checkpoint
This commit is contained in:
		
							
								
								
									
										589
									
								
								src/euler.rs
									
									
									
									
									
										Normal file
									
								
							
							
						
						
									
										589
									
								
								src/euler.rs
									
									
									
									
									
										Normal file
									
								
							@@ -0,0 +1,589 @@
 | 
			
		||||
use super::operators::{SbpOperator, UpwindOperator};
 | 
			
		||||
use super::Grid;
 | 
			
		||||
use ndarray::prelude::*;
 | 
			
		||||
use ndarray::{azip, Zip};
 | 
			
		||||
 | 
			
		||||
pub const GAMMA: f32 = 1.4;
 | 
			
		||||
 | 
			
		||||
#[derive(Clone, Debug)]
 | 
			
		||||
/// A 4 x ny x nx array
 | 
			
		||||
pub struct Field(pub(crate) Array3<f32>);
 | 
			
		||||
 | 
			
		||||
impl std::ops::Deref for Field {
 | 
			
		||||
    type Target = Array3<f32>;
 | 
			
		||||
    fn deref(&self) -> &Self::Target {
 | 
			
		||||
        &self.0
 | 
			
		||||
    }
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
impl std::ops::DerefMut for Field {
 | 
			
		||||
    fn deref_mut(&mut self) -> &mut Self::Target {
 | 
			
		||||
        &mut self.0
 | 
			
		||||
    }
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
impl Field {
 | 
			
		||||
    pub fn new(ny: usize, nx: usize) -> Self {
 | 
			
		||||
        let field = Array3::zeros((4, ny, nx));
 | 
			
		||||
 | 
			
		||||
        Self(field)
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    pub fn nx(&self) -> usize {
 | 
			
		||||
        self.0.shape()[2]
 | 
			
		||||
    }
 | 
			
		||||
    pub fn ny(&self) -> usize {
 | 
			
		||||
        self.0.shape()[1]
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    pub fn rho(&self) -> ArrayView2<f32> {
 | 
			
		||||
        self.slice(s![0, .., ..])
 | 
			
		||||
    }
 | 
			
		||||
    pub fn rhou(&self) -> ArrayView2<f32> {
 | 
			
		||||
        self.slice(s![1, .., ..])
 | 
			
		||||
    }
 | 
			
		||||
    pub fn rhov(&self) -> ArrayView2<f32> {
 | 
			
		||||
        self.slice(s![2, .., ..])
 | 
			
		||||
    }
 | 
			
		||||
    pub fn e(&self) -> ArrayView2<f32> {
 | 
			
		||||
        self.slice(s![3, .., ..])
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    pub fn rho_mut(&mut self) -> ArrayViewMut2<f32> {
 | 
			
		||||
        self.slice_mut(s![0, .., ..])
 | 
			
		||||
    }
 | 
			
		||||
    pub fn rhou_mut(&mut self) -> ArrayViewMut2<f32> {
 | 
			
		||||
        self.slice_mut(s![1, .., ..])
 | 
			
		||||
    }
 | 
			
		||||
    pub fn rhov_mut(&mut self) -> ArrayViewMut2<f32> {
 | 
			
		||||
        self.slice_mut(s![2, .., ..])
 | 
			
		||||
    }
 | 
			
		||||
    pub fn e_mut(&mut self) -> ArrayViewMut2<f32> {
 | 
			
		||||
        self.slice_mut(s![3, .., ..])
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    #[allow(unused)]
 | 
			
