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solver.h
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#define MAX(x, y) (((x) > (y)) ? (x) : (y))
#define MIN(x, y) (((x) < (y)) ? (x) : (y))
void solver(int Nx, int Ny)
{
FILE *vel_u, *vel_v, *vel_p, *itr, *vel_gridx, *vel_gridy;
vel_u = fopen("vel_u.dat","w");
vel_v = fopen("vel_v.dat","w");
vel_p = fopen("pressure.dat","w");
itr = fopen("Iteration.dat","w");
vel_gridx = fopen("xgrid.dat","w");
vel_gridy = fopen("ygrid.dat","w");
double a,b,c;
int m,n,o,ans=0;
double error_dp=1;
int counter = 0,iteration=0;
double error_p=1,\
error_u=1,\
error_v=1;
double total_error_p = 1,\
total_error_u = 1,\
total_error_v = 1;
//for(int m =0;m<5;m++)
while (total_error_v > epsilon && total_error_v > epsilon)
{
//printf("hello total error %f\n",total_error_u);
//velocity and pressure field updated
for(int i=0;i<=Ny;i++)
{
for(int j=0;j<=Nx;j++)
{
P_old[i][j] = Q_1[i][j];
U_old[i][j] = Q_2[i][j];
V_old[i][j] = Q_3[i][j];
}
}
error_p=1;
error_u=1;
error_v=1;
//printf("Iteration = %d\t%0.12f\t%0.12f\n",iteration,total_error_u,total_error_v);
m = 0,n=0,o=0;
while (error_p > epsilon && error_u > epsilon && error_v > epsilon)
{
//////////////////////////////////////////////////////
//Co-varient and contra-varient velocities calculated
for(int i=0;i<=Ny;i++)
{
for(int j=0;j<=Nx;j++)
{
U[i][j] = Q_2[i][j] * zeta_x[i][j];
V[i][j] = Q_3[i][j] * eta_y[i][j];
}
}
//print2d(U, Nx, Ny);
//Calculating Spectral Radius
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
rho_1[i][j] = (fabs(U[i][j]) + sqrt((U[i][j]*U[i][j]) + g11[i][j]))/J[i][j];
rho_2[i][j] = (fabs(V[i][j]) + sqrt((V[i][j]*V[i][j]) + g22[i][j]))/J[i][j];
}
}
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
rhox[i][j] = 0.5*(rho_1[i][j+1] + rho_1[i][j]);
rhoy[i][j] = 0.5*(rho_2[i+1][j] + rho_2[i][j]);
}
}
for(int i=2;i<Ny-1;i++)
{
for(int j=2;j<Nx-1;j++)
{
Q_half_x_1[i][j] = Q_1[i][j+2] - 3*Q_1[i][j+1] + 3*Q_1[i][j] - Q_1[i][j-1];
Q_half_x_2[i][j] = Q_2[i][j+2] - 3*Q_2[i][j+1] + 3*Q_2[i][j] - Q_2[i][j-1];
Q_half_x_3[i][j] = Q_3[i][j+2] - 3*Q_3[i][j+1] + 3*Q_3[i][j] - Q_3[i][j-1];
Q_half_y_1[i][j] = Q_1[i+2][j] - 3*Q_1[i+1][j] + 3*Q_1[i][j] - Q_1[i-1][j];
Q_half_y_2[i][j] = Q_2[i+2][j] - 3*Q_2[i+1][j] + 3*Q_2[i][j] - Q_2[i-1][j];
Q_half_y_3[i][j] = Q_3[i+2][j] - 3*Q_3[i+1][j] + 3*Q_3[i][j] - Q_3[i-1][j];
}
}
for(int i=2;i<Ny-1;i++)
{
for(int j=2;j<Nx-1;j++)
{
Diss_x_1[i][j] = epsi*((rhox[i][j]*Q_half_x_1[i][j]) - (rhox[i][j-1]*Q_half_x_1[i][j-1]));
Diss_x_2[i][j] = epsi*((rhox[i][j]*Q_half_x_2[i][j]) - (rhox[i][j-1]*Q_half_x_2[i][j-1]));
Diss_x_3[i][j] = epsi*((rhox[i][j]*Q_half_x_3[i][j]) - (rhox[i][j-1]*Q_half_x_3[i][j-1]));
Diss_y_1[i][j] = epsi*((rhoy[i][j]*Q_half_y_1[i][j]) - (rhoy[i-1][j]*Q_half_y_1[i-1][j]));
Diss_y_2[i][j] = epsi*((rhoy[i][j]*Q_half_y_2[i][j]) - (rhoy[i-1][j]*Q_half_y_2[i-1][j]));
