1 #include "pipe.h" 2 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); 17 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)); 24 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 } 29 30 PetscCall(DMDAVecRestoreArray(pipe->da, pipe->x, &x)); 31 PetscCall(DMDAVecRestoreArrayRead(cda, local, &coords)); 32 PetscFunctionReturn(0); 33 } 34 35 /* Function evalutions 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 } 48 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 } 59 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; 67 68 PetscFunctionBegin; 69 PetscCall(DMDAGetCorners(pipe->da, &start, 0, 0, &n, 0, 0)); 70 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; 79 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)); 83 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 } 88 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(0); 93 } 94