split advance into subfunctions
This commit is contained in:
Magnus Ulimoen
499
src/maxwell.rs
499
src/maxwell.rs
@@ -1,4 +1,5 @@
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use super::operators::SbpOperator;
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use super::Grid;
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use ndarray::prelude::*;
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use ndarray::{azip, Zip};
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@@ -96,11 +97,17 @@ impl Field {
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}
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}
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/// Solving (Au)_x + (Bu)_y
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/// with:
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/// A B
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/// [ 0, 0, 0] [ 0, 1, 0]
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/// [ 0, 0, -1] [ 1, 0, 0]
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/// [ 0, -1, 0] [ 0, 0, 0]
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pub(crate) fn advance<SBP>(
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&self,
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fut: &mut Self,
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dt: f32,
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grid: &super::Grid<SBP>,
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grid: &Grid<SBP>,
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work_buffers: Option<&mut WorkBuffers>,
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) where
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SBP: SbpOperator,
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@@ -131,248 +138,7 @@ impl Field {
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}
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};
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// Solving (Au)_x + (Bu)_y
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// with:
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// A B
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// [ 0, 0, 0] [ 0, 1, 0]
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// [ 0, 0, -1] [ 1, 0, 0]
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// [ 0, -1, 0] [ 0, 0, 0]
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// This flux is rotated by the grid metrics
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// (Au)_x + (Bu)_y = 1/J [
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// (J xi_x Au)_xi + (J eta_x Au)_eta
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// (J xi_y Bu)_xi + (J eta_y Bu)_eta
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// ]
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// where J is the grid determinant
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// ex = hz_y
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{
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ndarray::azip!((a in &mut tmp.0,
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&dxi_dy in &grid.detj_dxi_dy,
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&hz in &y.hz())
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*a = dxi_dy * hz
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);
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SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
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ndarray::azip!((b in &mut tmp.2,
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&deta_dy in &grid.detj_deta_dy,
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&hz in &y.hz())
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*b = deta_dy * hz
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);
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SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
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ndarray::azip!((flux in &mut k[i].ex_mut(), &ax in &tmp.1, &by in &tmp.3)
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*flux = ax + by
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);
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}
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{
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// hz = -ey_x + ex_y
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ndarray::azip!((a in &mut tmp.0,
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&dxi_dx in &grid.detj_dxi_dx,
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&dxi_dy in &grid.detj_dxi_dy,
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&ex in &y.ex(),
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&ey in &y.ey())
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*a = dxi_dx * -ey + dxi_dy * ex
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);
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SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
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ndarray::azip!((b in &mut tmp.2,
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&deta_dx in &grid.detj_deta_dx,
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&deta_dy in &grid.detj_deta_dy,
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&ex in &y.ex(),
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&ey in &y.ey())
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*b = deta_dx * -ey + deta_dy * ex
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);
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SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
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ndarray::azip!((flux in &mut k[i].hz_mut(), &ax in &tmp.1, &by in &tmp.3)
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*flux = ax + by
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);
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}
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// ey = -hz_x
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{
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ndarray::azip!((a in &mut tmp.0,
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&dxi_dx in &grid.detj_dxi_dx,
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&hz in &y.hz())
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*a = dxi_dx * -hz
