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3d_version_CD_2D_arrays.cpp
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#include<iostream>
#include<fstream>
#include<cmath>
#include<string.h>
#include<iterator>
#include<array>
using namespace std;
const double rey= 100.0; // length of container= 1unit, rho= 10^3 SI units, viscosity= 8.9x 10^-4
const double length= 1.0;// so that reynolds number is equal to 100 and peclet number less than two
const double dt= 0.005;// from peclet no. less than 1
const int N= 100;
const double rho= 1.0;
double tolerance=pow(10,-4);
const double NT=1000000;
double max_err=1.0;
// defining variables
double u_inf= 1.0;
double p[N*N][N],p_error[N*N][N]={0.0};
double u[N*N][N],u_n_1[N*N][N]={0.0};
double v[N*N][N],v_n_1[N*N][N]={0.0};
double w[N*N][N],w_n_1[N*N][N]={0.0};
double a(int ix, int iy, int n);
double a_w(int ix, int iy, int n);
double a_e(int ix, int iy, int n);
double a_s(int ix, int iy, int n);
double a_n(int ix, int iy, int n);
double a_b(int ix, int iy, int n);
double a_t(int ix, int iy, int n);
double p_e(int ix, int iy);
double p_s(int ix, int iy);
double p_n(int ix, int iy);
double p_w(int ix, int iy);
double p_t(int ix, int iy);
double p_b(int ix, int iy);
double boundary(int ix, int iy);
double dx= length/(N-1);
double viscosity= (rho*u_inf*length)/rey ;
const double D= viscosity/dx;
//under relaxation factors for u,v and p
const double ur_u=0.5;
const double ur_v=0.5;
const double ur_w=0.5;
const double ur_p=0.5;
void gs_vel(void);
void gs_p(void);
int main(){
// WRITING VALUES TO TOLERANCE FILE
ofstream fout15;
fout15.open("tolerance.dat");
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// SIMPLE algorithm
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
for(int it=NT;it>0;it--){
cout<<"Iteration number: "<<NT- it<<endl;
// copying values of velocities from previous iteration
std::copy(std::begin(u),std::end(u),std::begin(u_n_1));
std::copy(std::begin(v),std::end(v),std::begin(v_n_1));
std::copy(std::begin(w),std::end(w),std::begin(w_n_1));
// solving the system of linear equations for u and v momentum equations and pressure correction equation
gs_vel();
memset(p_error,0.0,sizeof(p_error));
gs_p();
for(int ix=0;ix<N*N;ix++){
p[ix][N-1]=0.0;
}
// updating pressure with under-relaxation factor
for(int ix=0;ix<N*N;ix++){
for(int iy=0;iy<N;iy++){
p[ix][iy]= p[ix][iy]+ ur_p*p_error[ix][iy];// here '0.5' is the under relaxation factor
}
}
