#*------------------------------------------------------------------------------*
#* 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 typing import List
import jax.numpy as jnp
from jaxfluids.stencils.spatial_derivative import SpatialDerivative
[docs]
class DerivativeFourthOrderFace(SpatialDerivative):
'''
4th order stencil for 1st derivative at the cell face
x
| | | | |
| i-1 | i | i+1 | i+2 |
| | | | |
'''
def __init__(self, nh: int, inactive_axis: List, offset: int = 0) -> None:
super(DerivativeFourthOrderFace, self).__init__(nh=nh, inactive_axis=inactive_axis, offset=offset)
self.s_ = [
[ jnp.s_[..., self.n-2:-self.n-1, self.nhy, self.nhz], # i-1
jnp.s_[..., self.n-1:-self.n , self.nhy, self.nhz], # i
jnp.s_[..., self.n :-self.n+1, self.nhy, self.nhz], # i+1
jnp.s_[..., jnp.s_[self.n+1:-self.n+2] if self.n != 2 else jnp.s_[self.n+1:None], self.nhy, self.nhz] ], # i+2
[ jnp.s_[..., self.nhx, self.n-2:-self.n-1, self.nhz],
jnp.s_[..., self.nhx, self.n-1:-self.n , self.nhz],
jnp.s_[..., self.nhx, self.n :-self.n+1, self.nhz],
jnp.s_[..., self.nhx, jnp.s_[self.n+1:-self.n+2] if self.n != 2 else jnp.s_[self.n+1:None], self.nhz] ],
[ jnp.s_[..., self.nhx, self.nhy, self.n-2:-self.n-1],
jnp.s_[..., self.nhx, self.nhy, self.n-1:-self.n ],
jnp.s_[..., self.nhx, self.nhy, self.n :-self.n+1],
jnp.s_[..., self.nhx, self.nhy, jnp.s_[self.n+1:-self.n+2] if self.n != 2 else jnp.s_[self.n+1:None]] ]
]
[docs]
def derivative_xi(self, primes: jnp.ndarray, dxi: jnp.ndarray, axis: int) -> jnp.ndarray:
s1_ = self.s_[axis]
deriv_xi = (1.0 / 24.0 / dxi) * (primes[s1_[0]] - 27.0 * primes[s1_[1]] + 27.0 * primes[s1_[2]] - primes[s1_[3]])
return deriv_xi