Interp1PrimFifthOrderCompactUpwindChar.c

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#include <stdio.h>
#include <basic.h>
#include <arrayfunctions.h>
#include <matmult_native.h>
#include <mathfunctions.h>
#include <interpolation.h>
#include <tridiagLU.h>
#include <mpivars.h>
#include <hypar.h>

#ifdef with_omp
#include <omp.h>
#endif

#undef  _MINIMUM_GHOSTS_

#define _MINIMUM_GHOSTS_ 3

int Interp1PrimFifthOrderCompactUpwindChar(
                                            double *fI,  
                                            double *fC,  
                                            double *u,   
                                            double *x,   
                                            int    upw,  
                                            int    dir,  
                                            void   *s,   
                                            void   *m,   
                                            int    uflag 
                                          )
{
  HyPar           *solver = (HyPar*)          s;
  MPIVariables    *mpi    = (MPIVariables*)   m;
  CompactScheme   *compact= (CompactScheme*)  solver->compact;
  TridiagLU       *lu     = (TridiagLU*)      solver->lusolver;
  int             sys,Nsys,d,v,k;
  _DECLARE_IERR_;

  int ghosts = solver->ghosts;
  int ndims  = solver->ndims;
  int nvars  = solver->nvars;
  int *dim   = solver->dim_local;

  /* define some constants */
  static const double three_by_ten          = 3.0/10.0,
                      six_by_ten            = 6.0/10.0,
                      one_by_ten            = 1.0/10.0,
                      one_by_thirty         = 1.0/30.0,
                      nineteen_by_thirty    = 19.0/30.0,
                      one_third             = 1.0/3.0,
                      thirteen_by_sixty     = 13.0/60.0,
                      fortyseven_by_sixty   = 47.0/60.0,
                      twentyseven_by_sixty  = 27.0/60.0,
                      one_by_twenty         = 1.0/20.0;

  /* create index and bounds for the outer loop, i.e., to loop over all 1D lines along
     dimension "dir"                                                                    */
  int indexC[ndims], indexI[ndims], index_outer[ndims], bounds_outer[ndims], bounds_inter[ndims];
  _ArrayCopy1D_(dim,bounds_outer,ndims); bounds_outer[dir] =  1;
  _ArrayCopy1D_(dim,bounds_inter,ndims); bounds_inter[dir] += 1;

  /* calculate total number of block tridiagonal systems to solve */
  _ArrayProduct1D_(bounds_outer,ndims,Nsys);

  /* allocate arrays for the averaged state, eigenvectors and characteristic interpolated f */
  double R[nvars*nvars], L[nvars*nvars], uavg[nvars];

  /* Allocate arrays for tridiagonal system */
  double *A = compact->A;
  double *B = compact->B;
  double *C = compact->C;
  double *F = compact->R;

#pragma omp parallel for schedule(auto) default(shared) private(sys,d,v,k,R,L,uavg,index_outer,indexC,indexI)
  for (sys=0; sys<Nsys; sys++) {
    _ArrayIndexnD_(ndims,sys,bounds_outer,index_outer,0);
    _ArrayCopy1D_(index_outer,indexC,ndims);
    _ArrayCopy1D_(index_outer,indexI,ndims);
    for (indexI[dir] = 0; indexI[dir] < dim[dir]+1; indexI[dir]++) {
      int qm1,qm2,qm3,qp1,qp2;
      if (upw > 0) {
        indexC[dir] = indexI[dir]-3; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qm3);
        indexC[dir] = indexI[dir]-2; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qm2);
        indexC[dir] = indexI[dir]-1; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qm1);
        indexC[dir] = indexI[dir]  ; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qp1);
        indexC[dir] = indexI[dir]+1; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qp2);
      } else {
        indexC[dir] = indexI[dir]+2; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qm3);
        indexC[dir] = indexI[dir]+1; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qm2);
        indexC[dir] = indexI[dir]  ; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qm1);
        indexC[dir] = indexI[dir]-1; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qp1);
        indexC[dir] = indexI[dir]-2; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qp2);
      }

      int p; /* 1D index of the interface */
      _ArrayIndex1D_(ndims,bounds_inter,indexI,0,p);

      /* find averaged state at this interface */
      IERR solver->AveragingFunction(uavg,&u[nvars*qm1],&u[nvars*qp1],solver->physics); CHECKERR(ierr);