// update the boundary conditions
//side of box
for(int iy=1;iy<N+1;iy++){
for(int ix=0;ix<N;ix++){
p[(N)*iy-1][ix]=p[(N)*iy-2][ix];//north side of cavity w.r.t to velocity in +ve x- direction
p[ix+(iy-1)*N][N-1]=p[ix+(iy-1)*N][N-2];// lid of cavity i.e. top of cavity
p[(iy-1)+(N-1)*N][ix]=p[(iy-1)+(N-2)*N][ix];// east side of cavity
p[(iy-1)*N][ix]=p[(iy-1)*N+1][ix];//south side of cavity
p[ix+(iy-1)*N][0]=p[ix+(iy-1)*N][1];// bottom of cavity
p[iy-1][ix]=p[(iy-1)+N][ix];// west side of cavity
}
}
// update velocity values using correction equations
// in the correction equations below, values are not updated in boundary planes: ix=0:N-1 and ix=N*N-N:N*N-1
for(int ix=N;ix<N*N-N;ix++){
for(int iy=1;iy<N;iy++){
u[ix][iy]= u[ix][iy]+ (dx*dx/a(ix,iy,1))*(p_error[ix-1][iy]-p_error[ix][iy]);//updating velocity values without using under relaxation factor
u[ix][iy]= ur_u*u[ix][iy]+ (1-ur_u)*u_n_1[ix][iy];// updating velocity values using under relaxation factor
}
}
// update velocity values using correction equations
for(int ix=N;ix<N*N-N;ix++){
for(int iy=1;iy<N;iy++){
v[ix][iy]= v[ix][iy]+ (dx*dx/a(ix,iy,2))*(p_error[ix][iy-1]-p_error[ix][iy]);//updating velocity values without using under relaxation factor
v[ix][iy]=ur_v*v[ix][iy]+ (1-ur_v)*v_n_1[ix][iy];// updating velocity values using under relaxation factor
}
}
// update velocity values using correction equations
for(int ix=N;ix<N*N-N;ix++){
for(int iy=1;iy<N;iy++){
w[ix][iy]= w[ix][iy]+ (dx*dx/a(ix,iy,3))*(p_error[ix-N][iy]-p_error[ix][iy]);//updating velocity values without using under relaxation factor
w[ix][iy]=ur_w*w[ix][iy]+ (1-ur_w)*w_n_1[ix][iy];// updating velocity values using under relaxation factor
}
}
//boundary conditions
for(int ix=1;ix<N+1;ix++){
for(int iy=0;iy<N;iy++){
// u-velocity
u[N*(ix-1)+iy][N-1]=u_inf;//lid
u[N*(ix-1)+iy][0]=0.0;//bottom
u[ix-1][iy]=0.0;//west side of cavity
u[(ix-1)+N*N-N][iy]=0.0;//east side of cavity
u[(ix-1)*N][iy]=0.0;//south side of cavity
u[N*ix-1][iy]=0.0;//north side of cavity
//v-velocity
v[N*(ix-1)+iy][N-1]=0.0;//lid
v[N*(ix-1)+iy][0]=0.0;//bottom
v[ix-1][iy]=0.0;//west side of cavity
v[(ix-1)+N*N-N][iy]=0.0;//east side of cavity
v[(ix-1)*N][iy]=0.0;//south side of cavity
v[N*ix-1][iy]=0.0;//north side of cavity
//w-velocity
w[N*(ix-1)+iy][N-1]=0.0;//lid
w[N*(ix-1)+iy][0]=0.0;//bottom
w[ix-1][iy]=0.0;//west side of cavity
w[(ix-1)+N*N-N][iy]=0.0;//east side of cavity
w[(ix-1)*N][iy]=0.0;//south side of cavity
