576 lines
16 KiB
Rust
576 lines
16 KiB
Rust
use super::grid::Grid;
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use super::integrate;
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use super::operators::{SbpOperator, UpwindOperator};
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use ndarray::azip;
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use ndarray::prelude::*;
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#[derive(Clone, Debug)]
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pub struct Field(pub(crate) Array3<f32>);
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impl std::ops::Deref for Field {
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type Target = Array3<f32>;
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fn deref(&self) -> &Self::Target {
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&self.0
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}
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}
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impl std::ops::DerefMut for Field {
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fn deref_mut(&mut self) -> &mut Self::Target {
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&mut self.0
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}
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}
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impl Field {
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pub fn new(height: usize, width: usize) -> Self {
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let field = Array3::zeros((3, height, width));
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Self(field)
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}
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pub fn nx(&self) -> usize {
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self.0.shape()[2]
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}
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pub fn ny(&self) -> usize {
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self.0.shape()[1]
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}
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pub fn ex(&self) -> ArrayView2<f32> {
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self.slice(s![0, .., ..])
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}
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pub fn hz(&self) -> ArrayView2<f32> {
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self.slice(s![1, .., ..])
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}
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pub fn ey(&self) -> ArrayView2<f32> {
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self.slice(s![2, .., ..])
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}
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pub fn ex_mut(&mut self) -> ArrayViewMut2<f32> {
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self.slice_mut(s![0, .., ..])
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}
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pub fn hz_mut(&mut self) -> ArrayViewMut2<f32> {
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self.slice_mut(s![1, .., ..])
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}
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pub fn ey_mut(&mut self) -> ArrayViewMut2<f32> {
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self.slice_mut(s![2, .., ..])
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}
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pub fn components_mut(
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&mut self,
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) -> (ArrayViewMut2<f32>, ArrayViewMut2<f32>, ArrayViewMut2<f32>) {
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let mut iter = self.0.outer_iter_mut();
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let ex = iter.next().unwrap();
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let hz = iter.next().unwrap();
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let ey = iter.next().unwrap();
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assert_eq!(iter.next(), None);
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(ex, hz, ey)
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}
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}
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#[derive(Debug, Clone)]
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pub struct System<SBP: SbpOperator> {
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sys: (Field, Field),
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wb: WorkBuffers,
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grid: Grid<SBP>,
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}
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impl<SBP: SbpOperator> System<SBP> {
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pub fn new(x: Array2<f32>, y: Array2<f32>) -> Self {
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assert_eq!(x.shape(), y.shape());
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let ny = x.shape()[0];
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let nx = x.shape()[1];
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let grid = Grid::new(x, y).unwrap();
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Self {
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sys: (Field::new(ny, nx), Field::new(ny, nx)),
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grid,
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wb: WorkBuffers::new(ny, nx),
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}
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}
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pub fn field(&self) -> &Field {
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&self.sys.0
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}
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pub fn set_gaussian(&mut self, x0: f32, y0: f32) {
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let (ex, hz, ey) = self.sys.0.components_mut();
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ndarray::azip!(
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(ex in ex, hz in hz, ey in ey,
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&x in &self.grid.x, &y in &self.grid.y)
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{
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*ex = 0.0;
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*ey = 0.0;
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*hz = gaussian(x, x0, y, y0)/32.0;
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});
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}
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pub fn advance(&mut self, dt: f32) {
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integrate::rk4(
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RHS,
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&self.sys.0,
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&mut self.sys.1,
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dt,
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&self.grid,
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&mut self.wb.k,
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&mut self.wb.tmp,
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);
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std::mem::swap(&mut self.sys.0, &mut self.sys.1);
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}
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}
