Real INSChorinPredictor::computeQpResidual()
{
// Vector object for test function
RealVectorValue test;
test(_component) = _test[_i][_qp];
// Tensor object for test function gradient
RealTensorValue grad_test;
for (unsigned k=0; k<3; ++k)
grad_test(_component, k) = _grad_test[_i][_qp](k);
// Decide what velocity vector, gradient to use:
RealVectorValue U;
RealTensorValue grad_U;
switch (_predictor_enum)
{
case OLD:
{
U = RealVectorValue(_u_vel_old[_qp], _v_vel_old[_qp], _w_vel_old[_qp]);
grad_U = RealTensorValue(_grad_u_vel_old[_qp], _grad_v_vel_old[_qp], _grad_w_vel_old[_qp]);
break;
}
case NEW:
{
U = RealVectorValue(_u_vel[_qp], _v_vel[_qp], _w_vel[_qp]);
grad_U = RealTensorValue(_grad_u_vel[_qp], _grad_v_vel[_qp], _grad_w_vel[_qp]);
break;
}
case STAR:
{
// Note: Donea and Huerta's book says you are supposed to use "star" velocity to make Chorin implicit, not U^{n+1}.
U = RealVectorValue(_u_vel_star[_qp], _v_vel_star[_qp], _w_vel_star[_qp]);
grad_U = RealTensorValue(_grad_u_vel_star[_qp], _grad_v_vel_star[_qp], _grad_w_vel_star[_qp]);
break;
}
default:
mooseError("Unrecognized Chorin predictor type requested.");
}
//
// Compute the different parts
//
// Note: _u is the component'th entry of "u_star" in Chorin's method.
RealVectorValue U_old(_u_vel_old[_qp], _v_vel_old[_qp], _w_vel_old[_qp]);
Real symmetric_part = (_u[_qp] - U_old(_component)) * _test[_i][_qp];
// Convective part. Remember to multiply by _dt!
Real convective_part = _dt * (grad_U * U) * test;
// Viscous part - we are using the Laplacian form here for simplicity.
// Remember to multiply by _dt!
Real viscous_part = _dt * (_mu/_rho) * grad_U.contract(grad_test);
return symmetric_part + convective_part + viscous_part;
}
//\begin{>>PPP_2d_Jacobi_1d_Part.tex}{\subsubsection{runBenchmark}}
void PPP_2d_Jacobi_1d_Part::
runBenchmark( )
//================================================================
// /Description: Executes the benchmarking code the specified
// number of times and stores the times in the array.
//
// /Return Values: None.
//
// /Errors:
// None.
//
// /Author: BJM
// /Date: 24 August 2000
//\end{PPP_2d_Jacobi_1d_Part.tex}
//================================================================
{
double theTime,theStartTime,theEndTime;
int theNumProcs = 1;
int thisProcNum = 0;
// MPI_Comm_size(MPI_COMM_WORLD, &theNumProcs);
// MPI_Comm_rank(MPI_COMM_WORLD, &thisProcNum);
Partitioning_Type Partitioning(Range(0,theNumProcs-1));
Partitioning.SpecifyInternalGhostBoundaryWidths(1,1);
Partitioning.SpecifyDecompositionAxes(1);