w[N*ix-1][iy]=0.0;//north side of cavity
}
}
//checking convergence
double maximum1=0.0;
double maximum2=0.0;
double maximum3=0.0;
double maximum4=0.0;
double maximum=0.0;
//error in x-momentum equation
for(int ix=0;ix<N*N;ix++){
for(int iy=0;iy<N;iy++){
if((abs(u_n_1[ix][iy]-u[ix][iy])/dt)>maximum1){
maximum1= abs(u_n_1[ix][iy]-u[ix][iy])/dt;
}
}
}
//error in y-momentum equation
for(int ix=0;ix<N*N;ix++){
for(int iy=0;iy<N;iy++){
if(abs((v_n_1[ix][iy]-v[ix][iy])/dt)>maximum2){
maximum2= abs(v_n_1[ix][iy]-v[ix][iy])/dt;
}
}
}
//error in z-momentum equation
for(int ix=0;ix<N*N;ix++){
for(int iy=0;iy<N;iy++){
if(abs((w_n_1[ix][iy]-w[ix][iy])/dt)>maximum3){
maximum3= abs(w_n_1[ix][iy]-w[ix][iy])/dt;
}
if(abs(p[ix][iy])>maximum4)
maximum4=abs(p[ix][iy]);
}
}
maximum= maximum1+maximum2+maximum3;
if(maximum<tolerance*tolerance*max_err)
break;
if(it==NT)
max_err=maximum;
cout<<"Value of error, u: "<<maximum1<<",v: "<<maximum2<<",w: "<<maximum3<<",p: "<<maximum4<<endl;
fout15<<NT-it<<" "<<maximum<<endl;
}
cout<<"Writing values to file."<<endl;
//write values to a file
ofstream fout12;
ofstream fout17;
ofstream fout18;
ofstream fout22;
fout12.open("pressure.dat");
fout17.open("x_vel.dat");
fout18.open("y_vel.dat");
fout22.open("z_vel.dat");
for(int iz=0;iz<N;iz++){
for(int iy=0;iy<N;iy++){
for(int ix=0;ix<N;ix++){
fout12<<p[ix+N*iz][iy]<<endl;// pressure field
}
}
}
for(int iz=0;iz<N;iz++){
for(int iy=0;iy<N;iy++){
for(int ix=0;ix<N;ix++){
fout17<<u[ix+N*iz][iy]<<endl;
}
}
}
for(int iz=0;iz<N;iz++){
for(int iy=0;iy<N;iy++){
for(int ix=0;ix<N;ix++){
fout18<<v[ix+N*iz][iy]<<endl;
}
}
}
for(int iz=0;iz<N;iz++){
for(int iy=0;iy<N;iy++){
for(int ix=0;ix<N;ix++){
fout22<<w[ix+N*iz][iy]<<endl;
}
}
}
fout12.close();
fout17.close();
fout18.close();
fout22.close();
fout15.close();
}
double boundary(int ix, int iy){
double ans=0.0;
return ans;
}
// momentum equation coefficients
double a_n(int ix, int iy,int n){
double ans=0.0;
if(n==1)
ans= dx*dx*(D -rho*(v_n_1[ix-1][iy+1]+v_n_1[ix][iy+1])/4.0);
else if(n==2)
ans= dx*dx*(D -rho*(v_n_1[ix][iy]+v_n_1[ix][iy+1])/4.0);
else if(n==3)
ans= dx*dx*(D -rho*(v_n_1[ix][iy+1]+v_n_1[ix-N][iy+1])/4.0);
return ans;
}
double a_s(int ix, int iy,int n){
double ans=0.0;
if(n==1)
ans= dx*dx*(D + rho*(v_n_1[ix-1][iy]+v_n_1[ix][iy])/4.0);
else if(n==2)
ans= dx*dx*(D + rho*(v_n_1[ix][iy-1]+v_n_1[ix][iy])/4.0);
else if(n==3)
ans= dx*dx*(D + rho*(v_n_1[ix][iy]+v_n_1[ix-N][iy])/4.0);
return ans;
}
double a_e(int ix, int iy,int n){