      /* Get the left and right eigenvectors */
      IERR solver->GetLeftEigenvectors  (uavg,L,solver->physics,dir); CHECKERR(ierr);
      IERR solver->GetRightEigenvectors (uavg,R,solver->physics,dir); CHECKERR(ierr);

      for (v=0; v<nvars; v++)  {

        /* calculate the characteristic flux components along this characteristic */
        double fm3, fm2, fm1, fp1, fp2;
        fm3 = fm2 = fm1 = fp1 = fp2 = 0;
        for (k = 0; k < nvars; k++) {
          fm3 += L[v*nvars+k] * fC[qm3*nvars+k];
          fm2 += L[v*nvars+k] * fC[qm2*nvars+k];
          fm1 += L[v*nvars+k] * fC[qm1*nvars+k];
          fp1 += L[v*nvars+k] * fC[qp1*nvars+k];
          fp2 += L[v*nvars+k] * fC[qp2*nvars+k];
        }

        if (   ((mpi->ip[dir] == 0                ) && (indexI[dir] == 0       ))
            || ((mpi->ip[dir] == mpi->iproc[dir]-1) && (indexI[dir] == dim[dir])) ) {
          /* Use 5th order upwind at the physical boundaries */
          for (k=0; k<nvars; k++) {
            A[(Nsys*indexI[dir]+sys)*nvars*nvars+v*nvars+k] = 0.0;
            C[(Nsys*indexI[dir]+sys)*nvars*nvars+v*nvars+k] = 0.0;
            B[(Nsys*indexI[dir]+sys)*nvars*nvars+v*nvars+k] = L[v*nvars+k];
          }
          F[(Nsys*indexI[dir]+sys)*nvars+v] =   one_by_thirty         * fm3
                                              - thirteen_by_sixty     * fm2
                                              + fortyseven_by_sixty   * fm1
                                              + twentyseven_by_sixty  * fp1
                                              - one_by_twenty         * fp2;
        } else {
          /* 5th order compact upwind at the interior points */
          if (upw > 0) {
            for (k=0; k<nvars; k++) {
              A[(Nsys*indexI[dir]+sys)*nvars*nvars+v*nvars+k] = three_by_ten * L[v*nvars+k];
              B[(Nsys*indexI[dir]+sys)*nvars*nvars+v*nvars+k] = six_by_ten   * L[v*nvars+k];
              C[(Nsys*indexI[dir]+sys)*nvars*nvars+v*nvars+k] = one_by_ten   * L[v*nvars+k];
            }
          } else {
            for (k=0; k<nvars; k++) {
              C[(Nsys*indexI[dir]+sys)*nvars*nvars+v*nvars+k] = three_by_ten * L[v*nvars+k];
              B[(Nsys*indexI[dir]+sys)*nvars*nvars+v*nvars+k] = six_by_ten   * L[v*nvars+k];
              A[(Nsys*indexI[dir]+sys)*nvars*nvars+v*nvars+k] = one_by_ten   * L[v*nvars+k];
            }
          }
          F[(Nsys*indexI[dir]+sys)*nvars+v] =   one_by_thirty      * fm2
                                              + nineteen_by_thirty * fm1
                                              + one_third          * fp1;
        }
      }
    }
  }

#ifdef serial

  /* Solve the tridiagonal system */
  IERR blocktridiagLU(A,B,C,F,dim[dir]+1,Nsys,nvars,lu,NULL); CHECKERR(ierr);

#else

  /* Solve the tridiagonal system */
  /* all processes except the last will solve without the last interface to avoid overlap */
  if (mpi->ip[dir] != mpi->iproc[dir]-1)  { 
    IERR blocktridiagLU(A,B,C,F,dim[dir]  ,Nsys,nvars,lu,&mpi->comm[dir]); CHECKERR(ierr); 
  } else { 
    IERR blocktridiagLU(A,B,C,F,dim[dir]+1,Nsys,nvars,lu,&mpi->comm[dir]); CHECKERR(ierr);
  }

  /* Now get the solution to the last interface from the next proc */
  double *sendbuf = compact->sendbuf;
  double *recvbuf = compact->recvbuf;
  MPI_Request req[2] = {MPI_REQUEST_NULL,MPI_REQUEST_NULL};
  if (mpi->ip[dir]) for (d=0; d<Nsys*nvars; d++) sendbuf[d] = F[d];
  if (mpi->ip[dir] != mpi->iproc[dir]-1) MPI_Irecv(recvbuf,Nsys*nvars,MPI_DOUBLE,mpi->ip[dir]+1,214,mpi->comm[dir],&req[0]);
  if (mpi->ip[dir])                      MPI_Isend(sendbuf,Nsys*nvars,MPI_DOUBLE,mpi->ip[dir]-1,214,mpi->comm[dir],&req[1]);
  MPI_Status status_arr[2];
  MPI_Waitall(2,&req[0],status_arr);
  if (mpi->ip[dir] != mpi->iproc[dir]-1) for (d=0; d<Nsys*nvars; d++) F[d+Nsys*nvars*dim[dir]] = recvbuf[d];

#endif

  /* save the solution to fI */
#pragma omp parallel for schedule(auto) default(shared) private(sys,d,v,k,R,L,uavg,index_outer,indexC,indexI)
  for (sys=0; sys<Nsys; sys++) {
    _ArrayIndexnD_(ndims,sys,bounds_outer,index_outer,0);
    _ArrayCopy1D_(index_outer,indexI,ndims);
    for (indexI[dir] = 0; indexI[dir] < dim[dir]+1; indexI[dir]++) {
      int p; _ArrayIndex1D_(ndims,bounds_inter,indexI,0,p);
      _ArrayCopy1D_((F+sys*nvars+Nsys*nvars*indexI[dir]),(fI+nvars*p),nvars);
    }
  }

  return(0);
}