Actual source code: pipeImpls.c

      1: #include "pipe.h"

      3: /* Initial Function for PIPE       */
      4: /*-------------------------------- */
      5: /*
      6:      Q(x) = Q0 (constant)
      7:      H(x) = H0 - (R/gA) Q0*|Q0|* x
      8:  */
      9: /* ----------------------------------- */
     10: PetscErrorCode PipeComputeSteadyState(Pipe pipe, PetscScalar Q0, PetscScalar H0)
     11: {
     12:   DM           cda;
     13:   PipeField   *x;
     14:   PetscInt     i, start, n;
     15:   Vec          local;
     16:   PetscScalar *coords, c = pipe->R / (GRAV * pipe->A);

     18:   PetscFunctionBegin;
     19:   PetscCall(DMGetCoordinateDM(pipe->da, &cda));
     20:   PetscCall(DMGetCoordinatesLocal(pipe->da, &local));
     21:   PetscCall(DMDAVecGetArray(pipe->da, pipe->x, &x));
     22:   PetscCall(DMDAVecGetArrayRead(cda, local, &coords));
     23:   PetscCall(DMDAGetCorners(pipe->da, &start, 0, 0, &n, 0, 0));

     25:   for (i = start; i < start + n; i++) {
     26:     x[i].q = Q0;
     27:     x[i].h = H0 - c * Q0 * PetscAbsScalar(Q0) * coords[i];
     28:   }

     30:   PetscCall(DMDAVecRestoreArray(pipe->da, pipe->x, &x));
     31:   PetscCall(DMDAVecRestoreArrayRead(cda, local, &coords));
     32:   PetscFunctionReturn(PETSC_SUCCESS);
     33: }

     35: /* Function evaluations for PIPE    */
     36: /*-------------------------------- */
     37: /* consider using a one-sided higher order fd derivative at boundary. */
     38: static inline PetscScalar dqdx(PipeField *x, PetscInt i, PetscInt ilast, PetscReal dx)
     39: {
     40:   if (i == 0) {
     41:     return (x[i + 1].q - x[i].q) / dx;
     42:   } else if (i == ilast) {
     43:     return (x[i].q - x[i - 1].q) / dx;
     44:   } else {
     45:     return (x[i + 1].q - x[i - 1].q) / (2 * dx);
     46:   }
     47: }

     49: static inline PetscScalar dhdx(PipeField *x, PetscInt i, PetscInt ilast, PetscReal dx)
     50: {
     51:   if (i == 0) {
     52:     return (x[i + 1].h - x[i].h) / dx;
     53:   } else if (i == ilast) {
     54:     return (x[i].h - x[i - 1].h) / dx;
     55:   } else {
     56:     return (x[i + 1].h - x[i - 1].h) / (2 * dx);
     57:   }
     58: }

     60: PetscErrorCode PipeIFunctionLocal_Lax(DMDALocalInfo *info, PetscReal ptime, PipeField *x, PipeField *xdot, PetscScalar *f, Pipe pipe)
     61: {
     62:   PetscInt    i, start, n, ilast;
     63:   PetscReal   a = pipe->a, A = pipe->A, R = pipe->R, c = a * a / (GRAV * A);
     64:   PetscReal   dx = pipe->length / (info->mx - 1), dt = pipe->dt;
     65:   PetscScalar qavg, xold_i, ha, hb, qa, qb;
     66:   PipeField  *xold = pipe->xold;

     68:   PetscFunctionBegin;
     69:   PetscCall(DMDAGetCorners(pipe->da, &start, 0, 0, &n, 0, 0));

     71:   /* interior and boundary */
     72:   ilast = start + n - 1;
     73:   for (i = start + 1; i < start + n - 1; i++) {
     74:     qavg = (xold[i + 1].q + xold[i - 1].q) / 2.0;
     75:     qa   = xold[i - 1].q;
     76:     qb   = xold[i + 1].q;
     77:     ha   = xold[i - 1].h;
     78:     hb   = xold[i + 1].h;

     80:     /* xdot[i].q = (x[i].q - old_i)/dt */
     81:     xold_i             = 0.5 * (qa + qb);
     82:     f[2 * (i - 1) + 2] = (x[i].q - xold_i) + dt * (GRAV * pipe->A * dhdx(xold, i, ilast, dx) + pipe->R * qavg * PetscAbsScalar(qavg));

     84:     /* xdot[i].h = (x[i].h - xold_i)/dt */
     85:     xold_i             = 0.5 * (ha + hb);
     86:     f[2 * (i - 1) + 3] = (x[i].h - xold_i) + dt * c * dqdx(xold, i, ilast, dx);
     87:   }

     89:   /* Characteristic equations */
     90:   f[start + 1] = x[start].q - xold[start + 1].q - ((GRAV * A) / a) * (x[start].h - xold[start + 1].h) + dt * R * xold[start + 1].q * PetscAbsScalar(xold[start + 1].q);
     91:   f[2 * ilast] = x[ilast].q - xold[ilast - 1].q + ((GRAV * A) / a) * (x[ilast].h - xold[ilast - 1].h) + dt * R * xold[ilast - 1].q * PetscAbsScalar(xold[ilast - 1].q);
     92:   PetscFunctionReturn(PETSC_SUCCESS);
     93: }