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);
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SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
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azip!((b in &mut tmp.2,
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&deta_dx in &grid.detj_deta_dx,
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&hz in &y.hz())
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*b = deta_dx * -hz
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);
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SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
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azip!((flux in &mut k[i].ey_mut(), &ax in &tmp.1, &by in &tmp.3)
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*flux = ax + by
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);
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}
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// Boundary conditions (SAT)
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let ny = self.ny();
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let nx = self.nx();
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fn positive_flux(kx: f32, ky: f32) -> [[f32; 3]; 3] {
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let r = (kx * kx + ky * ky).sqrt();
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[
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[ky * ky / r / 2.0, ky / 2.0, -kx * ky / r / 2.0],
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[ky / 2.0, r / 2.0, -kx / 2.0],
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[-kx * ky / r / 2.0, -kx / 2.0, kx * kx / r / 2.0],
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]
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}
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fn negative_flux(kx: f32, ky: f32) -> [[f32; 3]; 3] {
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let r = (kx * kx + ky * ky).sqrt();
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[
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[-ky * ky / r / 2.0, ky / 2.0, kx * ky / r / 2.0],
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[ky / 2.0, -r / 2.0, -kx / 2.0],
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[kx * ky / r / 2.0, -kx / 2.0, -kx * kx / r / 2.0],
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]
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}
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let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
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let g = y.slice(s![.., .., 0]);
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let v = y.slice(s![.., .., nx - 1]);
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{
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// East boundary
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let mut k = k[i].slice_mut(s![.., .., nx - 1]);
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for j in 0..ny {
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// East boundary, positive flux
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let tau = -1.0;
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let v = (v[(0, j)], v[(1, j)], v[(2, j)]);
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let g = (g[(0, j)], g[(1, j)], g[(2, j)]);
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let kx = grid.detj_dxi_dx[(j, nx - 1)];
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let ky = grid.detj_dxi_dy[(j, nx - 1)];
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let plus = positive_flux(kx, ky);
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k[(0, j)] += tau
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* hinv
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* (plus[0][0] * (v.0 - g.0)
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+ plus[0][1] * (v.1 - g.1)
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+ plus[0][2] * (v.2 - g.2));
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k[(1, j)] += tau
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* hinv
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* (plus[1][0] * (v.0 - g.0)
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+ plus[1][1] * (v.1 - g.1)
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+ plus[1][2] * (v.2 - g.2));
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k[(2, j)] += tau
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* hinv
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* (plus[2][0] * (v.0 - g.0)
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+ plus[2][1] * (v.1 - g.1)
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+ plus[2][2] * (v.2 - g.2));
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}
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}
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{
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// West boundary, negative flux
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let mut k = k[i].slice_mut(s![.., .., 0]);
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let (v, g) = (g, v);
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for j in 0..ny {
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let tau = 1.0;
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let v = (v[(0, j)], v[(1, j)], v[(2, j)]);
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let g = (g[(0, j)], g[(1, j)], g[(2, j)]);
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let kx = grid.detj_dxi_dx[(j, 0)];
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let ky = grid.detj_dxi_dy[(j, 0)];
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let minus = negative_flux(kx, ky);
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k[(0, j)] += tau
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* hinv
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* (minus[0][0] * (v.0 - g.0)
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+ minus[0][1] * (v.1 - g.1)
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+ minus[0][2] * (v.2 - g.2));
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k[(1, j)] += tau
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* hinv
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* (minus[1][0] * (v.0 - g.0)
