#*------------------------------------------------------------------------------*
#* 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 *
#* *
#*------------------------------------------------------------------------------*
from abc import ABC, abstractmethod
from typing import List
import jax.numpy as jnp
[docs]
class SpatialDerivative(ABC):
"""Abstract parent class for the computation of spatial derivatives.
Calculates either the first spatial derivative wrt to axis direction (derivative_xi),
or calculates the second spatial derivative wrt to axis1 and axis2 directions (
derivative_xi_xj).
"""
eps = jnp.finfo(jnp.float64).eps
def __init__(self, nh: int, inactive_axis: List, offset: int = 0) -> None:
self.n = nh - offset
self.nhx = jnp.s_[:] if "x" in inactive_axis else jnp.s_[self.n:-self.n]
self.nhy = jnp.s_[:] if "y" in inactive_axis else jnp.s_[self.n:-self.n]
self.nhz = jnp.s_[:] if "z" in inactive_axis else jnp.s_[self.n:-self.n]
self.eps = jnp.finfo(jnp.float64).eps
[docs]
@abstractmethod
def derivative_xi(self, buffer: jnp.ndarray, dxi: jnp.ndarray, axis: int) -> jnp.ndarray:
"""Calculates the derivative in the direction indicated by axis.
:param buffer: Buffer for which the derivative will be calculated
:type buffer: jnp.ndarray
:param dxi: Cell sizes along axis direction
:type dxi: jnp.ndarray
:param axis: Spatial axis along which derivative is calculated
:type axis: int
:return: Buffer with numerical derivative
:rtype: jnp.ndarray
"""
pass
[docs]
def derivative_xi_xj(self, buffer: jnp.ndarray, dxi: jnp.ndarray, dxj: jnp.ndarray, i: int, j: int) -> jnp.ndarray:
"""Calculates the second derivative in the directions indicated by i and j.
:param buffer: Buffer for which the second derivative will be calculated
:type buffer: jnp.ndarray
:param dxi: Cell sizes along i direction
:type dxi: jnp.ndarray
:param dxj: Cell sizes along j direction
:type dxj: jnp.ndarray
:param i: Spatial axis along which derivative is calculated
:type i: int
:param j: Spatial axis along which derivative is calculated
:type j: int
:return: Buffer with numerical derivative
:rtype: jnp.ndarray
"""
pass