		||||
    pub fn components(
 | 
			
		||||
        &self,
 | 
			
		||||
    ) -> (
 | 
			
		||||
        ArrayView2<f32>,
 | 
			
		||||
        ArrayView2<f32>,
 | 
			
		||||
        ArrayView2<f32>,
 | 
			
		||||
        ArrayView2<f32>,
 | 
			
		||||
    ) {
 | 
			
		||||
        (self.rho(), self.rhou(), self.rhov(), self.e())
 | 
			
		||||
    }
 | 
			
		||||
    #[allow(unused)]
 | 
			
		||||
    pub fn components_mut(
 | 
			
		||||
        &mut self,
 | 
			
		||||
    ) -> (
 | 
			
		||||
        ArrayViewMut2<f32>,
 | 
			
		||||
        ArrayViewMut2<f32>,
 | 
			
		||||
        ArrayViewMut2<f32>,
 | 
			
		||||
        ArrayViewMut2<f32>,
 | 
			
		||||
    ) {
 | 
			
		||||
        let mut iter = self.0.outer_iter_mut();
 | 
			
		||||
 | 
			
		||||
        let rho = iter.next().unwrap();
 | 
			
		||||
        let rhou = iter.next().unwrap();
 | 
			
		||||
        let rhov = iter.next().unwrap();
 | 
			
		||||
        let e = iter.next().unwrap();
 | 
			
		||||
        assert_eq!(iter.next(), None);
 | 
			
		||||
 | 
			
		||||
        (rho, rhou, rhov, e)
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    fn north(&self) -> ArrayView2<f32> {
 | 
			
		||||
        self.slice(s![.., self.ny() - 1, ..])
 | 
			
		||||
    }
 | 
			
		||||
    fn south(&self) -> ArrayView2<f32> {
 | 
			
		||||
        self.slice(s![.., 0, ..])
 | 
			
		||||
    }
 | 
			
		||||
    fn east(&self) -> ArrayView2<f32> {
 | 
			
		||||
        self.slice(s![.., .., self.nx() - 1])
 | 
			
		||||
    }
 | 
			
		||||
    fn west(&self) -> ArrayView2<f32> {
 | 
			
		||||
        self.slice(s![.., .., 0])
 | 
			
		||||
    }
 | 
			
		||||
    fn north_mut(&mut self) -> ArrayViewMut2<f32> {
 | 
			
		||||
        let ny = self.ny();
 | 
			
		||||
        self.slice_mut(s![.., ny - 1, ..])
 | 
			
		||||
    }
 | 
			
		||||
    fn south_mut(&mut self) -> ArrayViewMut2<f32> {
 | 
			
		||||
        self.slice_mut(s![.., 0, ..])
 | 
			
		||||
    }
 | 
			
		||||
    fn east_mut(&mut self) -> ArrayViewMut2<f32> {
 | 
			
		||||
        let nx = self.nx();
 | 
			
		||||
        self.slice_mut(s![.., .., nx - 1])
 | 
			
		||||
    }
 | 
			
		||||
    fn west_mut(&mut self) -> ArrayViewMut2<f32> {
 | 
			
		||||
        self.slice_mut(s![.., .., 0])
 | 
			
		||||
    }
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
#[allow(unused)]
 | 
			
