cPP.rar_格子玻尔兹曼_顶盖驱动流

# include<iostream> # include<cmath> # include<cstdlib> # include<iomanip> # include<fstream> # include<sstream> # include<string> using namespace std; const int Q=9; //D2Q9模型 const int NX=127; //x方向 const int NY=127; //y方向 const double U=0.05; //顶盖速度 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+1][NY+1],u[NX+1][NY+1][2],u0[NX+1][NY+1][2],f[NX+1][NY+1][Q],F[NX+1][NY+1][Q]; int i,j,k,ip,jp,n; double c,Re,dx,dy,Lx,Ly,dt,rho0,P0,tau_f,niu,error; void init(); double feq(int k,double rho,double u[2]); void evolution(); void output(int m); void Error(); int main() { using namespace std; init(); for(n=1; ;n++) { evolution(); if(n%10==0) { Error(); cout<<"the"<<n<<"th computation result:"<<endl<<"The u,v of point (NX/2,NY/2) is:"<<setprecision(6)<<u[NX/2][NY/2][0]<<","<<u[NX/2][NY/2][1]<<endl; cout<<"The max relative error of uv is:"<<setiosflags(ios::scientific)<<error<<endl; if(n>=10) {if(n%10==0) output(n); if(error<1.0e-6) break; } } } return 0; } void init() { dx=1.0; dy=1.0; Lx=dx*double(NY); Ly=dy*double(NX); dt=dx; c=dx/dt; //1.0 rho0=1.0; Re=100; niu=U*Lx/Re; tau_f=3.0*niu+0.5; std::cout<<"tau_f="<<tau_f<<endl; for(i=0;i<=NX;i++) //初始化 for(j=0;j<=NY;j++) { u[i][j][0]=0; u[i][j][1]=0; rho[i][j]=rho0; u[i][NY][0]=U; for(k=0;k<Q;k++) { f[i][j][k]=feq(k,rho[i][j],u[i][j]); } } } double feq(int k,double rho,double u[2]) //计算平衡态分布函数 { double eu,uv,feq; eu=(e[k][0]*u[0]+e[k][1]*u[1]); uv=(u[0]*u[0]+u[1]*u[1]); feq=w[k]*rho*(1.0+3.0*eu+4.5*eu*eu-1.5*uv); return feq; } void evolution() { for(i=1;i<NX;i++) //演化 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]+(feq(k,rho[ip][jp],u[ip][jp])-f[ip][jp][k])/tau_f; } for(i=1;i<NX;i++) //计算宏观量 for(j=1;j<NY;j++) { u0[i][j][0]=u[i][j][0]; u0[i][j][1]=u[i][j][1]; rho[i][j]=0; u[i][j][0]=0; u[i][j][1]=0; for(k=0;k<Q;k++) {f[i][j][k]=F[i][j][k]; rho[i][j]+=f[i][j][k]; u[i][j][0]+=e[k][0]*f[i][j][k]; u[i][j][1]+=e[k][1]*f[i][j][k]; } u[i][j][0]/=rho[i][j]; u[i][j][1]/=rho[i][j]; } //边界处理 for(j=1;j<NY;j++) //左右边界 for(k=0;k<Q;k++) { rho[NX][j]=rho[NX-1][j]; f[NX][j][k]=feq(k,rho[NX][j],u[NX][j])+f[NX-1][j][k]-feq(k,rho[NX-1][j],u[NX-1][j]); rho[0][j]=rho[1][j]; f[0][j][k]=feq(k,rho[0][j],u[0][j])+f[1][j][k]-feq(k,rho[1][j],u[1][j]); } for(i=0;i<=NX;i++) //上下边界 for(k=0;k<Q;k++) { rho[i][0]=rho[i][1]; f[i][0][k]=feq(k,rho[i][0],u[i][0])+f[i][1][k]-feq(k,rho[i][1],u[i][1]); rho[i][NY]=rho[i][NY-1]; u[i][NY][0]=U; f[i][NY][k]=feq(k,rho[i][NY],u[i][NY])+f[i][NY-1][k]-feq(k,rho[i][NY-1],u[i][NY-1]); } } void output(int m) //输出 { ostringstream name; name<<"cavity_"<<m<<".dat"; ofstream out(name.str().c_str()); out<<"Title=\"LBM Lid Driven Flow\"\n"<<"VARIABLES=\"X\",\"Y\",\"U\",\"V\"\n"<<"ZONE T=\"BOX\",I="<<NX+1<< ",J="<<NY+1<< ",F=point"<<endl; for(j=122;j<=123;j++) for(i=122;i<=123;i++) { out<<double(i)/Lx<<" "<<double(j)/Ly<<" "<<u[i][j][0]<<" "<<u[i][j][1]<<endl; } } void Error() { double temp1,temp2; temp1=0; temp2=0; for(i=1;i<NX;i++) for(j=1;j<NY;j++) { temp1+=((u[i][j][0]-u0[i][j][0])*(u[i][j][0]-u0[i][j][0])+(u[i][j][1]-u0[i][j][1])*(u[i][j][1]-u0[i][j][1])); temp2+=(u[i][j][0]*u[i][j][0]+u[i][j][1]*u[i][j][1]); } temp1=sqrt(temp1); temp2=sqrt(temp2); error=temp1/(temp2+1e-30); }