// calculates the inverted flux, for testing purposes
// it should return the same thing as riemann_solver(), only with minus sign
void NumericalFlux::riemann_solver_invert(double result[4], double w_l[4], double w_r[4])
{
double m[4][4];
double _w_l[4];
double _w_r[4];
double _tmp[4];
T_rot(m, M_PI);
dot_vector(_w_l, m, w_l);
dot_vector(_w_r, m, w_r);
riemann_solver(_tmp, _w_r, _w_l);
T_rot(m, -M_PI);
dot_vector(result, m, _tmp);
}
// Calculates the numerical flux in the normal (nx, ny) by rotating into the
// local system, solving the Riemann problem and rotating back. It returns the
// state as a 4-component vector.
void NumericalFlux::numerical_flux(double result[4], double w_l[4], double w_r[4],
double nx, double ny)
{
double alpha = atan2(ny, nx);
double mat_rot[4][4];
double mat_rot_inv[4][4];
double w_l_local[4];
double w_r_local[4];
double flux_local[4];
T_rot(mat_rot, alpha);
T_rot(mat_rot_inv, -alpha);
dot_vector(w_l_local, mat_rot, w_l);
dot_vector(w_r_local, mat_rot, w_r);
riemann_solver(flux_local, w_l_local, w_r_local);
dot_vector(result, mat_rot_inv, flux_local);
}
static void riemann_solver(m2vol *VL, m2vol *VR, int axis, double *F,
int suppress_extrapolation)
{
int q;
m2riemann_problem R = { .m2 = VL->m2 };
double *UL = R.Ul;
double *UR = R.Ur;
double *FL = R.Fl;
double *FR = R.Fr;
double *lamL = R.lamL;
double *lamR = R.lamR;
double yl[8], yr[8]; /* cell-centered left/right interpolation variables */
double yL[8], yR[8]; /* face-centered left/right interpolation variables */
double xL = m2vol_coordinate_centroid(VL, axis);
double xR = m2vol_coordinate_centroid(VR, axis);
double *n = R.nhat;
m2prim *PL = &R.Pl;
m2prim *PR = &R.Pr;
m2aux *AL = &R.Al;
m2aux *AR = &R.Ar;
int err[6];
int E = 1;
if (suppress_extrapolation) E = 0;
if (VL->m2->suppress_extrapolation_at_unhealthy_zones) {
if (VL->zone_health != 0) E = 0;
if (VR->zone_health != 0) E = 0;
}
if (VL->zone_type == M2_ZONE_TYPE_SHELL ||
VR->zone_type == M2_ZONE_TYPE_SHELL) {
return;
}
n[0] = 0.0;
n[1] = 0.0;
n[2] = 0.0;
n[3] = 0.0;
n[axis] = 1.0;
m2vol_to_interpolated(VL, yl, 1);
m2vol_to_interpolated(VR, yr, 1);
switch (axis) {
case 1:
for (q=0; q<8; ++q) yL[q] = yl[q] + E*VL->grad1[q] * (VL->x1[1] - xL);
for (q=0; q<8; ++q) yR[q] = yr[q] + E*VR->grad1[q] * (VR->x0[1] - xR);
break;
case 2:
for (q=0; q<8; ++q) yL[q] = yl[q] + E*VL->grad2[q] * (VL->x1[2] - xL);
for (q=0; q<8; ++q) yR[q] = yr[q] + E*VR->grad2[q] * (VR->x0[2] - xR);
break;
case 3:
for (q=0; q<8; ++q) yL[q] = yl[q] + E*VL->grad3[q] * (VL->x1[3] - xL);
for (q=0; q<8; ++q) yR[q] = yr[q] + E*VR->grad3[q] * (VR->x0[3] - xR);
break;
}
m2sim_from_interpolated(VL->m2, yL, PL);
m2sim_from_interpolated(VR->m2, yR, PR);
UL[B11] = PL->B1;
UL[B22] = PL->B2;
UL[B33] = PL->B3;
UR[B11] = PR->B1;
UR[B22] = PR->B2;
UR[B33] = PR->B3;
switch (axis) {
case 1: UL[B11] = UR[B11] = PL->B1 = PR->B1 = VL->Bflux1A / VL->area1; break;
case 2: UL[B22] = UR[B22] = PL->B2 = PR->B2 = VL->Bflux2A / VL->area2; break;
case 3: UL[B33] = UR[B33] = PL->B3 = PR->B3 = VL->Bflux3A / VL->area3; break;
}
err[0] = m2sim_from_primitive(VL->m2, PL, NULL, NULL, 1.0, UL, AL);
