def soln_momentum_density(face_mesh_velocity, outward_directed_normal_covector,
coords, time, dim):
return hydro.rest_mass_density(
coords, time, _soln_mean_velocity(dim), _soln_wave_vector(dim),
_soln_pressure, _soln_adiabatic_index,
_soln_perturbation_size) * hydro.spatial_velocity(
coords, time, _soln_mean_velocity(dim), _soln_wave_vector(dim),
_soln_pressure, _soln_adiabatic_index, _soln_perturbation_size)
def soln_energy_density(face_mesh_velocity, outward_directed_normal_covector,
coords, time, dim):
velocity = hydro.spatial_velocity(coords, time, _soln_mean_velocity(dim),
_soln_wave_vector(dim), _soln_pressure,
_soln_adiabatic_index,
_soln_perturbation_size)
int_energy = hydro.specific_internal_energy(coords, time,
_soln_mean_velocity(dim),
_soln_wave_vector(dim),
_soln_pressure,
_soln_adiabatic_index,
_soln_perturbation_size)
return hydro.rest_mass_density(
coords, time, _soln_mean_velocity(dim), _soln_wave_vector(dim),
_soln_pressure, _soln_adiabatic_index, _soln_perturbation_size) * (
0.5 * np.dot(velocity, velocity) + int_energy)
def soln_specific_enthalpy(coords, time):
return hydro.specific_enthalpy_relativistic(coords, time,
_soln_mean_velocity(),
_soln_wave_vector(),
_soln_pressure,
_soln_adiabatic_index,
_soln_perturbation_size)
def soln_flux_energy_density(face_mesh_velocity,
outward_directed_normal_covector, coords, time,
dim):
velocity = hydro.spatial_velocity(coords, time, _soln_mean_velocity(dim),
_soln_wave_vector(dim), _soln_pressure,
_soln_adiabatic_index,
_soln_perturbation_size)
pressure = hydro.pressure(coords, time, _soln_mean_velocity(dim),
_soln_wave_vector(dim), _soln_pressure,
_soln_adiabatic_index, _soln_perturbation_size)
return flux.energy_density_flux_impl(
soln_momentum_density(face_mesh_velocity,
outward_directed_normal_covector, coords, time,
dim),
soln_energy_density(face_mesh_velocity,
outward_directed_normal_covector, coords, time,
dim), velocity, pressure)
def soln_specific_internal_energy(face_mesh_velocity,
outward_directed_normal_covector, coords,
time, dim):
return hydro.specific_internal_energy(coords, time,
_soln_mean_velocity(dim),
_soln_wave_vector(dim),
_soln_pressure,
_soln_adiabatic_index,
_soln_perturbation_size)
def soln_tilde_d(face_mesh_velocity, outward_directed_normal_covector,
outward_directed_normal_vector, coords, time, dim):
rho = soln_rest_mass_density(face_mesh_velocity,
outward_directed_normal_covector,
outward_directed_normal_vector, coords, time,
dim)
W = hydro.lorentz_factor(coords, time, _soln_mean_velocity(dim),
_soln_wave_vector(dim), _soln_pressure,
_soln_adiabatic_index, _soln_perturbation_size)
# for smooth flow, sqrt_det_spatial_metric = 1
return rho * W
def soln_tilde_s(face_mesh_velocity, outward_directed_normal_covector,
outward_directed_normal_vector, coords, time, dim):
tilde_d = soln_tilde_d(face_mesh_velocity,
outward_directed_normal_covector,
outward_directed_normal_vector, coords, time, dim)
W = hydro.lorentz_factor(coords, time, _soln_mean_velocity(dim),
_soln_wave_vector(dim), _soln_pressure,
_soln_adiabatic_index, _soln_perturbation_size)
h = soln_specific_enthalpy(face_mesh_velocity,
outward_directed_normal_covector,
outward_directed_normal_vector, coords, time,
dim)
# for smooth flow, metric = identity ==> v_lower = v_upper
v_lower = soln_spatial_velocity(face_mesh_velocity,
outward_directed_normal_covector,
outward_directed_normal_vector, coords,
time, dim)
return tilde_d * W * h * v_lower
def soln_tilde_tau(face_mesh_velocity, outward_directed_normal_covector,
outward_directed_normal_vector, coords, time, dim):
rho = soln_rest_mass_density(face_mesh_velocity,
outward_directed_normal_covector,
outward_directed_normal_vector, coords, time,
dim)
eps = soln_specific_internal_energy(face_mesh_velocity,
outward_directed_normal_covector,
outward_directed_normal_vector, coords,
time, dim)
v = soln_spatial_velocity(face_mesh_velocity,
outward_directed_normal_covector,
outward_directed_normal_vector, coords, time,
dim)
v2 = v.dot(v)
W = hydro.lorentz_factor(coords, time, _soln_mean_velocity(dim),
_soln_wave_vector(dim), _soln_pressure,
_soln_adiabatic_index, _soln_perturbation_size)
# for smooth flow, sqrt_det_spatial_metric = 1
return W**2 * (rho * (eps + v2 * W / (W + 1.0)) + _soln_pressure * v2)
def soln_mass_density(coords, time):
return hydro.rest_mass_density(coords, time, _soln_mean_velocity(),
_soln_wave_vector(), _soln_pressure,
_soln_adiabatic_index,
_soln_perturbation_size)
def soln_specific_internal_energy(coords, time):
return hydro.specific_internal_energy(coords, time, _soln_mean_velocity(),
_soln_wave_vector(), _soln_pressure,
_soln_adiabatic_index,
_soln_perturbation_size)
def soln_lorentz_factor(coords, time):
return hydro.lorentz_factor(coords, time, _soln_mean_velocity(),
_soln_wave_vector(), _soln_pressure,
_soln_adiabatic_index, _soln_perturbation_size)