590 lines
15 KiB
Rust
590 lines
15 KiB
Rust
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use super::operators::{SbpOperator, UpwindOperator};
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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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pub const GAMMA: f32 = 1.4;
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#[derive(Clone, Debug)]
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/// A 4 x ny x nx array
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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(ny: usize, nx: usize) -> Self {
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let field = Array3::zeros((4, ny, nx));
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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 rho(&self) -> ArrayView2<f32> {
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self.slice(s![0, .., ..])
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}
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pub fn rhou(&self) -> ArrayView2<f32> {
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self.slice(s![1, .., ..])
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}
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pub fn rhov(&self) -> ArrayView2<f32> {
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self.slice(s![2, .., ..])
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}
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pub fn e(&self) -> ArrayView2<f32> {
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self.slice(s![3, .., ..])
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}
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pub fn rho_mut(&mut self) -> ArrayViewMut2<f32> {
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self.slice_mut(s![0, .., ..])
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}
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pub fn rhou_mut(&mut self) -> ArrayViewMut2<f32> {
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self.slice_mut(s![1, .., ..])
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}
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pub fn rhov_mut(&mut self) -> ArrayViewMut2<f32> {
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self.slice_mut(s![2, .., ..])
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}
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pub fn e_mut(&mut self) -> ArrayViewMut2<f32> {
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self.slice_mut(s![3, .., ..])
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}
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#[allow(unused)]
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pub fn components(
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&self,
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) -> (
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ArrayView2<f32>,
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ArrayView2<f32>,
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ArrayView2<f32>,
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ArrayView2<f32>,
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) {
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(self.rho(), self.rhou(), self.rhov(), self.e())
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}
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#[allow(unused)]
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pub fn components_mut(
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&mut self,
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) -> (
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ArrayViewMut2<f32>,
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ArrayViewMut2<f32>,
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ArrayViewMut2<f32>,
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ArrayViewMut2<f32>,
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) {
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let mut iter = self.0.outer_iter_mut();
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let rho = iter.next().unwrap();
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let rhou = iter.next().unwrap();
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let rhov = iter.next().unwrap();
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let e = iter.next().unwrap();
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assert_eq!(iter.next(), None);
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(rho, rhou, rhov, e)
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}
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fn north(&self) -> ArrayView2<f32> {
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self.slice(s![.., self.ny() - 1, ..])
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}
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fn south(&self) -> ArrayView2<f32> {
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self.slice(s![.., 0, ..])
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}
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fn east(&self) -> ArrayView2<f32> {
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self.slice(s![.., .., self.nx() - 1])
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}
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fn west(&self) -> ArrayView2<f32> {
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self.slice(s![.., .., 0])
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}
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fn north_mut(&mut self) -> ArrayViewMut2<f32> {
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let ny = self.ny();
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self.slice_mut(s![.., ny - 1, ..])
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}
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fn south_mut(&mut self) -> ArrayViewMut2<f32> {
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self.slice_mut(s![.., 0, ..])
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}
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fn east_mut(&mut self) -> ArrayViewMut2<f32> {
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let nx = self.nx();
