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#include<iostream>
#include<fstream>
#include<sstream>
#include<string>
#include<iomanip>
#include<cstdlib>
#include<cmath>
using namespace std;
const int Q=9;
const int NX=400;
const int NY=40;
const int wr=40;
const int wu=20;
const double U0=0.1;
int i,j,ip,jp,inext,jnext,k,n;
int Re=200;
double niu=U0*NY/Re,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 rho0=1.0,rho[NX+1][NY+1];
double ux0[NX+1][NY+1],uy0[NX+1][NY+1],ux[NX+1][NY+1],uy[NX+1][NY+1];
double f[NX+1][NY+1][Q],Fc[NX+1][NY+1][Q],F[NX+1][NY+1][Q];
void init();
void evolution();
void output(int);
double feq(int i,int j,int k);
int main()
{
using namespace std;
init();
for(n=0;;n++)
{
evolution();
if(n>0)
{
if(n%100==0) cout<<"n="<<n<<endl<<"The ux and uy of [NX/2][NY/2] is:"<<setiosflags(ios::scientific)<<ux[NX/2][NY/2]<<" , "<<uy[NX/2][NY/2]<<endl;
if(n%1000==0) output(n);
//if(n==20000) output(n);
}
}
system("pause");
return 0;
}
void init()
{
std::cout<<"tau="<<tau<<endl;
for(i=0;i<=NX;i++)
for(j=0;j<=NY;j++)
{
rho[i][j]=rho0;
ux[i][j]=0;
uy[i][j]=0;
for(k=0;k<Q;k++)
{
f[i][j][k]=feq(i,j,k);
}
}
for(j=wu+1;j<=NY-1;j++)
{
ux[0][j]=U0;
}
}
double feq(int i,int j, int k)
{
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+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];
inext=i+e[k][0];
jnext=j+e[k][1];
F[i][j][k]=f[ip][jp][k];
Fc[i][j][k]=F[i][j][k]+(feq(i,j,k)-f[i][j][k])/tau;
//F[i][j][k]=f[ip][jp][k]+(feq(ip,jp,k)-f[ip][jp][k])/tau;
}
for(i=1;i<=wr+1;i++)
for(j=wu+1;j<=NY-1;j++)
{
ux0[i][j]=ux[i][j];
uy0[i][j]=uy[i][j];
rho[i][j]=0;
ux[i][j]=0;
uy[i][j]=0;
for(k=0;k<Q;k++)
{
f[i][j][k]=Fc[i][j][k];
rho[i][j]+=f[i][j][k];
ux[i][j]+=e[k][0]*f[i][j][k];
uy[i][j]+=e[k][1]*f[i][j][k];
}
ux[i][j]/=rho[i][j];
uy[i][j]/=rho[i][j];
}
for(i=wr+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;
ux[i][j]=0;
uy[i][j]=0;
for(k=0;k<Q;k++)
{
f[i][j][k]=Fc[i][j][k];
rho[i][j]+=f[i][j][k];
ux[i][j]+=e[k][0]*f[i][j][k];
uy[i][j]+=e[k][1]*f[i][j][k];
}
ux[i][j]/=rho[i][j];
uy[i][j]/=rho[i][j];
}
for(i=1;i<NX;i++)
//for(k=0;k<Q;k++)
{
/*f[i][NY][2]=0;
f[i][NY][5]=0;
f[i][NY][6]=0;
f[i][NY][0]=f[i][NY][1]=f[i][NY][3]=0;
f[i][NY][4]=f[i][NY-1][2];
f[i][NY][7]=f[ip][NY-1][5];
f[i][NY][8]=f[inext][NY-1][6];*/
f[i][NY][4]=F[i][NY-1][2];
f[i][NY][7]=F[ip][NY-1][5];
f[i][NY][8]=F[inext][NY-1][6];
}
for(i=wr+1;i<NX;i++)
//for(k=0;k<Q;k++)
{
f[i][0][2]=F[i][1][4];
f[i][0][6]=F[ip][1][8];
f[i][0][5]=F[inext][1][7];
}
for(i=1;i<=wr;i++)
//for(k=0;k<Q;k++)
{
f[i][wu][2]=F[i][wu+1][4];
f[i][wu][6]=F[ip][wu+1][8];
f[i][wu][5]=F[inext][wu+1][7];
}
for(j=1;j<=wu;j++)
//for(k=0;k<Q;k++)
{
f[wr][j][1]=F[wr+1][j][3];
f[wr][j][5]=F[wr+1][jnext][7];
f[wr][j][8]=F[wr+1][jp][6];
}
for(j=wu+1;j<NY;j++)
for(k=0;k<Q;k++)
{
rho[0][j]=rho[1][j];
f[0][j][k]=feq(0,j,k)+f[1][j][k]-feq(1,j,k);
ux[0][j]=U0;
}
for(j=1;j<NY;j++)
for(k=0;k<Q;k++)
{
rho[NX][j]=rho[NX-1][j];
f[NX][j][k]=feq(NX,j,k)+f[NX-1][j][k]-feq(NX-1,j,k);
ux[NX][j]=ux[NX-1][j];
}
}
void output(int)
{
ostringstream name;
name<<"cavity_bounce2_"<<NX<<"+"<<NY<<"-"<<U0<<"-"<<Re<<"-"<<n<<".dat";
ofstream out(name.str().c_str());
out<<"Title=\"LBM 2D cavity Flow\"\n"<<
"VARIABLES= \"X\",\"Y\",\"U\",\"V\"\n"<<"ZONE T=\"BOX\",I="
<<NX+1<<",J="<<NY+1<<",F=POINT"<<endl;
for(j = 0;j <= NY;j++)
for(i = 0;i <=NX;i++)
{
out<<double(i)<<" "<<double(j)<<" "<<
ux[i][j]<<" "<<uy[i][j]<<endl;
}
}
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