void weno(double **f, //fluxes at each edge
double **ql, // left states
double **qr, // right states
int is, // start index of chain
int ie, // end index of chain
double epsw, // epsilon in limiter
int imax, // chainSize
int nq) // number of variables
{
int i,n,im,k;
double f0[imax-1],f1[imax-1],f2[imax-1];
epsw = 1e-15;
im = imax-2;
// 1st order upwind
// for (n=0;n<nq;n++)
// {
// for (i=is;i<im;i++) //loop through chain
// {
// ql[i][n] = f[i][n]; //left and right states are the same as the face
// qr[i][n] = f[i][n];
// }
// }
// return;
// 5th order weno scheme
for (n=0; n<nq; n++) // number of flow variable
{
for (i=0; i<=ie; i++) // loop through the chain
{
f0[i] = f[i][n];
}
for (i=is; i<im; i++)
{
ql[i][n]=weno5(f0[i-2],f0[i-1],f0[i],f0[i+1],f0[i+2],epsw);
//printf("ql:%f\n",ql[i][n]);
qr[i][n]=weno5(f0[i+2],f0[i+1],f0[i],f0[i-1],f0[i-2],epsw);
//printf("qr:%f\n",qr[i][n]);
}
} //loop for number of flow variable
} //end function
//------------------------------------------------------------------------------
int main(int argc, char *argv[])
{
PetscErrorCode ierr;
DM da;
Vec ug, ul;
PetscInt i, ibeg, nloc, nx=200;
const PetscInt sw = 3, ndof = 1; // stencil width
PetscMPIInt rank, size;
double cfl = 0.4;
ierr = PetscInitialize(&argc, &argv, (char*)0, help); CHKERRQ(ierr);
MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
MPI_Comm_size(PETSC_COMM_WORLD, &size);
ierr = DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, nx, ndof, sw, NULL, &da); CHKERRQ(ierr);
ierr = DMSetFromOptions(da); CHKERRQ(ierr);
ierr = DMSetUp(da); CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da, &ug); CHKERRQ(ierr);
ierr = DMDAGetCorners(da, &ibeg, 0, 0, &nloc, 0, 0); CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&nx,0,0,0,0,0,0,0,0,0,0,0); CHKERRQ(ierr);
PetscReal dx = (xmax - xmin) / (PetscReal)(nx);
PetscPrintf(PETSC_COMM_WORLD,"nx = %d, dx = %e\n", nx, dx);
for(i=ibeg; i<ibeg+nloc; ++i)
{
PetscReal x = xmin + i*dx;
PetscReal v = initcond(x);
ierr = VecSetValues(ug,1,&i,&v,INSERT_VALUES); CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(ug); CHKERRQ(ierr);
ierr = VecAssemblyEnd(ug); CHKERRQ(ierr);
savesol(nx, dx, ug);
// Get local view
ierr = DMGetLocalVector(da, &ul); CHKERRQ(ierr);
PetscInt il, nl;
ierr = DMDAGetGhostCorners(da,&il,0,0,&nl,0,0); CHKERRQ(ierr);
double res[nloc], uold[nloc];
double dt = cfl * dx;
double lam= dt/dx;
double tfinal = 2.0, t = 0.0;
while(t < tfinal)
{
if(t+dt > tfinal)
{
dt = tfinal - t;
lam = dt/dx;
}
for(int rk=0; rk<3; ++rk)
{
ierr = DMGlobalToLocalBegin(da, ug, INSERT_VALUES, ul); CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da, ug, INSERT_VALUES, ul); CHKERRQ(ierr);
PetscScalar *u;
ierr = DMDAVecGetArrayRead(da, ul, &u); CHKERRQ(ierr);
PetscScalar *unew;
ierr = DMDAVecGetArray(da, ug, &unew); CHKERRQ(ierr);
if(rk==0)
for(i=ibeg; i<ibeg+nloc; ++i) uold[i-ibeg] = u[i];
for(i=0; i<nloc; ++i)
res[i] = 0.0;
// Loop over faces and compute flux
for(i=0; i<nloc+1; ++i)
{
// face between j-1, j
int j = il+sw+i;
int jm1 = j-1;
int jm2 = j-2;
int jm3 = j-3;
int jp1 = j+1;
double uleft = weno5(u[jm3],u[jm2],u[jm1],u[j],u[jp1]);
double flux = uleft;
if(i==0)
{
res[i] -= flux;
}
else if(i==nloc)
{
res[i-1] += flux;
}
else
{
res[i] -= flux;
res[i-1] += flux;
}
}
// Update solution
for(i=ibeg; i<ibeg+nloc; ++i)
unew[i] = ark[rk]*uold[i-ibeg] + (1-ark[rk])*(u[i] - lam * res[i-ibeg]);
ierr = DMDAVecRestoreArrayRead(da, ul, &u); CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da, ug, &unew); CHKERRQ(ierr);
}
t += dt;
PetscPrintf(PETSC_COMM_WORLD,"t = %f\n", t);
}
savesol(nx, dx, ug);
// Destroy everything before finishing
ierr = DMDestroy(&da); CHKERRQ(ierr);
ierr = VecDestroy(&ug); CHKERRQ(ierr);
ierr = PetscFinalize(); CHKERRQ(ierr);
}