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self.slice_mut(s![.., .., nx - 1])
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}
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fn west_mut(&mut self) -> ArrayViewMut2<f32> {
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self.slice_mut(s![.., .., 0])
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}
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}
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#[allow(unused)]
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pub(crate) fn advance_upwind<UO>(
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prev: &Field,
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fut: &mut Field,
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dt: f32,
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grid: &Grid<UO>,
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work_buffers: Option<&mut WorkBuffers>,
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) where
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UO: UpwindOperator,
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{
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assert_eq!(prev.0.shape(), fut.0.shape());
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let mut wb: WorkBuffers;
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let (y, k, tmp) = if let Some(x) = work_buffers {
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(&mut x.y, &mut x.buf, &mut x.tmp)
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} else {
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wb = WorkBuffers::new(prev.nx(), prev.ny());
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(&mut wb.y, &mut wb.buf, &mut wb.tmp)
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};
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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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for i in 0..4 {
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// y = y0 + c*kn
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y.assign(&prev);
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match i {
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0 => {}
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1 | 2 => {
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y.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
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}
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3 => {
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y.scaled_add(dt, &k[i - 1]);
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}
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_ => {
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unreachable!();
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}
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};
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RHS_upwind(&mut k[i], &y, grid, &boundaries, tmp);
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}
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Zip::from(&mut fut.0)
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.and(&prev.0)
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.and(&*k[0])
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.and(&*k[1])
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.and(&*k[2])
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.and(&*k[3])
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.apply(|y1, &y0, &k1, &k2, &k3, &k4| *y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4));
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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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prev: &Field,
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fut: &mut Field,
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dt: f32,
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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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{
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assert_eq!(prev.0.shape(), fut.0.shape());
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let mut wb: WorkBuffers;
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let (y, k, tmp) = if let Some(x) = work_buffers {
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(&mut x.y, &mut x.buf, &mut x.tmp)
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} else {
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wb = WorkBuffers::new(prev.nx(), prev.ny());
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(&mut wb.y, &mut wb.buf, &mut wb.tmp)
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};
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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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for i in 0..4 {
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// y = y0 + c*kn
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y.assign(&prev);
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match i {
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0 => {}
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1 | 2 => {
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y.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
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}
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3 => {
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y.scaled_add(dt, &k[i - 1]);
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}
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_ => {
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unreachable!();
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}
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};
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RHS(&mut k[i], &y, grid, &boundaries, tmp);
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}
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Zip::from(&mut fut.0)
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.and(&prev.0)
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.and(&*k[0])