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+ minus[1][1] * (v.1 - g.1)
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+ minus[1][2] * (v.2 - g.2));
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k[(2, j)] += tau
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* hinv
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* (minus[2][0] * (v.0 - g.0)
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+ minus[2][1] * (v.1 - g.1)
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+ minus[2][2] * (v.2 - g.2));
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}
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}
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let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as f32);
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let g = y.slice(s![.., 0, ..]);
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let v = y.slice(s![.., ny - 1, ..]);
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{
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let mut k = k[i].slice_mut(s![.., ny - 1, ..]);
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for j in 0..nx {
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// North boundary, positive flux
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let tau = -1.0;
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let v = (v[(0, j)], v[(1, j)], v[(2, j)]);
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let g = (g[(0, j)], g[(1, j)], g[(2, j)]);
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let kx = grid.detj_deta_dx[(ny - 1, j)];
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let ky = grid.detj_deta_dy[(ny - 1, j)];
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let plus = positive_flux(kx, ky);
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k[(0, j)] += tau
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* hinv
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* (plus[0][0] * (v.0 - g.0)
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+ plus[0][1] * (v.1 - g.1)
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+ plus[0][2] * (v.2 - g.2));
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k[(1, j)] += tau
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* hinv
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* (plus[1][0] * (v.0 - g.0)
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+ plus[1][1] * (v.1 - g.1)
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+ plus[1][2] * (v.2 - g.2));
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k[(2, j)] += tau
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* hinv
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* (plus[2][0] * (v.0 - g.0)
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+ plus[2][1] * (v.1 - g.1)
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+ plus[2][2] * (v.2 - g.2));
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}
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}
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{
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let (v, g) = (g, v);
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let mut k = k[i].slice_mut(s![.., 0, ..]);
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for j in 0..nx {
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// South boundary, negative flux
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let tau = 1.0;
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let v = (v[(0, j)], v[(1, j)], v[(2, j)]);
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let g = (g[(0, j)], g[(1, j)], g[(2, j)]);
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let kx = grid.detj_deta_dx[(0, j)];
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let ky = grid.detj_deta_dy[(0, j)];
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let minus = negative_flux(kx, ky);
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k[(0, j)] += tau
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* hinv
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* (minus[0][0] * (v.0 - g.0)
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+ minus[0][1] * (v.1 - g.1)
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+ minus[0][2] * (v.2 - g.2));
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k[(1, j)] += tau
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* hinv
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* (minus[1][0] * (v.0 - g.0)
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+ minus[1][1] * (v.1 - g.1)
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+ minus[1][2] * (v.2 - g.2));
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k[(2, j)] += tau
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* hinv
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* (minus[2][0] * (v.0 - g.0)
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+ minus[2][1] * (v.1 - g.1)
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+ minus[2][2] * (v.2 - g.2));
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}
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}
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azip!((k in &mut k[i].0,
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&detj in &grid.detj.broadcast((3, ny, nx)).unwrap()) {
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*k /= detj;
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});
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RHS(&mut k[i], &y, grid, tmp);
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}
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Zip::from(&mut fut.0)
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@@ -387,6 +153,253 @@ impl Field {
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}
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}
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#[allow(non_snake_case)]
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/// This flux is rotated by the grid metrics
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/// (Au)_x + (Bu)_y = 1/J [
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/// (J xi_x Au)_xi + (J eta_x Au)_eta
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/// (J xi_y Bu)_xi + (J eta_y Bu)_eta
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/// ]
