13                            "                rho_t     + (rho*u)_x             = 0\n"
14                            "                (rho*u)_t + (rho*u^2 + c^2*rho)_x = 0\n"
647  * z = sqrt(rho*bulk), c = sqrt(rho/bulk)
658   PetscReal c; /* speed of sound: c = sqrt(bulk/rho) */
659   PetscReal z; /* impedance: z = sqrt(rho*bulk) */
777 …PetscCall(PetscOptionsReal("-physics_acoustics_c", "c = sqrt(bulk/rho)", "", user->c, &user->c, NU…  in PhysicsCreate_Acoustics()
778 …PetscCall(PetscOptionsReal("-physics_acoustics_z", "z = sqrt(bulk*rho)", "", user->z, &user->z, NU…  in PhysicsCreate_Acoustics()
873     PetscScalar rho, u;  in PhysicsRiemann_IsoGas_Exact()  member
878 …PetscCheck(L.rho > 0 && R.rho > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Reconstructed densi…  in PhysicsRiemann_IsoGas_Exact()
881     PetscScalar res, tmp, rho = 0.5 * (L.rho + R.rho); /* initial guess */  in PhysicsRiemann_IsoGas_Exact()  local
884       fl  = (L.rho < rho) ? (rho - L.rho) / PetscSqrtScalar(L.rho * rho) /* shock */  in PhysicsRiemann_IsoGas_Exact()
885                           : PetscLogScalar(rho) - PetscLogScalar(L.rho); /* rarefaction */  in PhysicsRiemann_IsoGas_Exact()
886       fr  = (R.rho < rho) ? (rho - R.rho) / PetscSqrtScalar(R.rho * rho) /* shock */  in PhysicsRiemann_IsoGas_Exact()
887                           : PetscLogScalar(rho) - PetscLogScalar(R.rho); /* rarefaction */  in PhysicsRiemann_IsoGas_Exact()
891         star.rho = rho;  in PhysicsRiemann_IsoGas_Exact()
895 …dfl = (L.rho < rho) ? 1 / PetscSqrtScalar(L.rho * rho) * (1 - 0.5 * (rho - L.rho) / rho) : 1 / rho;  in PhysicsRiemann_IsoGas_Exact()
896 …dfr = (R.rho < rho) ? 1 / PetscSqrtScalar(R.rho * rho) * (1 - 0.5 * (rho - R.rho) / rho) : 1 / rho;  in PhysicsRiemann_IsoGas_Exact()
897       tmp = rho - res / (c * (dfr + dfl));  in PhysicsRiemann_IsoGas_Exact()
898       if (tmp <= 0) rho /= 2; /* Guard against Newton shooting off to a negative density */  in PhysicsRiemann_IsoGas_Exact()
899       else rho = tmp;  in PhysicsRiemann_IsoGas_Exact()
900 …PetscCheck((rho > 0) && PetscIsNormalScalar(rho), PETSC_COMM_SELF, PETSC_ERR_FP, "non-normal itera…  in PhysicsRiemann_IsoGas_Exact()
902 …SETERRQ(PETSC_COMM_SELF, PETSC_ERR_CONV_FAILED, "Newton iteration for star.rho diverged after %" P…  in PhysicsRiemann_IsoGas_Exact()
907     ufan[0] = L.rho * PetscExpScalar(L.u / c - 1);  in PhysicsRiemann_IsoGas_Exact()
912     ufan[0] = R.rho * PetscExpScalar(-R.u / c - 1);  in PhysicsRiemann_IsoGas_Exact()
915 …} else if ((L.rho >= star.rho && L.u - c >= 0) || (L.rho < star.rho && (star.rho * star.u - L.rho …  in PhysicsRiemann_IsoGas_Exact()
918 …} else if ((star.rho <= R.rho && R.u + c <= 0) || (star.rho > R.rho && (R.rho * R.u - star.rho * s…  in PhysicsRiemann_IsoGas_Exact()
922     ustar[0] = star.rho;  in PhysicsRiemann_IsoGas_Exact()
923     ustar[1] = star.rho * star.u;  in PhysicsRiemann_IsoGas_Exact()
935     PetscScalar rho, u;  in PhysicsRiemann_IsoGas_Rusanov()  member
939 …PetscCheck(L.rho > 0 && R.rho > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Reconstructed densi…  in PhysicsRiemann_IsoGas_Rusanov()