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.and(&*k[1])
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.and(&*k[2])
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.and(&*k[3])
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.apply(|y1, &y0, &k1, &k2, &k3, &k4| *y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4));
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}
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fn pressure(gamma: f32, rho: f32, rhou: f32, rhov: f32, e: f32) -> f32 {
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(gamma - 1.0) * (e - (rhou * rhou + rhov * rhov) / (2.0 * rho))
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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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boundaries: &BoundaryTerms,
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tmp: &mut (Field, Field, Field, Field),
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) {
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let ehat = &mut tmp.0;
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let fhat = &mut tmp.1;
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fluxes([ehat, fhat], y, grid);
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let de = &mut tmp.2;
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let df = &mut tmp.3;
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SBP::diffxi(ehat.rho(), de.rho_mut());
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SBP::diffxi(ehat.rhou(), de.rhou_mut());
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SBP::diffxi(ehat.rhov(), de.rhov_mut());
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SBP::diffxi(ehat.e(), de.e_mut());
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SBP::diffeta(fhat.rho(), df.rho_mut());
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SBP::diffeta(fhat.rhou(), df.rhou_mut());
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SBP::diffeta(fhat.rhov(), df.rhov_mut());
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SBP::diffeta(fhat.e(), df.e_mut());
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// And dissipation...
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ndarray::azip!((out in &mut k.0,
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eflux in &de.0,
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fflux in &df.0,
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detj in &grid.detj.broadcast((4, y.ny(), y.nx())).unwrap()) {
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*out = (-eflux - fflux)/detj
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});
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SAT_characteristics(k, y, grid, boundaries);
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}
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#[allow(non_snake_case)]
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#[allow(unused)]
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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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boundaries: &BoundaryTerms,
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tmp: &mut (Field, Field, Field, Field),
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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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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>(k: [&mut Field; 2], y: &Field, grid: &Grid<SBP>) {
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let j_dxi_dx = grid.detj_dxi_dx.view();
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let j_dxi_dy = grid.detj_dxi_dy.view();
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let j_deta_dx = grid.detj_deta_dx.view();
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let j_deta_dy = grid.detj_deta_dy.view();
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let rho = y.rho();
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let rhou = y.rhou();
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let rhov = y.rhov();
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let e = y.e();
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for j in 0..y.ny() {
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for i in 0..y.nx() {
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let rho = rho[(j, i)];
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let rhou = rhou[(j, i)];
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let rhov = rhov[(j, i)];
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let e = e[(j, i)];
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let p = pressure(GAMMA, rho, rhou, rhov, e);
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let ef = [
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rhou,
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rhou * rhou / rho + p,
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rhou * rhov / rho,
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rhou * (e + p) / rho,
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];
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let ff = [
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rhov,
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rhou * rhov / rho,
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rhov * rhov / rho + p,
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rhov * (e + p) / rho,
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];
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for comp in 0..4 {
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let eflux = j_dxi_dx[(j, i)] * ef[comp] + j_dxi_dy[(j, i)] * ff[comp];
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let fflux = j_deta_dx[(j, i)] * ef[comp] + j_deta_dy[(j, i)] * ff[comp];
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k[0][(comp, j, i)] = eflux;
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k[1][(comp, j, i)] = fflux;
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}
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}
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}
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}
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#[allow(unused)]
