#*------------------------------------------------------------------------------*
#* 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_reconstruction import SpatialReconstruction
[docs]
class WENO7(SpatialReconstruction):
''' Balsara & Shu - 2000 - '''
def __init__(self, nh: int, inactive_axis: List) -> None:
super(WENO7, self).__init__(nh=nh, inactive_axis=inactive_axis)
self.dr_ = [
[1/35, 12/35, 18/35, 4/35],
[4/35, 18/35, 12/35, 1/35],
]
self.cr_ = [
[[-1/4, 13/12, -23/12, 25/12], [1/12, -5/12, 13/12, 1/4], [-1/12, 7/12, 7/12, -1/12], [1/4, 13/12, -5/12, 1/12]],
[[1/12, -5/12, 13/12, 1/4], [-1/12, 7/12, 7/12, -1/12], [1/4, 13/12, -5/12, 1/12], [25/12, -23/12, 13/12, -1/4]],
]
self._stencil_size = 8
self._slices = [
[
[ jnp.s_[..., self.n-4+j:-self.n-3+j, self.nhy, self.nhz],
jnp.s_[..., self.n-3+j:-self.n-2+j, self.nhy, self.nhz],
jnp.s_[..., self.n-2+j:-self.n-1+j, self.nhy, self.nhz],
jnp.s_[..., self.n-1+j:-self.n+j , self.nhy, self.nhz],
jnp.s_[..., self.n+j :-self.n+1+j, self.nhy, self.nhz],
jnp.s_[..., self.n+1+j:-self.n+2+j, self.nhy, self.nhz],
jnp.s_[..., self.n+2+j:-self.n+3+j, self.nhy, self.nhz], ],
[ jnp.s_[..., self.nhx, self.n-4+j:-self.n-3+j, self.nhz],
jnp.s_[..., self.nhx, self.n-3+j:-self.n-2+j, self.nhz],
jnp.s_[..., self.nhx, self.n-2+j:-self.n-1+j, self.nhz],
jnp.s_[..., self.nhx, self.n-1+j:-self.n+j , self.nhz],
jnp.s_[..., self.nhx, self.n+j :-self.n+1+j, self.nhz],
jnp.s_[..., self.nhx, self.n+1+j:-self.n+2+j, self.nhz],
jnp.s_[..., self.nhx, self.n+2+j:-self.n+3+j, self.nhz], ],
[ jnp.s_[..., self.nhx, self.nhy, self.n-4+j:-self.n-3+j],
jnp.s_[..., self.nhx, self.nhy, self.n-3+j:-self.n-2+j],
jnp.s_[..., self.nhx, self.nhy, self.n-2+j:-self.n-1+j],
jnp.s_[..., self.nhx, self.nhy, self.n-1+j:-self.n+j ],
jnp.s_[..., self.nhx, self.nhy, self.n+j :-self.n+1+j],
jnp.s_[..., self.nhx, self.nhy, self.n+1+j:-self.n+2+j],
jnp.s_[..., self.nhx, self.nhy, self.n+2+j:-self.n+3+j], ]
] for j in range(2)]
# check whether upper slicing limit is 0
for j in range(2):
if -self.n + 3 + j == 0:
self._slices[j][0][-1] = jnp.s_[..., self.n+2+j:None, self.nhy, self.nhz]
self._slices[j][1][-1] = jnp.s_[..., self.nhx, self.n+2+j:None, self.nhz]
self._slices[j][2][-1] = jnp.s_[..., self.nhx, self.nhy, self.n+2+j:None]
[docs]
def set_slices_stencil(self) -> None:
self._slices = [
[
[ jnp.s_[..., 0+j, None:None, None:None],
jnp.s_[..., 1+j, None:None, None:None],
jnp.s_[..., 2+j, None:None, None:None],
jnp.s_[..., 3+j, None:None, None:None],
jnp.s_[..., 4+j, None:None, None:None],
jnp.s_[..., 5+j, None:None, None:None],
jnp.s_[..., 6+j, None:None, None:None], ],
[ jnp.s_[..., None:None, 0+j, None:None],
jnp.s_[..., None:None, 1+j, None:None],
jnp.s_[..., None:None, 2+j, None:None],
jnp.s_[..., None:None, 3+j, None:None],
jnp.s_[..., None:None, 4+j, None:None],
jnp.s_[..., None:None, 5+j, None:None],
jnp.s_[..., None:None, 6+j, None:None], ],
[ jnp.s_[..., None:None, None:None, 0+j],
jnp.s_[..., None:None, None:None, 1+j],