		||||
pub(crate) fn advance_upwind<UO>(
 | 
			
		||||
    prev: &Field,
 | 
			
		||||
    fut: &mut Field,
 | 
			
		||||
    dt: f32,
 | 
			
		||||
    grid: &Grid<UO>,
 | 
			
		||||
    work_buffers: Option<&mut WorkBuffers>,
 | 
			
		||||
) where
 | 
			
		||||
    UO: UpwindOperator,
 | 
			
		||||
{
 | 
			
		||||
    assert_eq!(prev.0.shape(), fut.0.shape());
 | 
			
		||||
 | 
			
		||||
    let mut wb: WorkBuffers;
 | 
			
		||||
    let (y, k, tmp) = if let Some(x) = work_buffers {
 | 
			
		||||
        (&mut x.y, &mut x.buf, &mut x.tmp)
 | 
			
		||||
    } else {
 | 
			
		||||
        wb = WorkBuffers::new(prev.nx(), prev.ny());
 | 
			
		||||
        (&mut wb.y, &mut wb.buf, &mut wb.tmp)
 | 
			
		||||
    };
 | 
			
		||||
 | 
			
		||||
    let boundaries = BoundaryTerms {
 | 
			
		||||
        north: Boundary::This,
 | 
			
		||||
        south: Boundary::This,
 | 
			
		||||
        west: Boundary::This,
 | 
			
		||||
        east: Boundary::This,
 | 
			
		||||
    };
 | 
			
		||||
 | 
			
		||||
    for i in 0..4 {
 | 
			
		||||
        // y = y0 + c*kn
 | 
			
		||||
        y.assign(&prev);
 | 
			
		||||
        match i {
 | 
			
		||||
            0 => {}
 | 
			
		||||
            1 | 2 => {
 | 
			
		||||
                y.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
 | 
			
		||||
            }
 | 
			
		||||
            3 => {
 | 
			
		||||
                y.scaled_add(dt, &k[i - 1]);
 | 
			
		||||
            }
 | 
			
		||||
            _ => {
 | 
			
		||||
                unreachable!();
 | 
			
		||||
            }
 | 
			
		||||
        };
 | 
			
		||||
 | 
			
		||||
        RHS_upwind(&mut k[i], &y, grid, &boundaries, tmp);
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    Zip::from(&mut fut.0)
 | 
			
		||||
        .and(&prev.0)
 | 
			
		||||
        .and(&*k[0])
 | 
			
		||||
        .and(&*k[1])
 | 
			
		||||
        .and(&*k[2])
 | 
			
		||||
        .and(&*k[3])
 | 
			
		||||
        .apply(|y1, &y0, &k1, &k2, &k3, &k4| *y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4));
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
/// Solving (Au)_x + (Bu)_y
 | 
			
		||||
/// with:
 | 
			
		||||
///        A               B
 | 
			
		||||
///  [ 0,  0,  0]    [ 0,  1,  0]
 | 
			
		||||
///  [ 0,  0, -1]    [ 1,  0,  0]
 | 
			
		||||
///  [ 0, -1,  0]    [ 0,  0,  0]
 | 
			
		||||
pub(crate) fn advance<SBP>(
 | 
			
		||||
    prev: &Field,
 | 
			
		||||
    fut: &mut Field,
 | 
			
		||||
    dt: f32,
 | 
			
		||||
    grid: &Grid<SBP>,
 | 
			
		||||
    work_buffers: Option<&mut WorkBuffers>,
 | 
			
		||||
) where
 | 
			
		||||
    SBP: SbpOperator,
 | 
			
		||||
{
 | 
			
		||||
    assert_eq!(prev.0.shape(), fut.0.shape());
 | 
			
		||||
 | 
			
		||||
    let mut wb: WorkBuffers;
 | 
			
		||||
    let (y, k, tmp) = if let Some(x) = work_buffers {
 | 
			
		||||
        (&mut x.y, &mut x.buf, &mut x.tmp)
 | 
			
		||||
    } else {
 | 
			
		||||
        wb = WorkBuffers::new(prev.nx(), prev.ny());
 | 
			
		||||
        (&mut wb.y, &mut wb.buf, &mut wb.tmp)
 | 
			
		||||
    };
 | 
			
		||||
 | 
			
		||||
    let boundaries = BoundaryTerms {
 | 
			
		||||
        north: Boundary::This,
 | 
			
		||||
        south: Boundary::This,
 | 
			
		||||
        west: Boundary::This,
 | 
			
		||||
        east: Boundary::This,
 | 
			
		||||
    };
 | 
			
		||||
 | 
			
		||||
    for i in 0..4 {
 | 
			
		||||
        // y = y0 + c*kn
 | 
			
		||||
        y.assign(&prev);
 | 
			
		||||
        match i {
 | 
			
		||||
            0 => {}
 | 
			
		||||
            1 | 2 => {
 | 
			
		||||
                y.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
 | 
			
		||||
            }
 | 
			
		||||
            3 => {
 | 
			
		||||
                y.scaled_add(dt, &k[i - 1]);
 | 
			
		||||
            }
 | 
			
		||||
            _ => {
 | 
			
		||||
                unreachable!();
 | 
			
		||||
            }
 | 
			
		||||
        };
 | 
			
		||||
 | 
			
		||||
        RHS(&mut k[i], &y, grid, &boundaries, tmp);
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    Zip::from(&mut fut.0)
 | 
			
