Add D2 operator and heat equation

This commit is contained in:
Magnus Ulimoen 2020-09-18 17:57:57 +02:00
parent 0fc9ec64ec
commit b80ca3f5e8
5 changed files with 120 additions and 4 deletions

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@ -7,6 +7,7 @@ members = [
"maxwell", "maxwell",
"shallow_water", "shallow_water",
"gridgeneration", "gridgeneration",
"heat-equation",
] ]
default-members = ["sbp", "euler", "maxwell", "shallow_water"] default-members = ["sbp", "euler", "maxwell", "shallow_water"]

11
heat-equation/Cargo.toml Normal file
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@ -0,0 +1,11 @@
[package]
name = "heat-equation"
version = "0.1.0"
authors = ["Magnus Ulimoen <magnus@ulimoen.dev>"]
edition = "2018"
[dependencies]
sbp = { path = "../sbp" }
ndarray = "0.13.1"
plotters = { version = "0.3.0", default-features = false, features = ["bitmap_gif", "bitmap_backend", "line_series"] }

68
heat-equation/src/main.rs Normal file
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@ -0,0 +1,68 @@
use ndarray::Array1;
use plotters::prelude::*;
use sbp::{
integrate::{integrate, Rk4},
operators::{SbpOperator1d2, SBP4},
Float,
};
fn main() {
let drawing_area = BitMapBackend::gif("result.gif", (300, 300), 100)
.unwrap()
.into_drawing_area();
let mut chart = ChartBuilder::on(&drawing_area)
.x_label_area_size(40)
.y_label_area_size(40)
.build_cartesian_2d(0.0..1.0, -1.0..2.0)
.unwrap();
let nx: usize = 101;
let dt = 0.2 / nx.pow(2) as Float / 3.0;
let x = Array1::from_shape_fn((nx,), |i| i as Float / (nx - 1) as Float);
let v0 = x.map(|&x| 0.0 * x * x * x * x);
let op = SBP4;
let mut k = [v0.clone(), v0.clone(), v0.clone(), v0.clone()];
let rhs = move |fut: &mut Array1<Float>, prev: &Array1<Float>, _t: Float| {
fut.fill(0.0);
op.diff2(prev.view(), fut.view_mut());
let h = 1.0 / (nx - 1) as Float;
let tau = (1.0, -1.0);
let v0 = 1.0;
let vn = -1.0;
let d1 = op.d1();
for (d, fut) in d1.iter().zip(fut.iter_mut()) {
*fut += tau.0 / (h * h) * d * (prev[0] - v0);
}
for (d, fut) in d1.iter().zip(fut.iter_mut().rev().take(d1.len()).rev()) {
*fut += tau.1 / (h * h) * d * (prev[nx - 1] - vn);
}
};
let mut v1 = v0.clone();
let mut v2 = v0;
for i in 0..90 {
if i % 3 == 0 {
drawing_area.fill(&WHITE).unwrap();
chart
.configure_mesh()
.x_desc("x")
.y_desc("y")
.draw()
.unwrap();
chart
.draw_series(LineSeries::new(
x.iter().zip(v1.iter()).map(|(&x, &y)| (x, y)),
&BLACK,
))
.unwrap();
drawing_area.present().unwrap();
}
integrate::<Rk4, _, _, _>(rhs, &v1, &mut v2, &mut 0.0, dt, &mut k);
std::mem::swap(&mut v1, &mut v2);
}
}

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@ -17,6 +17,12 @@ pub trait SbpOperator1d: Send + Sync {
fn h_matrix(&self, n: usize) -> sprs::CsMat<Float>; fn h_matrix(&self, n: usize) -> sprs::CsMat<Float>;
} }
pub trait SbpOperator1d2: SbpOperator1d {
fn diff2(&self, prev: ArrayView1<Float>, fut: ArrayViewMut1<Float>);
/// Lacks a scaling of 1/h^2
fn d1(&self) -> &[Float];
}
pub trait SbpOperator2d: Send + Sync { pub trait SbpOperator2d: Send + Sync {
fn diffxi(&self, prev: ArrayView2<Float>, fut: ArrayViewMut2<Float>); fn diffxi(&self, prev: ArrayView2<Float>, fut: ArrayViewMut2<Float>);
fn diffeta(&self, prev: ArrayView2<Float>, fut: ArrayViewMut2<Float>); fn diffeta(&self, prev: ArrayView2<Float>, fut: ArrayViewMut2<Float>);

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@ -16,10 +16,22 @@ impl SBP4 {
]; ];
#[rustfmt::skip] #[rustfmt::skip]
const BLOCK: &'static [&'static [Float]] = &[ const BLOCK: &'static [&'static [Float]] = &[
&[-1.41176470588235e+00, 1.73529411764706e+00, -2.35294117647059e-01, -8.82352941176471e-02], &[-24.0/17.0, 59.0/34.0, -4.0/17.0, -3.0/34.0],
&[-5.00000000000000e-01, 0.00000000000000e+00, 5.00000000000000e-01], &[-1.0/2.0, 0.0, 1.0/2.0],
&[9.30232558139535e-02, -6.86046511627907e-01, 0.00000000000000e+00, 6.86046511627907e-01, -9.30232558139535e-02], &[4.0/43.0, -59.0/86.0, 0.0, 59.0/86.0, -4.0/43.0],
&[3.06122448979592e-02, 0.00000000000000e+00, -6.02040816326531e-01, 0.00000000000000e+00, 6.53061224489796e-01, -8.16326530612245e-02], &[3.0/98.0, 0.0, -59.0/98.0, 0.0, 32.0/49.0, -4.0/49.0]
];
#[rustfmt::skip]
const D2DIAG: &'static [Float] = &[
-1.0 / 12.0, 4.0 / 3.0, -5.0 / 2.0, 4.0 / 3.0, -1.0 / 12.0
];
#[rustfmt::skip]
const D2BLOCK: &'static [&'static [Float]] = &[
&[2.0, -5.0, 4.0, -1.0],
&[1.0, -2.0, 1.0],
&[-4.0/43.0, 59.0/43.0, -110.0/43.0, 59.0/43.0, -4.0/43.0],
&[-1.0/49.0, 0.0, 59.0/49.0, -118.0/49.0, 64.0/49.0, -4.0/49.0]
]; ];
} }
@ -81,6 +93,24 @@ impl<SBP: SbpOperator1d> SbpOperator2d for (&SBP, &SBP4) {
} }
} }
impl super::SbpOperator1d2 for SBP4 {
fn diff2(&self, prev: ArrayView1<Float>, mut fut: ArrayViewMut1<Float>) {
super::diff_op_1d(
Self::D2BLOCK,
Self::D2DIAG,
super::Symmetry::Symmetric,
super::OperatorType::Normal,
prev,
fut.view_mut(),
);
let hi = (prev.len() - 1) as Float;
fut.map_inplace(|x| *x *= hi)
}
fn d1(&self) -> &[Float] {
&[-88.0 / 17.0, 144.0 / 17.0, -72.0 / 17.0, 16.0 / 17.0]
}
}
#[test] #[test]
fn test_trad4() { fn test_trad4() {
use super::testing::*; use super::testing::*;