jnp.s_[..., None:None, None:None, 2+j],
jnp.s_[..., None:None, None:None, 3+j],
jnp.s_[..., None:None, None:None, 4+j],
jnp.s_[..., None:None, None:None, 5+j],
jnp.s_[..., None:None, None:None, 6+j], ],
] for j in range(2)]
[docs]
def reconstruct_xi(self, buffer: jnp.ndarray, axis: int, j: int, dx: float = None, **kwargs) -> jnp.ndarray:
s1_ = self._slices[j][axis]
beta_0 = buffer[s1_[0]] * (547 * buffer[s1_[0]] - 3882 * buffer[s1_[1]] + 4642 * buffer[s1_[2]] - 1854 * buffer[s1_[3]]) \
+ buffer[s1_[1]] * (7043 * buffer[s1_[1]] - 17246 * buffer[s1_[2]] + 7042 * buffer[s1_[3]]) \
+ buffer[s1_[2]] * (11003 * buffer[s1_[2]] - 9402 * buffer[s1_[3]]) \
+ buffer[s1_[3]] * (2107 * buffer[s1_[3]])
beta_1 = buffer[s1_[1]] * (267 * buffer[s1_[1]] - 1642 * buffer[s1_[2]] + 1602 * buffer[s1_[3]] - 494 * buffer[s1_[4]]) \
+ buffer[s1_[2]] * (2843 * buffer[s1_[2]] - 5966 * buffer[s1_[3]] + 1922 * buffer[s1_[4]]) \
+ buffer[s1_[3]] * (3443 * buffer[s1_[3]] - 2522 * buffer[s1_[4]]) \
+ buffer[s1_[4]] * (547 * buffer[s1_[4]])
beta_2 = buffer[s1_[2]] * (547 * buffer[s1_[2]] - 2522 * buffer[s1_[3]] + 1922 * buffer[s1_[4]] - 494 * buffer[s1_[5]]) \
+ buffer[s1_[3]] * (3443 * buffer[s1_[3]] - 5966 * buffer[s1_[4]] + 1602 * buffer[s1_[5]]) \
+ buffer[s1_[4]] * (2843 * buffer[s1_[4]] - 1642 * buffer[s1_[5]]) \
+ buffer[s1_[5]] * (267 * buffer[s1_[5]])
beta_3 = buffer[s1_[3]] * (2107 * buffer[s1_[3]] - 9402 * buffer[s1_[4]] + 7042 * buffer[s1_[5]] - 1854 * buffer[s1_[6]]) \
+ buffer[s1_[4]] * (11003 * buffer[s1_[4]] - 17246 * buffer[s1_[5]] + 4642 * buffer[s1_[6]]) \
+ buffer[s1_[5]] * (7043 * buffer[s1_[5]] - 3882 * buffer[s1_[6]]) \
+ buffer[s1_[6]] * (547 * buffer[s1_[6]])
one_beta_0_sq = 1.0 / ((self.eps + beta_0) * (self.eps + beta_0))
one_beta_1_sq = 1.0 / ((self.eps + beta_1) * (self.eps + beta_1))
one_beta_2_sq = 1.0 / ((self.eps + beta_2) * (self.eps + beta_2))
one_beta_3_sq = 1.0 / ((self.eps + beta_3) * (self.eps + beta_3))
alpha_0 = self.dr_[j][0] * one_beta_0_sq
alpha_1 = self.dr_[j][1] * one_beta_1_sq
alpha_2 = self.dr_[j][2] * one_beta_2_sq
alpha_3 = self.dr_[j][3] * one_beta_3_sq
one_alpha = 1.0 / (alpha_0 + alpha_1 + alpha_2 + alpha_3)
omega_0 = alpha_0 * one_alpha
omega_1 = alpha_1 * one_alpha
omega_2 = alpha_2 * one_alpha
omega_3 = alpha_3 * one_alpha
p_0 = self.cr_[j][0][0] * buffer[s1_[0]] + self.cr_[j][0][1] * buffer[s1_[1]] + self.cr_[j][0][2] * buffer[s1_[2]] + self.cr_[j][0][3] * buffer[s1_[3]]
p_1 = self.cr_[j][1][0] * buffer[s1_[1]] + self.cr_[j][1][1] * buffer[s1_[2]] + self.cr_[j][1][2] * buffer[s1_[3]] + self.cr_[j][1][3] * buffer[s1_[4]]
p_2 = self.cr_[j][2][0] * buffer[s1_[2]] + self.cr_[j][2][1] * buffer[s1_[3]] + self.cr_[j][2][2] * buffer[s1_[4]] + self.cr_[j][2][3] * buffer[s1_[5]]
p_3 = self.cr_[j][3][0] * buffer[s1_[3]] + self.cr_[j][3][1] * buffer[s1_[4]] + self.cr_[j][3][2] * buffer[s1_[5]] + self.cr_[j][3][3] * buffer[s1_[6]]
cell_state_xi_j = omega_0 * p_0 + omega_1 * p_1 + omega_2 * p_2 + omega_3 * p_3
return cell_state_xi_j