U(i + 1, j) - 2.0 * U(i, j) + U(i - 1, j));
+                du2dy2 = inverseDy * inverseDy *
+                         (U(i, j + 1) - 2.0 * U(i, j) + U(i, j - 1));
+                F(i, j) = U(i, j) +
+                          dt * (inverseRe * (du2dx2 + du2dy2) - du2dx - duvdy + gx);

                duvdx = inverseDx * 0.25 *
                            ((U(i, j) + U(i, j + 1)) * (V(i, j) + V(i + 1, j)) -
-                                (U(i - 1, j) + U(i - 1, j + 1)) * (V(i, j) + V(i - 1, j))) +
+                                (U(i - 1, j) + U(i - 1, j + 1)) *
+                                    (V(i, j) + V(i - 1, j))) +
                        gamma * inverseDx * 0.25 *
                            (fabs(U(i, j) + U(i, j + 1)) * (V(i, j) - V(i + 1, j)) +
                                fabs(U(i - 1, j) + U(i - 1, j + 1)) *
@@ -783,42 +776,42 @@ void computeFG(Solver* solver)
                            (fabs(V(i, j) + V(i, j + 1)) * (V(i, j) - V(i, j + 1)) +
                                fabs(V(i, j) + V(i, j - 1)) * (V(i, j) - V(i, j - 1)));

-                dv2dx2  = inverseDx * inverseDx * (V(i + 1, j) - 2.0 * V(i, j) + V(i - 1, j));
-                dv2dy2  = inverseDy * inverseDy * (V(i, j + 1) - 2.0 * V(i, j) + V(i, j - 1));
-                G(i, j) = V(i, j) + dt * (inverseRe * (dv2dx2 + dv2dy2) - duvdx - dv2dy + gy);
-            }
-            else
-            {
-                switch(S(i,j))
-                {
-                    case TOP:
-                        G(i,j)      = V(i,j);
-                        break;
-                    case BOTTOM:
-                        G(i,j-1)    = V(i,j-1);
-                        break;
-                    case LEFT:
-                        F(i-1,j)    = U(i-1,j);
-                        break;
-                    case RIGHT:
-                        F(i,j)      = U(i,j);
-                        break;
-                    case TOPLEFT:
-                        F(i-1,j)    = U(i-1,j);
-                        G(i,j)      = V(i,j);
-                        break;
-                    case TOPRIGHT:
-                        F(i,j)      = U(i,j);
-                        G(i,j)      = V(i,j);
-                        break;
-                    case BOTTOMLEFT:
-                        F(i-1,j)    = U(i-1,j);
-                        G(i,j-1)    = V(i,j-1);
-                        break;
-                    case BOTTOMRIGHT:
-                        F(i,j)      = U(i,j);
-                        G(i,j-1)    = V(i,j-1);
-                        break;
+                dv2dx2 = inverseDx * inverseDx *
+                         (V(i + 1, j) - 2.0 * V(i, j) + V(i - 1, j));
+                dv2dy2 = inverseDy * inverseDy *
+                         (V(i, j + 1) - 2.0 * V(i, j) + V(i, j - 1));
+                G(i, j) = V(i, j) +
+                          dt * (inverseRe * (dv2dx2 + dv2dy2) - duvdx - dv2dy + gy);
+            } else {
+                switch (S(i, j)) {
+                case TOP:
+                    G(i, j) = V(i, j);
+                    break;
+                case BOTTOM:
+                    G(i, j - 1) = V(i, j - 1);
+                    break;
+                case LEFT:
+                    F(i - 1, j) = U(i - 1, j);
+                    break;
+                case RIGHT:
+                    F(i, j) = U(i, j);
+                    break;
+                case TOPLEFT:
+                    F(i - 1, j) = U(i - 1, j);
+                    G(i, j)     = V(i, j);
+                    break;
+                case TOPRIGHT:
+                    F(i, j) = U(i, j);
+                    G(i, j) = V(i, j);
+                    break;
+                case BOTTOMLEFT:
+                    F(i - 1, j) = U(i - 1, j);
+                    G(i, j - 1) = V(i, j - 1);
+                    break;
+                case BOTTOMRIGHT:
+                    F(i, j)     = U(i, j);
+                    G(i, j - 1) = V(i, j - 1);
+                    break;
                }
            }
        }
@@ -852,10 +845,8 @@ void adaptUV(Solver* solver)

    double val = 0;

-    for (int j = 1; j < jmax + 1; j++) 
-    {
-        for (int i = 1; i < imax + 1; i++) 
-        {
+    for (int j = 1; j < jmax + 1; j++) {
+        for (int i = 1; i < imax + 1; i++) {
            U(i, j) = F(i, j) - (P(i + 1, j) - P(i, j)) * factorX;
            V(i, j) = G(i, j) - (P(i, j + 1) - P(i, j)) * factorY;
        }
--- a/BasicSolver/2D-seq/vector.plot
+++ b/BasicSolver/2D-seq/vector.plot
@@ -1,7 +1,7 @@
 set terminal png size 3600,768 enhanced font ,28
 set output 'velocity.png'
-set xrange[0:30]
-set yrange[0:4]
+set xrange[0:7]
+set yrange[0:1.5]
 set size ratio -1
 set datafile separator whitespace

--- a/BasicSolver/2D-seq/velocity.dat
+++ b/BasicSolver/2D-seq/velocity.dat
--- a/BasicSolver/2D-seq/velocity.png
+++ b/BasicSolver/2D-seq/velocity.png
--- a/BasicSolver/2D-seq/vis_files/backstep_animate.plot
+++ b/BasicSolver/2D-seq/vis_files/backstep_animate.plot
@@ -1,8 +1,10 @@
 unset border; unset tics; unset key;
-set term gif animate delay 50
+set term gif animate delay 10
 set output "trace.gif"
 set xrange [0:7]
 set yrange [0:1.5]
+set size ratio -1
+
 set object 1 rect from 0.0,0.0 to 1.0,0.5 lw 5


--- a/BasicSolver/2D-seq/vis_files/trace.gif
+++ b/BasicSolver/2D-seq/vis_files/trace.gif