"""
Hydrodynamic fluid equations: conversions between primitive and conserved
states and the basic thermodynamic relations (pressure, internal energy, total
energy and sound speed) for the (ideal-gas) Euler equations.
"""
# general
from functools import partial
# typing
from typing import Union
from jaxtyping import Array, Float, jaxtyped
from beartype import beartype as typechecker
# jax
import jax
import jax.numpy as jnp
# astronomix constants
from astronomix.option_classes.simulation_config import (
FIELD_TYPE,
STATE_TYPE,
)
# astronomix containers
from astronomix.option_classes.simulation_config import SimulationConfig
from astronomix.variable_registry.registered_variables import RegisteredVariables
from astronomix.option_classes.simulation_params import SimulationParams
# astronomix functions
from astronomix._modules._cosmic_rays.cr_fluid_equations import (
total_energy_from_primitives_with_crs,
total_pressure_from_conserved_with_crs,
)
# @jaxtyped(typechecker=typechecker)
[docs]
@partial(jax.jit, static_argnames=["config", "registered_variables"])
def primitive_state_from_conserved(
conserved_state: STATE_TYPE,
gamma: Union[float, Float[Array, ""]],
config: SimulationConfig,
registered_variables: RegisteredVariables,
) -> STATE_TYPE:
"""Convert the conserved state to the primitive state.
Args:
conserved_state: The conserved state.
gamma: The adiabatic index of the fluid.
Returns:
The primitive state.
"""
# The conserved variables share the same registry indices as the primitive
# ones, so velocity and momentum density (and pressure and energy) occupy the
# same slot; we read the conserved values out and overwrite them in place.
rho = conserved_state[registered_variables.density_index]
E = conserved_state[registered_variables.pressure_index]
if config.dimensionality == 1:
u = conserved_state[registered_variables.velocity_index] / rho
elif config.dimensionality == 2:
ux = conserved_state[registered_variables.velocity_index.x] / rho
uy = conserved_state[registered_variables.velocity_index.y] / rho
# The 1e-20 offset keeps the gradient of sqrt finite at u = 0, where
# d/dx sqrt(0) would otherwise be infinite. TODO: find a cleaner way.
u = jnp.sqrt(ux**2 + uy**2 + 1e-20)
elif config.dimensionality == 3:
ux = conserved_state[registered_variables.velocity_index.x] / rho
uy = conserved_state[registered_variables.velocity_index.y] / rho
uz = conserved_state[registered_variables.velocity_index.z] / rho
u = jnp.sqrt(ux**2 + uy**2 + uz**2 + 1e-20)
p = pressure_from_energy(E, rho, u, gamma)
if registered_variables.cosmic_ray_n_active:
p = total_pressure_from_conserved_with_crs(
conserved_state, registered_variables
)
else:
p = pressure_from_energy(E, rho, u, gamma)
# Write the recovered pressure and velocities into the primitive state.
primitive_state = conserved_state.at[registered_variables.pressure_index].set(p)
if config.dimensionality == 1:
primitive_state = primitive_state.at[registered_variables.velocity_index].set(u)
elif config.dimensionality == 2:
primitive_state = primitive_state.at[registered_variables.velocity_index.x].set(
ux
)
primitive_state = primitive_state.at[registered_variables.velocity_index.y].set(
uy
)
elif config.dimensionality == 3:
primitive_state = primitive_state.at[registered_variables.velocity_index.x].set(
ux
)
primitive_state = primitive_state.at[registered_variables.velocity_index.y].set(
uy
)
primitive_state = primitive_state.at[registered_variables.velocity_index.z].set(
uz
)
# All other variables (e.g. the mass density) coincide between the primitive
# and conserved representations, so they are left untouched.
return primitive_state
# -------------------------------------------------------------
# =============== ↓ Create the conserved state ↓ ==============
# -------------------------------------------------------------
# @jaxtyped(typechecker=typechecker)
[docs]
@partial(jax.jit, static_argnames=["config", "registered_variables"])
def conserved_state_from_primitive(
primitive_state: STATE_TYPE,
gamma: Union[float, Float[Array, ""]],
config: SimulationConfig,
registered_variables: RegisteredVariables,
) -> STATE_TYPE:
"""Convert the primitive state to the conserved state.
Args:
primitive_state: The primitive state.
gamma: The adiabatic index of the fluid.
Returns:
The conserved state.