		||||
        .and(&prev.0)
 | 
			
		||||
        .and(&*k[0])
 | 
			
		||||
        .and(&*k[1])
 | 
			
		||||
        .and(&*k[2])
 | 
			
		||||
        .and(&*k[3])
 | 
			
		||||
        .apply(|y1, &y0, &k1, &k2, &k3, &k4| *y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4));
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
fn pressure(gamma: f32, rho: f32, rhou: f32, rhov: f32, e: f32) -> f32 {
 | 
			
		||||
    (gamma - 1.0) * (e - (rhou * rhou + rhov * rhov) / (2.0 * rho))
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
#[allow(non_snake_case)]
 | 
			
		||||
/// This flux is rotated by the grid metrics
 | 
			
		||||
/// (Au)_x + (Bu)_y = 1/J [
 | 
			
		||||
///          (J xi_x Au)_xi + (J eta_x Au)_eta
 | 
			
		||||
///          (J xi_y Bu)_xi + (J eta_y Bu)_eta
 | 
			
		||||
///      ]
 | 
			
		||||
/// where J is the grid determinant
 | 
			
		||||
///
 | 
			
		||||
/// This is used both in fluxes and SAT terms
 | 
			
		||||
fn RHS<SBP: SbpOperator>(
 | 
			
		||||
    k: &mut Field,
 | 
			
		||||
    y: &Field,
 | 
			
		||||
    grid: &Grid<SBP>,
 | 
			
		||||
    boundaries: &BoundaryTerms,
 | 
			
		||||
    tmp: &mut (Field, Field, Field, Field),
 | 
			
		||||
) {
 | 
			
		||||
    let ehat = &mut tmp.0;
 | 
			
		||||
    let fhat = &mut tmp.1;
 | 
			
		||||
    fluxes([ehat, fhat], y, grid);
 | 
			
		||||
    let de = &mut tmp.2;
 | 
			
		||||
    let df = &mut tmp.3;
 | 
			
		||||
 | 
			
		||||
    SBP::diffxi(ehat.rho(), de.rho_mut());
 | 
			
		||||
    SBP::diffxi(ehat.rhou(), de.rhou_mut());
 | 
			
		||||
    SBP::diffxi(ehat.rhov(), de.rhov_mut());
 | 
			
		||||
    SBP::diffxi(ehat.e(), de.e_mut());
 | 
			
		||||
 | 
			
		||||
    SBP::diffeta(fhat.rho(), df.rho_mut());
 | 
			
		||||
    SBP::diffeta(fhat.rhou(), df.rhou_mut());
 | 
			
		||||
    SBP::diffeta(fhat.rhov(), df.rhov_mut());
 | 
			
		||||
    SBP::diffeta(fhat.e(), df.e_mut());
 | 
			
		||||
 | 
			
		||||
    // And dissipation...
 | 
			
		||||
 | 
			
		||||
    ndarray::azip!((out in &mut k.0,
 | 
			
		||||
                    eflux in &de.0,
 | 
			
		||||
                    fflux in &df.0,
 | 
			
		||||
                    detj in &grid.detj.broadcast((4, y.ny(), y.nx())).unwrap()) {
 | 
			
		||||
        *out = (-eflux - fflux)/detj
 | 
			
		||||
    });
 | 
			
		||||
 | 
			
		||||
    SAT_characteristics(k, y, grid, boundaries);
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
#[allow(non_snake_case)]
 | 
			