err[1] = m2sim_from_primitive(VR->m2, PR, NULL, NULL, 1.0, UR, AR);
err[2] = m2aux_eigenvalues(AL, n, lamL);
err[3] = m2aux_eigenvalues(AR, n, lamR);
err[4] = m2aux_fluxes(AL, n, FL);
err[5] = m2aux_fluxes(AR, n, FR);
if (err[2]) VL->zone_health |= (1<<M2_BIT_BAD_EIGENVALUES);
if (err[3]) VR->zone_health |= (1<<M2_BIT_BAD_EIGENVALUES);
if (err[2] || err[3]) {
if (suppress_extrapolation) {
MSGF(INFO, "eigenvalues for %d-interface [%d %d %d] could not be found",
axis, VL->global_index[1], VL->global_index[2], VL->global_index[3]);
lamL[0] = -1.0;
lamL[7] = +1.0;
lamR[0] = -1.0;
lamR[7] = +1.0;
}
else {
riemann_solver(VL, VR, axis, F, 1);
return;
}
}
R.Sl = M2_MIN3(lamL[0], lamR[0], 0.0);
R.Sr = M2_MAX3(lamL[7], lamR[7], 0.0);
switch (VL->m2->riemann_solver) {
case M2_RIEMANN_HLLE: riemann_solver_hlle(&R); break;
case M2_RIEMANN_HLLC: riemann_solver_hllc(&R); break;
default: MSG(FATAL, "invalid riemann solver"); break;
}
memcpy(F, R.F_hat, 8 * sizeof(double));
}
static double plm_gradient(double *xs, double *fs, double plm)
{
#define minval3(a,b,c) ((a<b) ? ((a<c) ? a : c) : ((b<c) ? b : c))
#define sign(x) ((x > 0.0) - (x < 0.0))
double xL = xs[0];
double x0 = xs[1];
double xR = xs[2];
double yL = fs[0];
double y0 = fs[1];
double yR = fs[2];
double a = (yL - y0) / (xL - x0) * plm;
double b = (yL - yR) / (xL - xR);
double c = (y0 - yR) / (x0 - xR) * plm;
double sa = sign(a), sb = sign(b), sc = sign(c);
double fa = fabs(a), fb = fabs(b), fc = fabs(c);
double g = 0.25 * fabs(sa + sb) * (sa + sc) * minval3(fa, fb, fc);
if (g != g) {
MSGF(FATAL, "got NAN gradient: [%f %f %f] [%f %f %f]",
xs[0], xs[1], xs[2], fs[0], fs[1], fs[2]);
}
return g;
#undef minval3
#undef sign
}
int m2sim_calculate_flux(m2sim *m2)
{
int i, j, k;
int *L = m2->local_grid_size;
int *G = m2->domain_resolution;
m2vol *V0, *V1, *V2, *V3;
double n1[4] = { 0.0, 1.0, 0.0, 0.0 };
double n2[4] = { 0.0, 0.0, 1.0, 0.0 };
double n3[4] = { 0.0, 0.0, 0.0, 1.0 };
#ifdef _OPENMP
#pragma omp parallel for private(V0,V1,V2,V3,j,k)
#endif
for (i=0; i<L[1]; ++i) {
for (j=0; j<L[2]; ++j) {
for (k=0; k<L[3]; ++k) {
V0 = M2_VOL(i+0, j+0, k+0);
V1 = M2_VOL(i+1, j+0, k+0);
V2 = M2_VOL(i+0, j+1, k+0);
V3 = M2_VOL(i+0, j+0, k+1);
if (V1 == NULL) m2aux_fluxes(&V0->aux, n1, V0->flux1);
else riemann_solver(V0, V1, 1, V0->flux1, 0);
if (V2 == NULL) m2aux_fluxes(&V0->aux, n2, V0->flux2);
else riemann_solver(V0, V2, 2, V0->flux2, 0);
if (V3 == NULL) m2aux_fluxes(&V0->aux, n3, V0->flux3);
else riemann_solver(V0, V3, 3, V0->flux3, 0);
}
}
}
for (i=0; i<L[1]; ++i) {
for (j=0; j<L[2]; ++j) {
for (k=0; k<L[3]; ++k) {
V0 = M2_VOL(i, j, k);
if (m2->periodic_dimension[1] == 0 &&
(V0->global_index[1] == -1 ||
V0->global_index[1] == G[1] - 1)) {
if (m2->boundary_conditions_flux1) {
m2->boundary_conditions_flux1(V0);
}
}
if (m2->periodic_dimension[2] == 0 &&
(V0->global_index[2] == -1 ||
V0->global_index[2] == G[2] - 1)) {
if (m2->boundary_conditions_flux2) {
m2->boundary_conditions_flux2(V0);
}
}
if (m2->periodic_dimension[3] == 0 &&
(V0->global_index[3] == -1 ||
V0->global_index[3] == G[3] - 1)) {
if (m2->boundary_conditions_flux3) {
m2->boundary_conditions_flux3(V0);
}
}
}
}
}
return 0;
}