double ans=0.0;
if(n==1)
ans= dx*dx*(D -rho*(u_n_1[ix][iy]+u_n_1[ix+1][iy])/4.0);
else if(n==2)
ans= dx*dx*(D -rho*(u_n_1[ix+1][iy]+u_n_1[ix+1][iy-1])/4.0);
else if(n==3)
ans= dx*dx*(D -rho*(u_n_1[ix+1][iy]+u_n_1[ix+1-N][iy])/4.0);
return ans;
}
double a_w(int ix, int iy,int n){
double ans=0.0;
if(n==1)
ans= dx*dx*(D + rho*(u_n_1[ix-1][iy]+u_n_1[ix][iy])/4.0);
else if(n==2)
ans= dx*dx*(D + rho*(u_n_1[ix][iy]+u_n_1[ix][iy-1])/4.0 );
else if(n==3)
ans= dx*dx*(D + rho*(u_n_1[ix][iy]+u_n_1[ix-N][iy])/4.0);
return ans;
}
double a_t(int ix, int iy,int n){
double ans=0.0;
if(ix+N>N*N-1){
if(n==1)
ans= dx*dx*(D -rho*(0.0+0.0)/4.0);
else if(n==2)
ans= dx*dx*(D -rho*(0.0+0.0)/4.0);
else if(n==3)
ans= dx*dx*(D -rho*(w_n_1[ix][iy]+0.0)/4.0);
}else{
if(n==1)
ans= dx*dx*(D -rho*(w_n_1[ix+N][iy]+w_n_1[ix-1+N][iy])/4.0);
else if(n==2)
ans= dx*dx*(D -rho*(w_n_1[ix+N][iy]+w_n_1[ix+N][iy-1])/4.0);
else if(n==3)
ans= dx*dx*(D -rho*(w_n_1[ix][iy]+w_n_1[ix+N][iy])/4.0);
}
return ans;
}
double a_b(int ix, int iy,int n){
double ans=0.0;
if(n==1)
ans= dx*dx*(D + rho*(w_n_1[ix-1][iy]+w_n_1[ix][iy])/4.0);
else if(n==2)
ans= dx*dx*(D +rho*(w_n_1[ix][iy]+w_n_1[ix][iy-1])/4.0);
else if(n==3)
ans= dx*dx*(D + rho*(w_n_1[ix-N][iy]+w_n_1[ix][iy])/4.0);
return ans;
}
double a(int ix, int iy,int n){
double ans=0.0;
if(n==1)
ans= 12.0*dx*dx*D -(a_w(ix,iy,1)+a_e(ix,iy,1)+a_n(ix,iy,1)+a_s(ix,iy,1)+a_t(ix,iy,1)+a_b(ix,iy,1));
else if(n==2)
ans= 12.0*dx*dx*D -(a_w(ix,iy,2)+a_e(ix,iy,2)+a_n(ix,iy,2)+a_s(ix,iy,2)+a_t(ix,iy,2)+a_b(ix,iy,2));
else if(n==3)
ans= 12.0*dx*dx*D -(a_w(ix,iy,3)+a_e(ix,iy,3)+a_n(ix,iy,3)+a_s(ix,iy,3)+a_t(ix,iy,3)+a_b(ix,iy,3));
return ans;
}
// pressure correction equation coefficients
double p_e(int ix, int iy){
double answer=0.0;
answer= rho*dx*dx*dx*dx/a(ix+1,iy,1);
return answer;
}
double p_n(int ix, int iy){
double answer=0.0;
answer= rho*dx*dx*dx*dx/a(ix,iy+1,2);
return answer;
}
double p_w(int ix, int iy){
double answer=0.0;
answer= rho*dx*dx*dx*dx/a(ix,iy,1);
return answer;
}
double p_s(int ix, int iy){
double answer=0.0;
answer= rho*dx*dx*dx*dx/a(ix,iy,2);
return answer;
}
double p_t(int ix, int iy){
double answer=0.0;
answer= rho*dx*dx*dx*dx/a(ix+N,iy,3);
return answer;
}
double p_b(int ix, int iy){
double answer=0.0;
answer= rho*dx*dx*dx*dx/a(ix,iy,3);
return answer;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void gs_vel(void){
for(int ix=N;ix<N*N-N;ix++){
for(int iy=1;iy<N-1;iy++){
if(ix%N==0||(ix+1)%(N)==0){