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impl<UO: UpwindOperator> System<UO> {
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/// Using artificial dissipation with the upwind operator
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pub fn advance_upwind(&mut self, dt: f32) {
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integrate::rk4(
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RHS_upwind,
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&self.sys.0,
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&mut self.sys.1,
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dt,
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&self.grid,
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&mut self.wb.k,
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&mut self.wb.tmp,
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);
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std::mem::swap(&mut self.sys.0, &mut self.sys.1);
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}
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}
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fn gaussian(x: f32, x0: f32, y: f32, y0: f32) -> f32 {
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use std::f32;
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let x = x - x0;
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let y = y - y0;
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let sigma = 0.05;
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1.0 / (2.0 * f32::consts::PI * sigma * sigma) * (-(x * x + y * y) / (2.0 * sigma * sigma)).exp()
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}
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#[allow(non_snake_case)]
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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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///
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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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let boundaries = BoundaryTerms {
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north: Boundary::This,
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south: Boundary::This,
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west: Boundary::This,
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east: Boundary::This,
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};
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SAT_characteristics(k, y, grid, &boundaries);
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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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#[allow(non_snake_case)]
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fn RHS_upwind<UO: UpwindOperator>(
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k: &mut Field,
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y: &Field,
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grid: &Grid<UO>,
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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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dissipation(k, y, grid, tmp);
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let boundaries = BoundaryTerms {
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north: Boundary::This,
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south: Boundary::This,
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west: Boundary::This,
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east: Boundary::This,
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};
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SAT_characteristics(k, y, grid, &boundaries);
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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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fn dissipation<UO: UpwindOperator>(
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k: &mut Field,
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y: &Field,
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grid: &Grid<UO>,
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tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
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) {
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// ex component
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{
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ndarray::azip!((a in &mut tmp.0,
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&kx in &grid.detj_dxi_dx,
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&ky 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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let r = f32::hypot(kx, ky);
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*a = ky*ky/r * ex + -kx*ky/r*ey;
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});
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UO::dissxi(tmp.0.view(), tmp.1.view_mut());
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ndarray::azip!((b in &mut tmp.2,
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&kx in &grid.detj_deta_dx,
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&ky 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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let r = f32::hypot(kx, ky);
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*b = ky*ky/r * ex + -kx*ky/r*ey;
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});
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UO::disseta(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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// hz component
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{
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ndarray::azip!((a in &mut tmp.0,
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&kx in &grid.detj_dxi_dx,
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&ky in &grid.detj_dxi_dy,
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&hz in &y.hz()) {
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let r = f32::hypot(kx, ky);
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*a = r * hz;
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});
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UO::dissxi(tmp.0.view(), tmp.1.view_mut());
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ndarray::azip!((b in &mut tmp.2,
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&kx in &grid.detj_deta_dx,
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&ky in &grid.detj_deta_dy,
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&hz in &y.hz()) {
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let r = f32::hypot(kx, ky);
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*b = r * hz;
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});
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UO::disseta(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
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{
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ndarray::azip!((a in &mut tmp.0,
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&kx in &grid.detj_dxi_dx,
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&ky 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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let r = f32::hypot(kx, ky);
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*a = -kx*ky/r * ex + kx*kx/r*ey;
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});
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UO::dissxi(tmp.0.view(), tmp.1.view_mut());
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ndarray::azip!((b in &mut tmp.2,
