#*------------------------------------------------------------------------------*
#* JAX-FLUIDS - *
#* *
#* A fully-differentiable CFD solver for compressible two-phase flows. *
#* Copyright (C) 2022 Deniz A. Bezgin, Aaron B. Buhendwa, Nikolaus A. Adams *
#* *
#* This program is free software: you can redistribute it and/or modify *
#* it under the terms of the GNU General Public License as published by *
#* the Free Software Foundation, either version 3 of the License, or *
#* (at your option) any later version. *
#* *
#* This program is distributed in the hope that it will be useful, *
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
#* GNU General Public License for more details. *
#* *
#* You should have received a copy of the GNU General Public License *
#* along with this program. If not, see <https://www.gnu.org/licenses/>. *
#* *
#*------------------------------------------------------------------------------*
#* *
#* CONTACT *
#* *
#* deniz.bezgin@tum.de // aaron.buhendwa@tum.de // nikolaus.adams@tum.de *
#* *
#*------------------------------------------------------------------------------*
#* *
#* Munich, April 15th, 2022 *
#* *
#*------------------------------------------------------------------------------*
import jax.numpy as jnp
from jaxfluids.domain_information import DomainInformation
from jaxfluids.materials.material_manager import MaterialManager
from jaxfluids.solvers.riemann_solvers.eigendecomposition import Eigendecomposition
from jaxfluids.stencils.spatial_reconstruction import SpatialReconstruction
from jaxfluids.utilities import get_fluxes_xi
[docs]
class FluxSplittingScheme:
"""Base class for the Flux-Splitting Scheme. The flux-splitting schemes
transforms conservative variables and physical fluxes into the characteristic
space, performs a flux-splitting in characteristic space, and transforms
the final flux back to physical space.
The eigenvalues - which are used according to the user-specified flux-splitting -
determine the numerical flux.
Details are given in Bezgin, Buhendwa, Adams - 2022 - JAX-FLUIDS.
"""
def __init__(self, material_manager: MaterialManager, domain_information: DomainInformation,
flux_splitting: str, reconstruction_stencil: SpatialReconstruction) -> None:
self.material_manager = material_manager
self.reconstruction_stencil = reconstruction_stencil
self.reconstruction_stencil.set_slices_stencil()
self.flux_splitting = flux_splitting
self.eigendecomposition = Eigendecomposition(self.material_manager, self.reconstruction_stencil._stencil_size, domain_information, flux_splitting=flux_splitting)
self.cell_sizes = domain_information.cell_sizes
[docs]
def compute_fluxes_xi(self, primes: jnp.ndarray, cons: jnp.ndarray, axis: int, **kwargs) -> jnp.ndarray:
"""Computes the numerical flux in axis direction.
:param primes: Buffer of primitive variables
:type primes: jnp.ndarray
:param cons: Buffer of primitive variables
:type cons: jnp.ndarray
:param axis: Spatial direction along which flux is calculated.
:type axis: int
:return: Numerical flux in axis direction.
:rtype: jnp.ndarray
"""
physical_flux = get_fluxes_xi(primes, cons, axis)
stencil_cons_window = self.eigendecomposition.get_stencil_window(cons, axis=axis)
stencil_prime_window = self.eigendecomposition.get_stencil_window(primes, axis=axis)
physical_flux_window = self.eigendecomposition.get_stencil_window(physical_flux, axis=axis)
right_eigs, left_eigs, eigvals = self.eigendecomposition.eigendecomp_cons(stencil_prime_window, axis=axis)
char = self.eigendecomposition.transformtochar(stencil_cons_window, left_eigs, axis=axis)
char_flux = self.eigendecomposition.transformtochar(physical_flux_window, left_eigs, axis=axis)
positive_char_flux = 0.5 * (char_flux + self.eigendecomposition.transformtochar(char, eigvals, axis))
negative_char_flux = 0.5 * (char_flux - self.eigendecomposition.transformtochar(char, eigvals, axis))
char_flux_xi_L = self.reconstruction_stencil.reconstruct_xi(positive_char_flux, axis, 0, dx=self.cell_sizes[axis])
char_flux_xi_R = self.reconstruction_stencil.reconstruct_xi(negative_char_flux, axis, 1, dx=self.cell_sizes[axis])
char_flux_xi = char_flux_xi_L + char_flux_xi_R
fluxes_xi = self.eigendecomposition.transformtophysical(char_flux_xi, right_eigs)
return fluxes_xi