continue;
}else{
u[ix][iy]= (dx*dx*(p[ix-1][iy]-p[ix][iy]) + u[ix+N][iy]*(a_t(ix,iy,1))+ u[ix-N][iy]*(a_b(ix,iy,1))+ u[ix+1][iy]*(a_e(ix,iy,1)) + u[ix][iy+1]*(a_n(ix,iy,1)) + u[ix-1][iy]*(a_w(ix,iy,1)) + u[ix][iy-1]*(a_s(ix,iy,1)))/(a(ix,iy,1));
v[ix][iy]= (dx*dx*(p[ix][iy-1]-p[ix][iy]) + v[ix+1][iy]*(a_e(ix,iy,2))+ v[ix][iy+1]*(a_n(ix,iy,2))+ v[ix-1][iy]*(a_w(ix,iy,2)) + v[ix][iy-1]*(a_s(ix,iy,2)) + v[ix+N][iy]*(a_t(ix,iy,2)) + v[ix-N][iy]*(a_b(ix,iy,2)))/(a(ix,iy,2));
w[ix][iy]= (dx*dx*(p[ix-N][iy]-p[ix][iy]) + w[ix+1][iy]*(a_e(ix,iy,3))+ w[ix][iy+1]*(a_n(ix,iy,3))+ w[ix-1][iy]*(a_w(ix,iy,3)) + w[ix][iy-1]*(a_s(ix,iy,3)) + w[ix+N][iy]*(a_t(ix,iy,3)) + w[ix-N][iy]*(a_b(ix,iy,3)))/(a(ix,iy,3));
}
if(u[ix][iy]!=u[ix][iy]){
cout<<"Pressure grad: "<<p[ix-1][iy]-p[ix][iy]<<endl;
cout<<"U_top: "<< u[ix+N][iy]<<" U_bottom: "<<u[ix-N][iy]<<" U_north: "<<u[ix][iy+1]<<" U_south: "<<u[ix][iy-1]<<" U_east: "<<u[ix+1][iy]<<" U_west: "<<u[ix-1][iy]<<endl;
cout<<" Top: "<<a_t(ix,iy,1)<<" Bottom: "<<a_b(ix,iy,1)<<" North: "<<a_n(ix,iy,1)<<" South: "<<a_s(ix,iy,1)<<" East: "<<a_e(ix,iy,1)<<" West: "<<a_w(ix,iy,1)<<endl;
cout<<" Total: "<<a(ix,iy,1)<<endl;
cout<<" Location: "<<ix<<","<<iy<<endl;
break;
}
}
}
}
void gs_p(void){
for(int ix=N;ix<N*N-N;ix++){
for(int iy=1;iy<N-1;iy++){
if(ix%N==0||(ix+1)%(N)==0){
continue;
}else{
p_error[ix][iy]= ((rho*dx*dx*(u[ix][iy]-u[ix+1][iy]+v[ix][iy]-v[ix][iy+1]+w[ix][iy]-w[ix+N][iy]))+(p_error[ix+1][iy]*p_e(ix,iy) + p_error[ix-1][iy]*p_w(ix,iy) + p_error[ix][iy-1]*p_s(ix,iy) + p_error[ix][iy+1]*p_n(ix,iy)+ p_error[ix+N][iy]*p_t(ix,iy)+ p_error[ix-N][iy]*p_b(ix,iy)) + boundary(ix,iy))/(p_n(ix,iy)+p_w(ix,iy)+p_e(ix,iy)+p_s(ix,iy)+p_t(ix,iy)+p_b(ix,iy));
}
if(p_error[ix][iy]!=p_error[ix][iy]){
cout<<"Vel. correction: "<<u[ix][iy]-u[ix+1][iy]+v[ix][iy]-v[ix][iy+1]+w[ix][iy]-w[ix+N][iy]<<endl;
cout<<"P_top: "<< p_error[ix+N][iy]<<" P_bottom: "<<p_error[ix-N][iy]<<" P_north: "<<p_error[ix][iy+1]<<" P_south: "<<p_error[ix][iy-1]<<" P_east: "<<p_error[ix+1][iy]<<" P_west: "<<p_error[ix-1][iy]<<endl;
cout<<" Top: "<<p_t(ix,iy)<<" Bottom: "<<p_b(ix,iy)<<" North: "<<p_n(ix,iy)<<" South: "<<p_s(ix,iy)<<" East: "<<p_e(ix,iy)<<" West: "<<p_w(ix,iy)<<endl;
cout<<" Momentum eq coefficients: west,east,north,south,top,bottom "<<a_w(ix+N,iy,3)<<","<<a_e(ix+N,iy,3)<<","<<a_n(ix+N,iy,3)<<","<<a_s(ix+N,iy,3)<<","<<a_t(ix+N,iy,3)<<","<<a_b(ix+N,iy,3)<<endl;
cout<<" Location: "<<ix<<","<<iy<<endl;
break;
}
}
}
}