int theArraySideLength = sqrt( mUnknownsPerProc * theNumProcs );
printf ("theArraySideLength = %d \n",theArraySideLength);
doubleArray U_old(theArraySideLength,theArraySideLength,Partitioning);
U_old = 0.0;
Index I (1,theArraySideLength-2);
Index J (1,theArraySideLength-2);
int i;
// printf ("Warming up ... \n");
for(i=0;i< mNumberOfWarmupIterations;i++)
{
U_old(I,J) =
(U_old(I+1,J+1) + U_old(I+1,J) + U_old(I+1,J-1) + U_old(I,J+1) +
U_old(I,J-1) + U_old(I-1,J+1) + U_old(I-1,J) + U_old(I-1,J-1)) / 8.0;
}
// Now time the problem
// printf ("Running timing loop ... \n");
for (i=0; i < mNumberOfTimingIterations; i++)
{
// printf ("Running timing loop iteration %d \n",i);
theStartTime = Communication_Manager::Wall_Clock_Time();
// theStartTime = clock();
U_old(I,J) =
(U_old(I+1,J+1) + U_old(I+1,J) + U_old(I+1,J-1) + U_old(I,J+1) +
U_old(I,J-1) + U_old(I-1,J+1) + U_old(I-1,J) + U_old(I-1,J-1)) / 8.0;
theEndTime = Communication_Manager::Wall_Clock_Time();
// theEndTime = clock();
theTime = theEndTime - theStartTime;
mTimes[0][i] = theTime;
printf("time= %f\n",theTime);
}//end of loop over timed iterations
}
void VideoFluids::trackVelocity(Matrix& Zn1,Matrix& Zn,Matrix& U,Matrix& V)
{
Matrix Zx(height,width),Zy(height,width),ZZx(height,width),ZZy(height,width),Zt(height,width),ZZt(height,width),ZZtx(height,width),ZZty(height,width);
Matrix Au1(height,width),Au2(height,width),Av1(height,width),Av2(height,width);
Matrix Z2x(height,width),Z2y(height,width),Z2(height,width);
Matrix Cu(height,width),Cv(height,width);
Matrix tmp(height,width),tmp1(height,width);
Matrix U_old(height,width),V_old(height,width),Ux(height,width),Uy(height,width),Vx(height,width),Vy(height,width),Uax(height,width),Uay(height,width),Vax(height,width),Vay(height,width),Uxy(height,width),Vxy(height,width);
Matrix Coe(height,width);
Zt = Zn;
Zt -= Zn1;
DotMul(Zn,Zt,ZZt);
Zn.output("Zn.txt");
Zn1.output("Zn1.txt");
Zt.output("Zt.txt");
Partial(ZZt,ZZtx,AXIS_X);
Partial(ZZt,ZZty,AXIS_Y);
Partial(Zn,Zx,AXIS_X);
Partial(Zn,Zy,AXIS_Y);
DotMul(Zn,Zx,ZZx);
DotMul(Zn,Zy,ZZy);
DotMul(Zx,Zx,Au1);
Partial(ZZx,tmp,AXIS_X);
Au1-=tmp;
DotMul(Zn,Zn,tmp);
Au1+=tmp;
Au1+=2*alpha*alpha;
DotMul(Zx,Zy,Au2);
Partial(ZZy,tmp,AXIS_X);
Au2-=tmp;
DotMul(Zx,Zy,Av1);
Partial(ZZx,tmp,AXIS_Y);
Av1-=tmp;
DotMul(Zy,Zy,Av2);
Partial(ZZy,tmp,AXIS_Y);
Av2-=tmp;
DotMul(Zn,Zn,tmp);
Av2+=tmp;
Av2+=2*alpha*alpha;
DotMul(Zn,Zn,Z2);
Partial(Z2,Z2x,AXIS_X);
Partial(Z2,Z2y,AXIS_Y);
for (int i = 0;i<height;i++)
for (int j = 0;j<width;j++)
Coe[i][j] = 1.0/(Au1[i][j]*Av2[i][j]-Au2[i][j]*Av1[i][j]);