"""
rho = primitive_state[registered_variables.density_index]
u = get_absolute_velocity(primitive_state, config, registered_variables)
p = primitive_state[registered_variables.pressure_index]
if registered_variables.cosmic_ray_n_active:
E = total_energy_from_primitives_with_crs(primitive_state, registered_variables)
else:
E = total_energy_from_primitives(rho, u, p, gamma)
conserved_state = primitive_state.at[registered_variables.pressure_index].set(E)
if config.dimensionality == 1:
conserved_state = conserved_state.at[registered_variables.velocity_index].set(
rho * primitive_state[registered_variables.velocity_index]
)
elif config.dimensionality == 2:
conserved_state = conserved_state.at[registered_variables.velocity_index.x].set(
rho * primitive_state[registered_variables.velocity_index.x]
)
conserved_state = conserved_state.at[registered_variables.velocity_index.y].set(
rho * primitive_state[registered_variables.velocity_index.y]
)
elif config.dimensionality == 3:
conserved_state = conserved_state.at[registered_variables.velocity_index.x].set(
rho * primitive_state[registered_variables.velocity_index.x]
)
conserved_state = conserved_state.at[registered_variables.velocity_index.y].set(
rho * primitive_state[registered_variables.velocity_index.y]
)
conserved_state = conserved_state.at[registered_variables.velocity_index.z].set(
rho * primitive_state[registered_variables.velocity_index.z]
)
else:
raise ValueError("Invalid dimension.")
return conserved_state
# -------------------------------------------------------------
# =============== ↑ Create the conserved state ↑ ==============
# -------------------------------------------------------------
# -------------------------------------------------------------
# ===================== ↓ Fluid physics ↓ =====================
# -------------------------------------------------------------
# @jaxtyped(typechecker=typechecker)
[docs]
@partial(jax.jit, static_argnames=["config", "registered_variables"])
def get_absolute_velocity(
primitive_state: STATE_TYPE,
config: SimulationConfig,
registered_variables: RegisteredVariables,
) -> Union[
Float[Array, "num_cells"],
Float[Array, "num_cells_x num_cells_y"],
Float[Array, "num_cells_x num_cells_y num_cells_z"],
]:
"""Get the absolute velocity of the fluid.
Args:
primitive_state: The primitive state of the fluid.
config: The simulation configuration.
registered_variables: The registered variables.
Returns:
The absolute velocity.
"""
if config.dimensionality == 1:
return jnp.abs(primitive_state[registered_variables.velocity_index])
elif config.dimensionality == 2:
return jnp.sqrt(
primitive_state[registered_variables.velocity_index.x] ** 2
+ primitive_state[registered_variables.velocity_index.y] ** 2
+ 1e-20
)
elif config.dimensionality == 3:
return jnp.sqrt(
primitive_state[registered_variables.velocity_index.x] ** 2
+ primitive_state[registered_variables.velocity_index.y] ** 2
+ primitive_state[registered_variables.velocity_index.z] ** 2
+ 1e-20
)
else:
raise ValueError("Invalid dimension.")
[docs]
@jax.jit
def pressure_from_internal_energy(e, rho, gamma):
"""
Calculate the pressure from the internal energy.
Args:
e: The internal energy.
rho: The density.
gamma: The adiabatic index.
Returns:
The pressure.
"""
return (gamma - 1) * rho * e
[docs]
@jax.jit
def internal_energy_from_energy(E, rho, u):
"""Calculate the internal energy from the total energy.
Args:
E: The total energy.
rho: The density.
u: The velocity.
Returns:
The internal energy.
"""
return E / rho - 0.5 * u**2
[docs]
@jax.jit
def pressure_from_energy(E, rho, u, gamma):
"""Calculate the pressure from the total energy.
Args:
E: The total energy.
rho: The density.
u: The velocity.
gamma: The adiabatic index.
Returns:
The pressure.
"""
e = internal_energy_from_energy(E, rho, u)
return pressure_from_internal_energy(e, rho, gamma)
[docs]
@jax.jit
def total_energy_from_primitives(rho, u, p, gamma):
"""Calculate the total energy from the primitive variables.
Args:
rho: The density.
u: The velocity.
p: The pressure.
gamma: The adiabatic index.
Returns:
The total energy.
"""
return p / (gamma - 1) + 0.5 * rho * u**2
[docs]
@jax.jit
def speed_of_sound(rho, p, gamma):
"""Calculate the speed of sound.
Args:
rho: The density.
p: The pressure.
gamma: The adiabatic index.
Returns:
The speed of sound.
"""
return jnp.sqrt(gamma * p / rho)
# -------------------------------------------------------------
# ===================== ↑ Fluid physics ↑ =====================
# -------------------------------------------------------------