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/// where J is the grid determinant
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///
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/// This is used both in fluxes and SAT terms
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fn RHS<SBP: SbpOperator>(
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k: &mut Field,
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y: &Field,
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grid: &Grid<SBP>,
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tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
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) {
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fluxes(k, y, grid, tmp);
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SAT_characteristics(k, y, grid);
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azip!((k in &mut k.0,
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&detj in &grid.detj.broadcast((3, y.ny(), y.nx())).unwrap()) {
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*k /= detj;
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});
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}
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fn fluxes<SBP: SbpOperator>(
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k: &mut Field,
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y: &Field,
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grid: &Grid<SBP>,
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tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
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) {
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// ex = hz_y
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{
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ndarray::azip!((a in &mut tmp.0,
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&dxi_dy in &grid.detj_dxi_dy,
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&hz in &y.hz())
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*a = dxi_dy * hz
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);
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SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
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ndarray::azip!((b in &mut tmp.2,
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&deta_dy in &grid.detj_deta_dy,
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&hz in &y.hz())
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*b = deta_dy * hz
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);
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SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
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ndarray::azip!((flux in &mut k.ex_mut(), &ax in &tmp.1, &by in &tmp.3)
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*flux = ax + by
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);
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}
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{
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// hz = -ey_x + ex_y
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ndarray::azip!((a in &mut tmp.0,
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&dxi_dx in &grid.detj_dxi_dx,
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&dxi_dy in &grid.detj_dxi_dy,
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&ex in &y.ex(),
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&ey in &y.ey())
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*a = dxi_dx * -ey + dxi_dy * ex
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);
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SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
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ndarray::azip!((b in &mut tmp.2,
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&deta_dx in &grid.detj_deta_dx,
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&deta_dy in &grid.detj_deta_dy,
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&ex in &y.ex(),
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&ey in &y.ey())
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*b = deta_dx * -ey + deta_dy * ex
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);
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SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
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ndarray::azip!((flux in &mut k.hz_mut(), &ax in &tmp.1, &by in &tmp.3)
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*flux = ax + by
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);
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}
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// ey = -hz_x
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{
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ndarray::azip!((a in &mut tmp.0,
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&dxi_dx in &grid.detj_dxi_dx,
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&hz in &y.hz())
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*a = dxi_dx * -hz
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);
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SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
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azip!((b in &mut tmp.2,
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&deta_dx in &grid.detj_deta_dx,
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&hz in &y.hz())
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*b = deta_dx * -hz
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);
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SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
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azip!((flux in &mut k.ey_mut(), &ax in &tmp.1, &by in &tmp.3)
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*flux = ax + by
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);
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}
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}
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#[allow(non_snake_case)]
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fn SAT_characteristics<SBP: SbpOperator>(k: &mut Field, y: &Field, grid: &Grid<SBP>) {