		||||
#[allow(unused)]
 | 
			
		||||
fn RHS_upwind<UO: UpwindOperator>(
 | 
			
		||||
    k: &mut Field,
 | 
			
		||||
    y: &Field,
 | 
			
		||||
    grid: &Grid<UO>,
 | 
			
		||||
    boundaries: &BoundaryTerms,
 | 
			
		||||
    tmp: &mut (Field, Field, Field, Field),
 | 
			
		||||
) {
 | 
			
		||||
    // fluxes(k, y, grid, tmp);
 | 
			
		||||
    // dissipation(k, y, grid, tmp);
 | 
			
		||||
 | 
			
		||||
    SAT_characteristics(k, y, grid, boundaries);
 | 
			
		||||
 | 
			
		||||
    azip!((k in &mut k.0,
 | 
			
		||||
                    &detj in &grid.detj.broadcast((3, y.ny(), y.nx())).unwrap()) {
 | 
			
		||||
        *k /= detj;
 | 
			
		||||
    });
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
fn fluxes<SBP: SbpOperator>(k: [&mut Field; 2], y: &Field, grid: &Grid<SBP>) {
 | 
			
		||||
    let j_dxi_dx = grid.detj_dxi_dx.view();
 | 
			
		||||
    let j_dxi_dy = grid.detj_dxi_dy.view();
 | 
			
		||||
    let j_deta_dx = grid.detj_deta_dx.view();
 | 
			
		||||
    let j_deta_dy = grid.detj_deta_dy.view();
 | 
			
		||||
 | 
			
		||||
    let rho = y.rho();
 | 
			
		||||
    let rhou = y.rhou();
 | 
			
		||||
    let rhov = y.rhov();
 | 
			
		||||
    let e = y.e();
 | 
			
		||||
 | 
			
		||||
    for j in 0..y.ny() {
 | 
			
		||||
        for i in 0..y.nx() {
 | 
			
		||||
            let rho = rho[(j, i)];
 | 
			
		||||
            let rhou = rhou[(j, i)];
 | 
			
		||||
            let rhov = rhov[(j, i)];
 | 
			
		||||
            let e = e[(j, i)];
 | 
			
		||||
            let p = pressure(GAMMA, rho, rhou, rhov, e);
 | 
			
		||||
 | 
			
		||||
            let ef = [
 | 
			
		||||
                rhou,
 | 
			
		||||
                rhou * rhou / rho + p,
 | 
			
		||||
                rhou * rhov / rho,
 | 
			
		||||
                rhou * (e + p) / rho,
 | 
			
		||||
            ];
 | 
			
		||||
            let ff = [
 | 
			
		||||
                rhov,
 | 
			
		||||
                rhou * rhov / rho,
 | 
			
		||||
                rhov * rhov / rho + p,
 | 
			
		||||
                rhov * (e + p) / rho,
 | 
			
		||||
            ];
 | 
			
		||||
 | 
			
		||||
            for comp in 0..4 {
 | 
			
		||||
                let eflux = j_dxi_dx[(j, i)] * ef[comp] + j_dxi_dy[(j, i)] * ff[comp];
 | 
			
		||||
                let fflux = j_deta_dx[(j, i)] * ef[comp] + j_deta_dy[(j, i)] * ff[comp];
 | 
			
		||||
 | 
			
		||||
                k[0][(comp, j, i)] = eflux;
 | 
			
		||||
                k[1][(comp, j, i)] = fflux;
 | 
			
		||||
            }
 | 
			
		||||
        }
 | 
			
		||||
    }
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
#[allow(unused)]
 | 
			
		||||
fn dissipation<UO: UpwindOperator>(
 | 
			
		||||
    k: &mut Field,
 | 
			
		||||
    y: &Field,
 | 
			
		||||
    grid: &Grid<UO>,
 | 
			
		||||
    tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
 | 
			
		||||
) {
 | 
			
		||||
    todo!()
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
#[derive(Clone, Debug)]
 | 
			
		||||
pub enum Boundary {
 | 
			
		||||
    This,
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
#[derive(Clone, Debug)]
 | 
			
		||||
pub struct BoundaryTerms {
 | 
			
		||||
    pub north: Boundary,
 | 
			
		||||
    pub south: Boundary,
 | 
			
		||||
    pub east: Boundary,
 | 
			
		||||
    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),
 | 
			
		||||
        }
 | 
			
		||||
    }
 | 
			
		||||
}
 | 
			
		||||
							
								
								