U = 0.0;
V = 0.0;
for (int iter_time = 0;iter_time<iterationTime;iter_time++)
{
V_old = V;
U_old = U;
Partial(U,Ux,AXIS_X);
Partial(U,Uy,AXIS_Y);
Partial(V,Vx,AXIS_X);
Partial(V,Vy,AXIS_Y);
Partial(Vx,Vxy,AXIS_Y);
Partial(Ux,Uxy,AXIS_Y);
Average(U,Uax,AXIS_X);
Average(U,Uay,AXIS_Y);
Average(V,Vax,AXIS_X);
Average(V,Vay,AXIS_Y);
DotMul(Z2x,Ux,Cu);
DotMul(ZZy,Vx,tmp);
Cu += tmp;
tmp = ZZx*-1;
tmp+=Z2x;
DotMul(tmp,Vy,tmp1);
Cu+=tmp1;
tmp = Z2;
tmp+=alpha*alpha;
DotMul(tmp,Uax,tmp1);
Cu+=tmp1;
tmp1=Uay;
tmp1*=alpha*alpha;
Cu+=tmp1;
DotMul(Z2,Vxy,tmp1);
Cu+=tmp1;
DotMul(Zx,Zt,tmp);
Cu-=tmp;
Cu+=ZZtx;
DotMul(Z2y,Vy,Cv);
DotMul(ZZx,Uy,tmp);
Cv += tmp;
tmp = ZZy;
tmp*=-1;
tmp+=Z2y;
DotMul(tmp,Ux,tmp1);
Cv+=tmp1;
tmp = Z2;
tmp+=alpha*alpha;
DotMul(tmp,Vay,tmp1);
Cv+=tmp1;
tmp1=Vax;
tmp1*=alpha*alpha;
Cv+=tmp1;
DotMul(Z2,Uxy,tmp1);
Cv+=tmp1;
DotMul(Zy,Zt,tmp);
Cv-=tmp;
Cv+=ZZty;
for (int i = 0;i<height;i++)
for (int j = 0;j<width;j++)
{
U[i][j] = Coe[i][j]*(Av2[i][j]*Cu[i][j]-Au2[i][j]*Cv[i][j]);
V[i][j] = Coe[i][j]*(-Av1[i][j]*Cu[i][j]+Au1[i][j]*Cv[i][j]);
}
for (int i = 0;i<height;i++)
{
U[i][0] = U[i][1];
U[i][width-1] = U[i][width-2];
V[i][0] = V[i][1];
V[i][width-1] =V[i][width-2];
}
for (int i = 0;i<width;i++)
{
U[0][i] = U[1][i];
U[height-1][i] = U[height-2][i];
V[0][i] = V[1][i];
V[height-1][i] =V[height-2][i];
}
FILE* fp;
// Au1.output("Au1.txt");
// Au2.output("Au2.txt");
// Av1.output("Av1.txt");
// Av2.output("Av2.txt");
// Cu.output("Cu.txt");
// Cv.output("Cv.txt");
float d1 = Difference(U,U_old);
float d2 = Difference(V,V_old);
// U.output("U.txt");
// U_old.output("U_old.txt");
// V.output("V.txt");
cout<<d1<<' '<<d2<<endl;
if (d1<iterationTorlerance && d2<iterationTorlerance)
break;
}
U.output("U.txt");
cv::Mat showV(height,width,CV_8UC3);
float lowv=10000000,lowu=10000000,highu=-10000000,highv=-1000000;
for(int j=0;j<height;j++){
for(int k=0;k<width;k++){
if(U[j][k]>highu)
highu=U[j][k];
if(U[j][k]<lowu)
lowu=U[j][k];
if(V[j][k]>highv)
highv=V[j][k];
if(V[j][k]<lowv)
lowv=V[j][k];
}
}
for(int j=0;j<height;j++){
for(int k=0;k<width;k++){
//printf("%d %d\n",j,k);
//if(sfs_list[i][j][k]<low)
// showH.at<uchar>(j,k)=0;
//else
float u=(U[j][k]-lowu)/(highu-lowu);
float v=(V[j][k]-lowv)/(highv-lowv);
if(u>0.5)
showV.at<cv::Vec3b>(j,k)[2]=255;
else
showV.at<cv::Vec3b>(j,k)[2]=255*u;
if(v>0.5){
showV.at<cv::Vec3b>(j,k)[0]=255;
showV.at<cv::Vec3b>(j,k)[1]=255*(1-v);
}
else{
showV.at<cv::Vec3b>(j,k)[1]=255;
showV.at<cv::Vec3b>(j,k)[0]=255*v;
}
}
}
cv::imwrite("testV.bmp",showV);
printf("show you");
}