Diss_y_3[i][j] = epsi*((rhoy[i][j]*Q_half_y_3[i][j]) - (rhoy[i-1][j]*Q_half_y_3[i-1][j]));
}
}
for(int i=0;i<=Ny;i++)
{
for(int j=0;j<=Nx;j++)
{
E_1_compute_x_1[i][j] = U[i][j]/J[i][j];
E_1_compute_x_2[i][j] = (Q_2[i][j]*U[i][j])/J[i][j];
E_1_compute_x_3[i][j] = (Q_3[i][j]*U[i][j])/J[i][j];
E_2_compute_y_1[i][j] = V[i][j]/J[i][j];
E_2_compute_y_2[i][j] = (Q_2[i][j]*V[i][j])/J[i][j];
E_2_compute_y_3[i][j] = (Q_3[i][j]*V[i][j])/J[i][j];
}
}
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
DE_1_compute_x_1[i][j] = 0.5*(E_1_compute_x_1[i][j+1] - E_1_compute_x_1[i][j-1]) + Diss_x_1[i][j];
DE_1_compute_x_2[i][j] = 0.5*(E_1_compute_x_2[i][j+1] - E_1_compute_x_2[i][j-1]) + Diss_x_2[i][j];
DE_1_compute_x_3[i][j] = 0.5*(E_1_compute_x_3[i][j+1] - E_1_compute_x_3[i][j-1]) + Diss_x_3[i][j];
DE_2_compute_y_1[i][j] = 0.5*(E_2_compute_y_1[i+1][j] - E_2_compute_y_1[i-1][j]) + Diss_y_1[i][j];
DE_2_compute_y_2[i][j] = 0.5*(E_2_compute_y_2[i+1][j] - E_2_compute_y_2[i-1][j]) + Diss_y_2[i][j];
DE_2_compute_y_3[i][j] = 0.5*(E_2_compute_y_3[i+1][j] - E_2_compute_y_3[i-1][j]) + Diss_y_3[i][j];
}
}
//print2d(DE_1_compute_x_1,Nx,Ny);
for(int i=0;i<Ny;i++)
{
for(int j=0;j<Nx;j++)
{
J_half_x[i][j] = 0.5*(J[i][j+1] + J[i][j]);
J_half_y[i][j] = 0.5*(J[i+1][j] + J[i][j]);
zeta_x_half[i][j] = pow(0.5*(zeta_x[i][j+1] + zeta_x[i][j]),2);
eta_y_half[i][j] = pow(0.5*(eta_y[i+1][j] + eta_y[i][j]),2);
u_11[i][j] = (Q_2[i][j+1] - Q_2[i][j]);
u_12[i][j] = (Q_3[i][j+1] - Q_3[i][j]);
Ev_1_compute_x_1[i][j] = 0;
Ev_1_compute_x_2[i][j] = (zeta_x_half[i][j]*u_11[i][j])/J_half_x[i][j];
Ev_1_compute_x_3[i][j] = (zeta_x_half[i][j]*u_12[i][j])/J_half_x[i][j];
u_21[i][j] = Q_2[i+1][j] - Q_2[i][j];
u_22[i][j] = Q_3[i+1][j] - Q_3[i][j];
Ev_2_compute_y_1[i][j] = 0;
Ev_2_compute_y_2[i][j] = eta_y_half[i][j]*u_21[i][j]/J_half_y[i][j];
Ev_2_compute_y_3[i][j] = eta_y_half[i][j]*u_22[i][j]/J_half_y[i][j];
}
}
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
DEv_1_compute_x_2[i][j] = (Ev_1_compute_x_2[i][j] - Ev_1_compute_x_2[i][j-1])/Re;
DEv_2_compute_y_2[i][j] = (Ev_2_compute_y_2[i][j] - Ev_2_compute_y_2[i-1][j])/Re;
DEv_1_compute_x_3[i][j] = (Ev_1_compute_x_3[i][j] - Ev_1_compute_x_3[i][j-1])/Re;
DEv_2_compute_y_3[i][j] = (Ev_2_compute_y_3[i][j] - Ev_2_compute_y_3[i-1][j])/Re;
}
}
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
grad_P_x[i][j] = J[i][j]*0.5*((Q_1[i][j+1]*zeta_x[i][j+1]/J[i][j+1])\
- (Q_1[i][j-1]*zeta_x[i][j-1]/J[i][j-1]));
grad_P_y[i][j] = J[i][j]*0.5*((Q_1[i+1][j]*eta_y[i+1][j]/J[i+1][j])\
- (Q_1[i-1][j]*eta_y[i-1][j]/J[i-1][j]));
}
}
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
RHS_compute_1[i][j] = J[i][j]*(-DE_1_compute_x_1[i][j] \
-DE_2_compute_y_1[i][j] \
+DEv_1_compute_x_1[i][j] \
+DEv_2_compute_y_1[i][j]);
RHS_compute_2[i][j] = J[i][j]*(-DE_1_compute_x_2[i][j]\
-DE_2_compute_y_2[i][j]\
+DEv_1_compute_x_2[i][j]\
+DEv_2_compute_y_2[i][j]);