									
										24
									
								
								src/grid.rs
									
									
									
									
									
								
							
							
						
						
									
										24
									
								
								src/grid.rs
									
									
									
									
									
								
							@@ -16,9 +16,10 @@ where
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
impl<SBP: super::operators::SbpOperator> Grid<SBP> {
 | 
			
		||||
    pub fn new(nx: usize, ny: usize, x: &[f32], y: &[f32]) -> Result<Self, ndarray::ShapeError> {
 | 
			
		||||
        let x = Array2::from_shape_vec((ny, nx), x.to_vec())?;
 | 
			
		||||
        let y = Array2::from_shape_vec((ny, nx), y.to_vec())?;
 | 
			
		||||
    pub fn new(x: Array2<f32>, y: Array2<f32>) -> Result<Self, ndarray::ShapeError> {
 | 
			
		||||
        assert_eq!(x.shape(), y.shape());
 | 
			
		||||
        let ny = x.shape()[0];
 | 
			
		||||
        let nx = x.shape()[1];
 | 
			
		||||
 | 
			
		||||
        let mut dx_dxi = Array2::zeros((ny, nx));
 | 
			
		||||
        SBP::diffxi(x.view(), dx_dxi.view_mut());
 | 
			
		||||
@@ -63,4 +64,21 @@ impl<SBP: super::operators::SbpOperator> Grid<SBP> {
 | 
			
		||||
            operator: std::marker::PhantomData,
 | 
			
		||||
        })
 | 
			
		||||
    }
 | 
			
		||||
    pub fn new_from_slice(
 | 
			
		||||
        ny: usize,
 | 
			
		||||
        nx: usize,
 | 
			
		||||
        x: &[f32],
 | 
			
		||||
        y: &[f32],
 | 
			
		||||
    ) -> Result<Self, ndarray::ShapeError> {
 | 
			
		||||
        let x = Array2::from_shape_vec((ny, nx), x.to_vec())?;
 | 
			
		||||
        let y = Array2::from_shape_vec((ny, nx), y.to_vec())?;
 | 
			
		||||
 | 
			
		||||
        Self::new(x, y)
 | 
			
		||||
    }
 | 
			
		||||
    pub fn nx(&self) -> usize {
 | 
			
		||||
        self.x.shape()[1]
 | 
			
		||||
    }
 | 
			
		||||
    pub fn ny(&self) -> usize {
 | 
			
		||||
        self.x.shape()[0]
 | 
			
		||||
    }
 | 
			
		||||
}
 | 
			
		||||
 
 | 
			
		||||
							
								
								
									
										132
									
								
								src/lib.rs
									
									
									
									
									
								
							
							
						
						
									
										132
									
								
								src/lib.rs
									
									
									
									
									
								
							@@ -1,5 +1,6 @@
 | 
			
		||||
use wasm_bindgen::prelude::*;
 | 
			
		||||
 | 
			
		||||
mod euler;
 | 
			
		||||
mod grid;
 | 
			
		||||
mod maxwell;
 | 
			
		||||
pub mod operators;
 | 
			
		||||
@@ -62,7 +63,7 @@ impl<SBP: operators::SbpOperator> System<SBP> {
 | 
			
		||||
        assert_eq!((width * height), x.len());
 | 
			
		||||
        assert_eq!((width * height), y.len());
 | 
			
		||||
 | 
			
		||||
        let grid = Grid::new(width, height, x, y).expect(
 | 
			
		||||
        let grid = Grid::new_from_slice(height, width, x, y).expect(
 | 
			
		||||
            "Could not create grid. Different number of elements compared to width*height?",
 | 
			
		||||
        );
 | 
			
		||||
        Self {
 | 
			
		||||
@@ -119,3 +120,132 @@ fn gaussian(x: f32, x0: f32, y: f32, y0: f32) -> f32 {
 | 
			
