Example of Neumann boundary

This commit is contained in:
Magnus Ulimoen 2020-09-18 18:40:10 +02:00
parent b80ca3f5e8
commit 0cfd41845b
1 changed files with 78 additions and 10 deletions

View File

@ -1,4 +1,4 @@
use ndarray::Array1;
use ndarray::{Array1, ArrayView1};
use plotters::prelude::*;
use sbp::{
integrate::{integrate, Rk4},
@ -7,31 +7,37 @@ use sbp::{
};
fn main() {
let drawing_area = BitMapBackend::gif("result.gif", (300, 300), 100)
let nx: usize = 101;
let x = Array1::from_shape_fn((nx,), |i| i as Float / (nx - 1) as Float);
let v0 = x.map(|&x| (-(x - 0.5).powi(2) / 0.1).exp());
dual_dirichlet(v0.view(), 1.0, 1.0);
// Neumann boundary is introducing energy into the system
neumann_dirichlet(v0.view(), -0.2, 1.0);
}
fn dual_dirichlet(v: ArrayView1<Float>, v0: Float, vn: Float) {
let drawing_area = BitMapBackend::gif("dual_dirichlet.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)
.build_cartesian_2d(0.0..1.01, -1.0..2.0)
.unwrap();
let nx: usize = 101;
let nx = v.len();
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 mut k = [v.to_owned(), v.to_owned(), v.to_owned(), v.to_owned()];
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();
@ -43,8 +49,70 @@ fn main() {
}
};
let mut v1 = v0.clone();
let mut v2 = v0;
let mut v1 = v.to_owned();
let mut v2 = v.to_owned();
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);
}
}
fn neumann_dirichlet(v: ArrayView1<Float>, v0: Float, vn: Float) {
let drawing_area = BitMapBackend::gif("neumann_dirichlet.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..1.01, -1.0..2.0)
.unwrap();
let nx = v.len();
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 op = SBP4;
let mut k = [v.to_owned(), v.to_owned(), v.to_owned(), v.to_owned()];
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 d1 = op.d1();
fut[0] += tau.0 / (h * h)
* (d1
.iter()
.zip(prev.iter())
.map(|(x, y)| x * y)
.sum::<Float>()
- 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 = v.to_owned();
let mut v2 = v.to_owned();
for i in 0..90 {
if i % 3 == 0 {
drawing_area.fill(&WHITE).unwrap();