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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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todo!()
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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,
|
||
|
|
}
|
||
|
|
|
||
|
|
#[allow(non_snake_case)]
|
||
|
|
/// Boundary conditions (SAT)
|
||
|
|
fn SAT_characteristics<SBP: SbpOperator>(
|
||
|
|
k: &mut Field,
|
||
|
|
y: &Field,
|
||
|
|
grid: &Grid<SBP>,
|
||
|
|
_boundaries: &BoundaryTerms,
|
||
|
|
) {
|
||
|
|
// North boundary
|
||
|
|
{
|
||
|
|
let hi = (k.ny() - 1) as f32 * SBP::h()[0];
|
||
|
|
let sign = -1.0;
|
||
|
|
let tau = 1.0;
|
||
|
|
let slice = s![y.nx() - 1, ..];
|
||
|
|
SAT_characteristic(
|
||
|
|
k.north_mut(),
|
||
|
|
y.north(),
|
||
|
|
y.south(), // Self South
|
||
|
|
hi,
|
||
|
|
sign,
|
||
|
|
tau,
|
||
|
|
grid.detj.slice(slice),
|
||
|
|
grid.detj_deta_dx.slice(slice),
|
||
|
|
grid.detj_deta_dy.slice(slice),
|
||
|
|
);
|
||
|
|
}
|
||
|
|
// South boundary
|
||
|
|
{
|
||
|
|
let hi = (k.ny() - 1) as f32 * SBP::h()[0];
|
||
|
|
let sign = 1.0;
|
||
|
|
let tau = -1.0;
|
||
|
|
let slice = s![0, ..];
|
||
|
|
SAT_characteristic(
|
||
|
|
k.south_mut(),
|
||
|
|
y.south(),
|
||
|
|
y.north(), // Self North
|
||
|
|
hi,
|
||
|
|
sign,
|
||
|
|
tau,
|
||
|
|
grid.detj.slice(slice),
|
||
|
|
grid.detj_deta_dx.slice(slice),
|
||
|
|
grid.detj_deta_dy.slice(slice),
|
||
|
|
);
|
||
|
|
}
|
||
|
|
// West Boundary
|
||
|
|
{
|
||
|
|
let hi = (k.nx() - 1) as f32 * SBP::h()[0];
|
||
|
|
let sign = 1.0;
|
||
|
|
let tau = -1.0;
|
||
|
|
let slice = s![.., 0];
|
||
|
|
println!("{:?}", slice);
|
||
|
|
SAT_characteristic(
|
||
|
|
k.west_mut(),
|
||
|
|
y.west(),
|
||
|
|
y.east(), // Self East
|
||
|
|
hi,
|
||
|
|
sign,
|
||
|
|
tau,
|
||
|
|
grid.detj.slice(slice),
|
||
|
|
grid.detj_dxi_dx.slice(slice),
|
||
|
|
grid.detj_dxi_dy.slice(slice),
|
||
|
|
);
|
||
|
|
}
|
||
|
|
// East Boundary
|
||
|
|
{
|
||
|
|
let hi = (k.nx() - 1) as f32 * SBP::h()[0];
|
||
|
|
let sign = -1.0;
|
||
|
|
let tau = 1.0;
|
||
|
|
let slice = s![.., y.nx() - 1];
|
||
|
|
SAT_characteristic(
|
||
|
|
k.east_mut(),
|
||
|
|
y.east(),
|
||
|
|
y.west(), // Self West
|
||
|
|
hi,
|
||
|
|
sign,
|
||
|
|
tau,
|
||
|
|
grid.detj.slice(slice),
|
||
|
|
grid.detj_dxi_dx.slice(slice),
|
||
|
|
grid.detj_dxi_dy.slice(slice),
|
||
|
|
);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#[allow(non_snake_case)]
|
||
|
|
/// Boundary conditions (SAT)
|
||
|
|
fn SAT_characteristic(
|
||
|
|
mut k: ArrayViewMut2<f32>,
|
||
|
|
y: ArrayView2<f32>,
|
||
|
|
z: ArrayView2<f32>, // Size 4 x n (all components in line)
|
||
|
|
hi: f32,
|
||
|
|
sign: f32,
|
||
|
|
tau: f32,
|
||
|
|
detj: ArrayView1<f32>,
|
||
|
|
detj_d_dx: ArrayView1<f32>,
|
||
|
|
detj_d_dy: ArrayView1<f32>,
|
||
|
|
) {
|
||
|
|
assert_eq!(detj.shape(), detj_d_dx.shape());
|
||
|
|
assert_eq!(detj.shape(), detj_d_dy.shape());
|
||
|
|
assert_eq!(y.shape(), z.shape());
|
||
|
|
assert_eq!(y.shape()[0], 4);
|
||
|
|
assert_eq!(y.shape()[1], detj.shape()[0]);
|
||
|
|
|
||
|
|
for i in 0..z.shape()[1] {
|
||
|
|
let rho = y[(0, i)];
|
||
|
|
let rhou = y[(1, i)];
|
||
|
|
let rhov = y[(2, i)];
|
||
|
|
let e = y[(3, i)];
|
||
|
|
|
||
|
|
let kx_ = detj_d_dx[i] / detj[i];
|
||
|
|
let ky_ = detj_d_dy[i] / detj[i];
|
||
|
|
|
||
|
|
let (kx, ky) = {
|
||
|
|
let r = f32::hypot(kx_, ky_);
|
||
|
|
(kx_ / r, ky_ / r)
|
||
|
|
};
|
||
|
|
|
||
|
|
let u = rhou / rho;
|
||
|
|
let v = rhov / rho;
|
||
|
|
|
||
|
|
let theta = kx * u + ky * v;
|
||
|
|
|
||
|
|
let p = pressure(GAMMA, rho, rhou, rhov, e);
|
||
|
|
let c = (GAMMA * p / rho).sqrt();
|
||
|
|
let phi2 = (GAMMA - 1.0) * (u * u + v * v) / 2.0;
|
||
|
|
|
||
|
|
let phi2_c2 = (phi2 + c * c) / (GAMMA - 1.0);
|
||
|
|
|
||
|
|
let T = [
|
||
|
|
[1.0, 0.0, 1.0, 1.0],
|
||
|
|
[u, ky, u + kx * c, u - kx * c],
|
||
|
|
[v, -kx, v + ky * c, v - ky * c],
|
||
|
|
[
|
||
|
|
phi2 / (GAMMA - 1.0),
|
||
|
|
ky * u - kx * v,
|
||
|
|
phi2_c2 + c * theta,
|
||
|
|
phi2_c2 - c * theta,
|
||
|
|
],
|
||
|
|
];
|
||
|
|
let U = kx_ * u + ky_ * v;
|
||
|
|
let L = [
|
||
|
|
U,
|
||
|
|
U,
|
||
|
|
U + c * f32::hypot(kx_, ky_),
|
||
|
|
U - c * f32::hypot(kx_, ky_),
|
||
|
|
];
|
||
|
|
let beta = 1.0 / (2.0 * c * c);
|
||
|
|
let TI = [
|
||
|
|
[
|
||
|
|
1.0 - phi2 / (c * c),
|
||
|
|
(GAMMA - 1.0) * u / (c * c),
|
||
|
|
(GAMMA - 1.0) * v / (c * c),
|
||
|
|
-(GAMMA - 1.0) / (c * c),
|
||
|
|
],
|
||
|
|
[-(ky * u - kx * v), ky, -kx, 0.0],
|
||
|
|
[
|
||
|
|
beta * (phi2 - c * theta),
|
||
|
|
beta * (kx * c - (GAMMA - 1.0) * u),
|
||
|
|
beta * (ky * c - (GAMMA - 1.0) * v),
|
||
|
|
beta * (GAMMA - 1.0),
|
||
|
|
],
|
||
|
|
[
|
||
|
|
beta * (phi2 + c * theta),
|
||
|
|
-beta * (kx * c + (GAMMA - 1.0) * u),
|
||
|
|
-beta * (ky * c + (GAMMA - 1.0) * v),
|
||
|
|
beta * (GAMMA - 1.0),
|
||
|
|
],
|
||
|
|
];
|
||
|
|
|
||
|
|
let res = [
|
||
|
|
rho - z[(0, i)],
|
||
|
|
rhou - z[(1, i)],
|
||
|
|
rhov - z[(2, i)],
|
||
|
|
e - z[(3, i)],
|
||
|
|
];
|
||
|
|
let mut TIres = [0.0; 4];
|
||
|
|
for row in 0..4 {
|
||
|
|
for col in 0..4 {
|
||
|
|
TIres[row] += TI[row][col] * res[col];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// L + sign(abs(L)) * TIres
|
||
|
|
let mut LTIres = [0.0; 4];
|
||
|
|
for row in 0..4 {
|
||
|
|
LTIres[row] = (L[row] + sign * L[row].abs()) * TIres[row];
|
||
|
|
}
|
||
|
|
|
||
|
|
// T*LTIres
|
||
|
|
let mut TLTIres = [0.0; 4];
|
||
|
|
for row in 0..4 {
|
||
|
|
for col in 0..4 {
|
||
|
|
TLTIres[row] += T[row][col] * LTIres[col];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
for comp in 0..4 {
|
||
|
|
k[(comp, i)] += hi * tau * TLTIres[comp];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
pub struct WorkBuffers {
|
||
|
|
y: Field,
|
||
|
|
buf: [Field; 4],
|
||
|
|
tmp: (Field, Field, Field, Field),
|
||
|
|
}
|
||
|
|
|
||
|
|
impl WorkBuffers {
|
||
|
|
pub fn new(nx: usize, ny: usize) -> Self {
|
||
|
|
let arr3 = Field::new(nx, ny);
|
||
|
|
Self {
|
||
|
|
y: arr3.clone(),
|
||
|
|
buf: [arr3.clone(), arr3.clone(), arr3.clone(), arr3.clone()],
|
||
|
|
tmp: (arr3.clone(), arr3.clone(), arr3.clone(), arr3),
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|