		||||
 | 
			
		||||
    1.0 / (2.0 * f32::consts::PI * sigma * sigma) * (-(x * x + y * y) / (2.0 * sigma * sigma)).exp()
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
pub struct EulerSystem<SBP: operators::SbpOperator> {
 | 
			
		||||
    sys: (euler::Field, euler::Field),
 | 
			
		||||
    wb: euler::WorkBuffers,
 | 
			
		||||
    grid: Grid<SBP>,
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
#[wasm_bindgen]
 | 
			
		||||
pub struct EulerUniverse(EulerSystem<operators::Upwind4>);
 | 
			
		||||
 | 
			
		||||
impl EulerUniverse {
 | 
			
		||||
    pub fn new(x: ndarray::Array2<f32>, y: ndarray::Array2<f32>) -> Self {
 | 
			
		||||
        Self(EulerSystem::new(x, y))
 | 
			
		||||
    }
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
#[wasm_bindgen]
 | 
			
		||||
impl EulerUniverse {
 | 
			
		||||
    #[wasm_bindgen(constructor)]
 | 
			
		||||
    pub fn new_with_slice(height: usize, width: usize, x: &[f32], y: &[f32]) -> Self {
 | 
			
		||||
        let x = ndarray::Array2::from_shape_vec((height, width), x.to_vec()).unwrap();
 | 
			
		||||
        let y = ndarray::Array2::from_shape_vec((height, width), y.to_vec()).unwrap();
 | 
			
		||||
        Self(EulerSystem::new(x, y))
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    pub fn init(&mut self, x0: f32, y0: f32) {
 | 
			
		||||
        // Should parametrise such that we have radius, drop in pressure at center, etc
 | 
			
		||||
        let rstar = 0.5;
 | 
			
		||||
        let eps = 1.0;
 | 
			
		||||
        #[allow(non_snake_case)]
 | 
			
		||||
        let M = 0.1;
 | 
			
		||||
 | 
			
		||||
        let p_inf = 1.0 / (euler::GAMMA * M * M);
 | 
			
		||||
        let t = 0.0;
 | 
			
		||||
 | 
			
		||||
        let nx = self.0.grid.nx();
 | 
			
		||||
        let ny = self.0.grid.ny();
 | 
			
		||||
 | 
			
		||||
        for j in 0..ny {
 | 
			
		||||
            for i in 0..nx {
 | 
			
		||||
                let x = self.0.grid.x[(j, i)];
 | 
			
		||||
                let y = self.0.grid.y[(j, i)];
 | 
			
		||||
 | 
			
		||||
                let dx = (x - x0) - t;
 | 
			
		||||
                let dy = (y - y0) - t;
 | 
			
		||||
                let f = (1.0 - (dx * dx + dy * dy)) / (rstar * rstar);
 | 
			
		||||
 | 
			
		||||
                use euler::GAMMA;
 | 
			
		||||
                use std::f32::consts::PI;
 | 
			
		||||
                let u =
 | 
			
		||||
                    1.0 - eps * dy / (2.0 * PI * p_inf.sqrt() * rstar * rstar) * (f / 2.0).exp();
 | 
			
		||||
                let v =
 | 
			
		||||
                    0.0 + eps * dx / (2.0 * PI * p_inf.sqrt() * rstar * rstar) * (f / 2.0).exp();
 | 
			