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&kx in &grid.detj_deta_dx,
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&ky 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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let r = f32::hypot(kx, ky);
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*b = -kx*ky/r * ex + kx*kx/r*ey;
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});
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UO::disseta(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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}
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#[derive(Clone, Debug)]
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pub enum Boundary {
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This,
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}
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#[derive(Clone, Debug)]
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pub struct BoundaryTerms {
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pub north: Boundary,
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pub south: Boundary,
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pub east: Boundary,
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pub west: Boundary,
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}
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#[allow(non_snake_case)]
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/// Boundary conditions (SAT)
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fn SAT_characteristics<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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boundaries: &BoundaryTerms,
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) {
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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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{
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let g = match boundaries.east {
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Boundary::This => y.slice(s![.., .., 0]),
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};
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// East boundary
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let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
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for ((((mut k, v), g), &kx), &ky) in k
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.slice_mut(s![.., .., nx - 1])
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.gencolumns_mut()
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.into_iter()
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.zip(y.slice(s![.., .., nx - 1]).gencolumns())
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.zip(g.gencolumns())
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.zip(grid.detj_dxi_dx.slice(s![.., nx - 1]))
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.zip(grid.detj_dxi_dy.slice(s![.., nx - 1]))
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{
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// East boundary, positive flux
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let tau = -1.0;
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let v = (v[0], v[1], v[2]);
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let g = (g[0], g[1], g[2]);
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let plus = positive_flux(kx, ky);
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k[0] += 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] += 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] += tau
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* hinv
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* (plus[2][0] * (v.0 - g.0) + plus[2][1] * (v.1 - g.1) + 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 g = match boundaries.east {
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Boundary::This => y.slice(s![.., .., nx - 1]),
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};
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let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
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for ((((mut k, v), g), &kx), &ky) in k
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.slice_mut(s![.., .., 0])
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.gencolumns_mut()
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.into_iter()
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.zip(y.slice(s![.., .., 0]).gencolumns())
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.zip(g.gencolumns())
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.zip(grid.detj_dxi_dx.slice(s![.., 0]))
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.zip(grid.detj_dxi_dy.slice(s![.., 0]))
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{
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let tau = 1.0;
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let v = (v[0], v[1], v[2]);
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let g = (g[0], g[1], g[2]);
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let minus = negative_flux(kx, ky);
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k[0] += 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] += 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] += 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)
|
|
+ minus[2][2] * (v.2 - g.2));
|
|
}
|
|
}
|
|
|
|
{
|
|
let g = match boundaries.north {
|
|
Boundary::This => y.slice(s![.., 0, ..]),
|
|
};
|
|
let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as f32);
|
|
for ((((mut k, v), g), &kx), &ky) in k
|
|
.slice_mut(s![.., ny - 1, ..])
|
|
.gencolumns_mut()
|
|
.into_iter()
|
|
.zip(y.slice(s![.., ny - 1, ..]).gencolumns())
|
|
.zip(g.gencolumns())
|
|
.zip(grid.detj_deta_dx.slice(s![ny - 1, ..]))
|
|
.zip(grid.detj_deta_dy.slice(s![ny - 1, ..]))
|
|
{
|
|
// North boundary, positive flux
|
|
let tau = -1.0;
|
|
let v = (v[0], v[1], v[2]);
|
|
let g = (g[0], g[1], g[2]);
|
|
|
|
let plus = positive_flux(kx, ky);
|
|
|
|
k[0] += 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] += 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] += tau
|
|
* hinv
|
|
* (plus[2][0] * (v.0 - g.0) + plus[2][1] * (v.1 - g.1) + plus[2][2] * (v.2 - g.2));
|
|
}
|
|
}
|
|
|
|
{
|
|
let g = match boundaries.south {
|
|
Boundary::This => y.slice(s![.., ny - 1, ..]),
|
|
};
|
|
let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as f32);
|
|
for ((((mut k, v), g), &kx), &ky) in k
|
|
.slice_mut(s![.., 0, ..])
|
|
.gencolumns_mut()
|
|
.into_iter()
|
|
.zip(y.slice(s![.., 0, ..]).gencolumns())
|
|
.zip(g.gencolumns())
|
|
.zip(grid.detj_deta_dx.slice(s![0, ..]))
|
|
.zip(grid.detj_deta_dy.slice(s![0, ..]))
|
|
{
|
|
// South boundary, negative flux
|
|
|
|
let tau = 1.0;
|
|
let v = (v[0], v[1], v[2]);
|
|
let g = (g[0], g[1], g[2]);
|
|
|
|
let minus = negative_flux(kx, ky);
|
|
|
|
k[0] += 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] += 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] += tau
|
|
* hinv
|
|
* (minus[2][0] * (v.0 - g.0)
|
|
+ minus[2][1] * (v.1 - g.1)
|
|
+ minus[2][2] * (v.2 - g.2));
|
|
}
|
|
}
|
|
}
|
|
|
|
#[derive(Clone, Debug)]
|
|
pub struct WorkBuffers {
|
|
k: [Field; 4],
|
|
tmp: (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
|
|
}
|
|
|
|
impl WorkBuffers {
|
|
pub fn new(ny: usize, nx: usize) -> Self {
|
|
let arr2 = Array2::zeros((ny, nx));
|
|
let arr3 = Field::new(ny, nx);
|
|
Self {
|
|
k: [arr3.clone(), arr3.clone(), arr3.clone(), arr3],
|
|
tmp: (arr2.clone(), arr2.clone(), arr2.clone(), arr2),
|
|
}
|
|
}
|
|
}
|