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#include<iostream>
#include<fstream>
#include<sstream>
#include<string>
#include<cmath>
#include<cstdlib>
#include<iomanip>
using namespace std;
const int Q=9;
const int NX=100;
const int NY=50;
const int Re=200;
const double U0=0.1;
const double rho0=1.0;
int k,n,i,j,ip,jp;
double niu=NY*U0/Re;
double tau=3.0*niu+0.5;
int e[Q][2]={{0,0},{1,0},{0,1},{-1,0},{0,-1},{1,1},{-1,1},{-1,-1},{1,-1}};
double w[Q]={4.0/9,1.0/9,1.0/9,1.0/9,1.0/9,1.0/36,1.0/36,1.0/36,1.0/36};
double rho[NX][NY];
double ux0[NX][NY],uy0[NX][NY],ux[NX][NY],uy[NX][NY];
double f[NX][NY][Q],F[NX][NY][Q];
void init();
void evolution();
void output(int m);
double feq(int k,int i,int j);
int main()
{
using namespace std;
init();
for(n=0;n<=50000;n++)
{
evolution();
if(n%100==0)
std::cout<<"The ux and uy of [NX/2][NY/2]:"<<setprecision(6)<<ux[NX/2][NY/2]<<" , "<<uy[NX/2][NY/2]<<endl;
if(n%1000==0)
output(n);
}
system("pause");
return 0;
}
void init()
{
for(i=0;i<=NX;i++)
for(j=0;j<=NY;j++)
{
ux[i][j]=0.0;
uy[i][j]=0.0;
rho[i][j]=rho0;
ux[0][j]=U0;
for(k=0;k<Q;k++)
{
f[i][j][k]=feq(k,i,j);
}
}
}
double feq(int k,int i,int j)
{
double eu,uu,feq;
eu=(e[k][0]*ux[i][j]+e[k][1]*uy[i][j]);
uu=(ux[i][j]*ux[i][j]+uy[i][j]*uy[i][j]);
feq=w[k]*rho[i][j]*(1.0+3.0*eu+4.5*eu*eu-1.5*uu);
return feq;
}
void evolution()
{
for(i=1;i<NX;i++)
for(j=1;j<NY;j++)
for(k=0;k<Q;k++)
{
ip=i-e[k][0];
jp=j-e[k][1];
F[i][j][k]=f[ip][jp][k]-(f[ip][jp][k]-feq(k,ip,jp))/tau;
}
for(i=1;i<NX;i++)
for(j=1;j<NY;j++)
{
ux0[i][j]=ux[i][j];
uy0[i][j]=uy[i][j];
rho[i][j]=0.0;
ux[i][j]=0.0;
uy[i][j]=0.0;
for(k=0;k<Q;k++)
{
f[i][j][k]=F[i][j][k];
rho[i][j]+=f[i][j][k];
ux[i][j]+=f[i][j][k]*e[k][0];
uy[i][j]+=f[i][j][k]*e[k][1];
}
ux[i][j]/=rho[i][j];
uy[i][j]/=rho[i][j];
}
for(i=0;i<=NX;i++)
for(k=0;k<Q;k++)
{
rho[i][0]=rho[i][1];
f[i][0][k]=feq(k,i,0)+f[i][1][k]-feq(k,i,1);
rho[i][NY]=rho[i][NY-1];
f[i][NY][k]=feq(k,i,NY)+f[i][NY-1][k]-feq(k,i,NY-1);
}
for(j=0;j<=NY;j++)
for(k=0;k<Q;k++)
{
rho[0][j]=rho[1][j];
ux[0][j]=U0;
f[0][j][k]=feq(k,0,j)+f[1][j][k]-feq(k,1,j);
rho[NX][j]=rho[NX-1][j];
f[NX][j][k]=feq(k,NX,j)+f[NX-1][j][k]-feq(k,NX-1,j);
}
}
void output(int m)
{
ostringstream name;
name<<"2D flow_"<<m<<".dat";
ofstream out(name.str().c_str());
for(i=0;i<=NX;i++)
for(j=0;j<=NY;j++)
{
out<<double(i)/NX<<" "<<double(j)/NY<<" "<<ux[i][j]<<" "<<uy[i][j]<<endl;
}
}
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