		||||
                let rho = f32::powf(
 | 
			
		||||
                    1.0 - eps * eps * (GAMMA - 1.0) * M * M
 | 
			
		||||
                        / (8.0 * PI * PI * p_inf * rstar * rstar)
 | 
			
		||||
                        * f.exp(),
 | 
			
		||||
                    1.0 / (GAMMA - 1.0),
 | 
			
		||||
                );
 | 
			
		||||
                assert!(rho > 0.0);
 | 
			
		||||
                let p = rho.powf(GAMMA) * p_inf;
 | 
			
		||||
                assert!(p > 0.0);
 | 
			
		||||
                let e = p / (GAMMA - 1.0) + rho * (u * u + v * v) / 2.0;
 | 
			
		||||
                assert!(e > 0.0);
 | 
			
		||||
 | 
			
		||||
                self.0.sys.0[(0, j, i)] = rho;
 | 
			
		||||
                self.0.sys.0[(1, j, i)] = rho * u;
 | 
			
		||||
                self.0.sys.0[(2, j, i)] = rho * v;
 | 
			
		||||
                self.0.sys.0[(3, j, i)] = e;
 | 
			
		||||
            }
 | 
			
		||||
        }
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    pub fn advance(&mut self, dt: f32) {
 | 
			
		||||
        self.0.advance(dt)
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    pub fn advance_upwind(&mut self, _dt: f32) {
 | 
			
		||||
        todo!()
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    pub fn get_rho_ptr(&self) -> *const u8 {
 | 
			
		||||
        self.0.sys.0.rho().as_ptr() as *const u8
 | 
			
		||||
    }
 | 
			
		||||
    pub fn get_rhou_ptr(&self) -> *const u8 {
 | 
			
		||||
        self.0.sys.0.rhou().as_ptr() as *const u8
 | 
			
		||||
    }
 | 
			
		||||
    pub fn get_rhov_ptr(&self) -> *const u8 {
 | 
			
		||||
        self.0.sys.0.rhov().as_ptr() as *const u8
 | 
			
		||||
    }
 | 
			
		||||
    pub fn get_e_ptr(&self) -> *const u8 {
 | 
			
		||||
        self.0.sys.0.e().as_ptr() as *const u8
 | 
			
		||||
    }
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
impl<SBP: operators::SbpOperator> EulerSystem<SBP> {
 | 
			
		||||
    pub fn new(x: ndarray::Array2<f32>, y: ndarray::Array2<f32>) -> Self {
 | 
			
		||||
        let grid = Grid::new(x, y).expect(
 | 
			
		||||
            "Could not create grid. Different number of elements compared to width*height?",
 | 
			
		||||
        );
 | 
			
		||||
        let nx = grid.nx();
 | 
			
		||||
        let ny = grid.ny();
 | 
			
		||||
        Self {
 | 
			
		||||
            sys: (euler::Field::new(ny, nx), euler::Field::new(ny, nx)),
 | 
			
		||||
            grid,
 | 
			
		||||
            wb: euler::WorkBuffers::new(ny, nx),
 | 
			
		||||
        }
 | 
			
		||||
    }
 | 
			
		||||
 | 
			
		||||
    pub fn advance(&mut self, dt: f32) {
 | 
			
		||||
        euler::advance(
 | 
			
		||||
            &self.sys.0,
 | 
			
		||||
            &mut self.sys.1,
 | 
			
		||||
            dt,
 | 
			
		||||
            &self.grid,
 | 
			
		||||
            Some(&mut self.wb),
 | 
			
		||||
        );
 | 
			
		||||
        std::mem::swap(&mut self.sys.0, &mut self.sys.1);
 | 
			
		||||
    }
 | 
			
		||||
}
 | 
			
		||||
 | 
			
		||||
#[test]
 | 
			
		||||
fn start_and_advance_euler() {
 | 
			
		||||
    let x = ndarray::Array2::from_shape_fn((20, 10), |(_j, i)| i as f32 / (10 - 1) as f32);
 | 
			
		||||
    let y = ndarray::Array2::from_shape_fn((20, 10), |(j, _i)| j as f32 / (20 - 1) as f32);
 | 
			
		||||
    let mut universe = EulerUniverse::new(x, y);
 | 
			
		||||
    universe.init(0.5, 0.5);
 | 
			
		||||
    universe.advance(0.01);
 | 
			
		||||
}
 | 
			
		||||
 
 | 
			
		||||
		Reference in New Issue
	
	Block a user