RHS_compute_3[i][j] = J[i][j]*(-DE_1_compute_x_3[i][j]\
-DE_2_compute_y_3[i][j]\
+DEv_1_compute_x_3[i][j]\
+DEv_2_compute_y_3[i][j]);
}
}
//print2d(RHS_compute_3,Nx,Ny);
//////////////////////////////////////////////////////////////////
for(int i=0;i<=Ny;i++)
{
for(int j=0;j<=Nx;j++)
{
rho_1[i][j] = 0;
rho_2[i][j] = 0;
}
}
for(int i=0;i<=Ny;i++)
{
for(int j=0;j<=Nx;j++)
{
rho_1[i][j] = (fabs(U[i][j]) + sqrt(pow(U[i][j],2) + g11[i][j]))/J[i][j];
rho_2[i][j] = (fabs(V[i][j]) + sqrt(pow(V[i][j],2) + g22[i][j]))/J[i][j];
dtau_cfl[i][j] = cfl/(J[i][j]*MAX(rho_1[i][j],rho_2[i][j]));
dtau_VN[i][j] = Re*VN/(MAX(g11[i][j],g22[i][j]));
dtau[i][j] = MIN(dtau_cfl[i][j], dtau_VN[i][j]);
//printf("%f\t%f\n",MIN(dtau_cfl[i][j], dtau_VN[i][j]),MAX(g11[i][j],g22[i][j]));
}
}
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
ustar[i][j] = Q_2[i][j] + dtau[i][j]*(RHS_compute_2[i][j] - grad_P_x[i][j]);
vstar[i][j] = Q_3[i][j] + dtau[i][j]*(RHS_compute_3[i][j] - grad_P_y[i][j]);
}
}
//Updating boundary conditions for ustar ?? make it an argument
/*for(int i=(Ny/2 + 1);i<=Ny;i++)
{
ustar[i][0] = Ub*(1-(pow(((y[i][0] - 1.5*h)/(0.5*h)),2)));
ustar[i][Nx] = ustar[i][Nx-1];
}
for(int i=0;i<=Ny;i++)
{
ustar[i][Nx] = ustar[i][Nx-1];
}
//print2d(ustar,Nx,Ny);*/
backward_boundary(Nx,Ny);
//Calculating Divergence of ustar
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
diver[i][j] = 0.5*J[i][j]*((ustar[i][j+1]*zeta_x[i][j+1]/J[i][j+1])\
- (ustar[i][j-1]*zeta_x[i][j-1]/J[i][j-1])\
+ (vstar[i+1][j]* eta_y[i+1][j]/J[i+1][j])\
- (vstar[i-1][j]* eta_y[i-1][j]/J[i-1][j]));
}
}
//print2d(diver,Nx,Ny);
for(int i=0;i<=Ny;i++)
{
for(int j=0;j<=Nx;j++)
{
dp[i][j] = 0;
dp1[i][j] = 0;
}
}
counter = 0;
error_dp =1;
while (error_dp > epsilon/10)
{
//error_dp = 0;
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
dp[i][j] = dp1[i][j];
}
}
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
a = J[i][j]*( (g11_half[i][j]*dp[i][j+1]/J_half_x[i][j])\
+ (g11_half[i][j-1]*dp[i][j-1]/J_half_x[i][j-1])\
+ (g22_half[i][j]*dp[i+1][j]/J_half_y[i][j])\
+ (g22_half[i-1][j]*dp[i-1][j]/J_half_y[i-1][j]));
b = -J[i][j]*( (g11_half[i][j]/J_half_x[i][j])\
+ (g11_half[i][j-1]/J_half_x[i][j-1])\
+ (g22_half[i][j]/J_half_y[i][j])\
+ (g22_half[i-1][j]/J_half_y[i-1][j]));
dp1[i][j] = ((diver[i][j]/dtau[i][j]) - a)/b;
error_dp = error_dp + pow((dp1[i][j] - dp[i][j]),2);
//printf("error_dp = %0.10f\n",error_dp);
error_dp = sqrt(error_dp)/(Nx*Ny);
}
}
counter = counter +1;
//printf("\nThe error from SIMPLE is %0.15f in iteration = %d\n",error_dp,counter);
}
/////////////////////////////////////////////////////////////////////////////////end of while loop
//Calculating Gradient of delta Pressure
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
dp[i][j] = dp1[i][j];
grad_dp_x[i][j] = 0.5*J[i][j]*((dp[i][j+1]*zeta_x[i][j+1]/J[i][j+1]) - (dp[i][j-1]*zeta_x[i][j-1]/J[i][j-1]));