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// Boundary conditions (SAT)
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let ny = y.ny();
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let nx = y.nx();
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fn positive_flux(kx: f32, ky: f32) -> [[f32; 3]; 3] {
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let r = (kx * kx + ky * ky).sqrt();
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[
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[ky * ky / r / 2.0, ky / 2.0, -kx * ky / r / 2.0],
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[ky / 2.0, r / 2.0, -kx / 2.0],
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[-kx * ky / r / 2.0, -kx / 2.0, kx * kx / r / 2.0],
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]
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}
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fn negative_flux(kx: f32, ky: f32) -> [[f32; 3]; 3] {
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let r = (kx * kx + ky * ky).sqrt();
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[
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[-ky * ky / r / 2.0, ky / 2.0, kx * ky / r / 2.0],
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[ky / 2.0, -r / 2.0, -kx / 2.0],
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[kx * ky / r / 2.0, -kx / 2.0, -kx * kx / r / 2.0],
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]
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}
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let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
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let g = y.slice(s![.., .., 0]);
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let v = y.slice(s![.., .., nx - 1]);
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{
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// East boundary
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let mut k = k.slice_mut(s![.., .., nx - 1]);
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for j in 0..ny {
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// East boundary, positive flux
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let tau = -1.0;
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let v = (v[(0, j)], v[(1, j)], v[(2, j)]);
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let g = (g[(0, j)], g[(1, j)], g[(2, j)]);
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let kx = grid.detj_dxi_dx[(j, nx - 1)];
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let ky = grid.detj_dxi_dy[(j, nx - 1)];
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let plus = positive_flux(kx, ky);
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k[(0, j)] += tau
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* hinv
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* (plus[0][0] * (v.0 - g.0) + plus[0][1] * (v.1 - g.1) + plus[0][2] * (v.2 - g.2));
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k[(1, j)] += tau
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* hinv
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* (plus[1][0] * (v.0 - g.0) + plus[1][1] * (v.1 - g.1) + plus[1][2] * (v.2 - g.2));
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||||
k[(2, j)] += tau
|
||||
* hinv
|
||||
* (plus[2][0] * (v.0 - g.0) + plus[2][1] * (v.1 - g.1) + plus[2][2] * (v.2 - g.2));
|
||||
}
|
||||
}
|
||||
{
|
||||
// West boundary, negative flux
|
||||
let mut k = k.slice_mut(s![.., .., 0]);
|
||||
let (v, g) = (g, v);
|
||||
for j in 0..ny {
|
||||
let tau = 1.0;
|
||||
|
||||
let v = (v[(0, j)], v[(1, j)], v[(2, j)]);
|
||||
let g = (g[(0, j)], g[(1, j)], g[(2, j)]);
|
||||
|
||||
let kx = grid.detj_dxi_dx[(j, 0)];
|
||||
let ky = grid.detj_dxi_dy[(j, 0)];
|
||||
|
||||
let minus = negative_flux(kx, ky);
|
||||
|
||||
k[(0, j)] += tau
|
||||
* hinv
|
||||
* (minus[0][0] * (v.0 - g.0)
|
||||
+ minus[0][1] * (v.1 - g.1)
|
||||
+ minus[0][2] * (v.2 - g.2));
|
||||
k[(1, j)] += tau
|
||||
* hinv
|
||||
* (minus[1][0] * (v.0 - g.0)
|
||||
+ minus[1][1] * (v.1 - g.1)
|
||||
+ minus[1][2] * (v.2 - g.2));
|
||||
k[(2, j)] += tau
|
||||
* hinv
|
||||
* (minus[2][0] * (v.0 - g.0)
|
||||
+ minus[2][1] * (v.1 - g.1)
|
||||
+ minus[2][2] * (v.2 - g.2));
|
||||
}
|
||||
}
|
||||
|
||||
let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as f32);
|
||||
let g = y.slice(s![.., 0, ..]);
|
||||
let v = y.slice(s![.., ny - 1, ..]);
|
||||
{
|
||||
let mut k = k.slice_mut(s![.., ny - 1, ..]);
|
||||
|
||||
for j in 0..nx {
|
||||
// North boundary, positive flux
|
||||
let tau = -1.0;
|
||||
let v = (v[(0, j)], v[(1, j)], v[(2, j)]);
|
||||
let g = (g[(0, j)], g[(1, j)], g[(2, j)]);
|
||||
|
||||
let kx = grid.detj_deta_dx[(ny - 1, j)];
|
||||
let ky = grid.detj_deta_dy[(ny - 1, j)];
|
||||
|
||||
let plus = positive_flux(kx, ky);
|
||||
|
||||
k[(0, j)] += tau
|
||||
* hinv
|
||||
* (plus[0][0] * (v.0 - g.0) + plus[0][1] * (v.1 - g.1) + plus[0][2] * (v.2 - g.2));
|
||||
k[(1, j)] += tau
|
||||
* hinv
|
||||
* (plus[1][0] * (v.0 - g.0) + plus[1][1] * (v.1 - g.1) + plus[1][2] * (v.2 - g.2));
|
||||
k[(2, j)] += tau
|
||||
* hinv
|
||||
* (plus[2][0] * (v.0 - g.0) + plus[2][1] * (v.1 - g.1) + plus[2][2] * (v.2 - g.2));
|
||||
}
|
||||
}
|
||||
|
||||
{
|
||||
let (v, g) = (g, v);
|
||||
let mut k = k.slice_mut(s![.., 0, ..]);
|
||||
for j in 0..nx {
|
||||
// South boundary, negative flux
|
||||
let tau = 1.0;
|
||||
let v = (v[(0, j)], v[(1, j)], v[(2, j)]);
|
||||
let g = (g[(0, j)], g[(1, j)], g[(2, j)]);
|
||||
|
||||
let kx = grid.detj_deta_dx[(0, j)];
|
||||
let ky = grid.detj_deta_dy[(0, j)];
|
||||
|
||||
let minus = negative_flux(kx, ky);
|
||||
|
||||
k[(0, j)] += tau
|
||||
* hinv
|
||||
* (minus[0][0] * (v.0 - g.0)
|
||||
+ minus[0][1] * (v.1 - g.1)
|
||||
+ minus[0][2] * (v.2 - g.2));
|
||||
k[(1, j)] += tau
|
||||
* hinv
|
||||
* (minus[1][0] * (v.0 - g.0)
|
||||
+ minus[1][1] * (v.1 - g.1)
|
||||
+ minus[1][2] * (v.2 - g.2));
|
||||
k[(2, j)] += tau
|
||||
* hinv
|
||||
* (minus[2][0] * (v.0 - g.0)
|
||||
+ minus[2][1] * (v.1 - g.1)
|
||||
+ minus[2][2] * (v.2 - g.2));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
pub struct WorkBuffers {
|
||||
y: Field,
|
||||
buf: [Field; 4],
|
||||
|
||||
Reference in New Issue
Block a user