grad_dp_y[i][j] = 0.5*J[i][j]*((dp[i+1][j]*eta_y[i+1][j]/J[i+1][j]) - (dp[i-1][j]*eta_y[i-1][j]/J[i-1][j]));
}
}
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
Pressure_new[i][j] = Q_1[i][j] + dp[i][j];
u_new[i][j] = ustar[i][j] - dtau[i][j]*grad_dp_x[i][j];
v_new[i][j] = vstar[i][j] - dtau[i][j]*grad_dp_y[i][j];
}
}
//print2d(dp,Nx,Ny);
for(int i=0;i<=Ny;i++)
{
Pressure_new[i][0] = Pressure_new[i][1];
Pressure_new[i][Nx] = Pressure_new[i][Nx-1];
u_new[i][Nx] = u_new[i][Nx-1];
v_new[i][Nx] = v_new[i][Nx-1];
}
for(int j=0;j<=Nx;j++)
{
Pressure_new[0][j] = Pressure_new[1][j];
Pressure_new[Ny][j]= Pressure_new[Ny-1][j];
}
error_p = 0;
error_u = 0;
error_v = 0;
//print2d(Pressure_new,Nx,Ny);
for(int i=1;i<Ny;i++)
{
for(int j=1;j<Nx;j++)
{
error_p = error_p + pow(((Pressure_new[i][j] - Q_1[i][j])),2);
error_u = error_u + pow(((u_new[i][j] - ustar[i][j])),2);
error_v = error_v + pow(((v_new[i][j] - vstar[i][j])),2);
}
}
error_p = sqrt(error_p)/(Nx*Ny);
error_u = sqrt(error_u)/(Nx*Ny);
error_v = sqrt(error_v)/(Nx*Ny);
for(int i=0;i<=Ny;i++)
{
for(int j=0;j<=Nx;j++)
{
Q_1[i][j] = Pressure_new[i][j];
Q_2[i][j] = u_new[i][j];
Q_3[i][j] = v_new[i][j];
Q_1[0][j] = Q_1[1][j];
Q_1[Ny][j] = Q_1[Ny-1][j];
Q_1[i][0] = Q_1[i][1];
Q_1[i][Nx] = Q_1[i][Nx-1];
}
}
ans = m+n+o;
}
////////////////////////////////////////////////////////////////////////////////////////////////////end of while loop
//printf("Error_p = %0.10f\tError_u = %0.10f\tError_v = %0.10f\n",error_p,error_u,error_v);
total_error_p = 0;
total_error_u = 0;
total_error_v = 0;
//printf("%d\t%0.12f\t%0.12f\n",iteration,total_error_u,total_error_v);
for(int i=0;i<=Ny;i++)
{
for(int j=0;j<=Nx;j++)
{
total_error_p = total_error_p + fabs((Q_1[i][j] - P_old[i][j]));
total_error_u = total_error_u + fabs((Q_2[i][j] - U_old[i][j]));
total_error_v = total_error_v + fabs((Q_3[i][j] - V_old[i][j]));
//printf("total error is %d\n",abs(Q_2[i][j] - U_old[i][j]));
}
}
//total_error_p = sqrt(total_error_p)/(Nx*Ny);
//total_error_u = sqrt(total_error_u)/(Nx*Ny);
//total_error_v = sqrt(total_error_v)/(Nx*Ny);
iteration = iteration + 1;
printf("%d\t%0.12f\t%0.12f\n",iteration,total_error_u,total_error_v);
fprintf(itr,"%d\t%0.12f\t%0.12f\n",iteration,total_error_u,total_error_v);
}
//print2d(U_old,Nx,Ny);
for(int i=0;i<=Ny;i++)
{
for(int j=0;j<=Nx;j++)
{
fprintf(vel_u,"%0.10f\t",Q_2[i][j]);
fprintf(vel_v,"%0.10f\t",Q_3[i][j]);
fprintf(vel_p,"%0.10f\t",Q_1[i][j]);
fprintf(vel_gridx,"%0.10f\t",x[i][j]);
fprintf(vel_gridy,"%0.10f\t",y[i][j]);
}
fprintf(vel_u,"\n");
fprintf(vel_v,"\n");
fprintf(vel_p,"\n");
fprintf(vel_gridx,"%\n");
fprintf(vel_gridy,"\n");
}
fclose(vel_u);
fclose(vel_v);
fclose(vel_p);
fclose(itr);
fclose(vel_gridx);
fclose(vel_gridy);
//////////////////////////////////////////////////////////////////////////////////////////////////////end of while loop
}