colin/fdtd-coremem
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Fix the math errors so that 2d simulations appear to now conserve energy.

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Colin
2020-07-15 23:34:51 -07:00
parent a82c2f60e7
commit b890d8dc3a
2 changed files with 19 additions and 15 deletions
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8
examples/coremem.rs
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@@ -4,13 +4,13 @@ use coremem::consts;
use std::{thread, time};
fn main() {
let mut state = SimState::new(16, 4);
let mut state = SimState::new(16, 5);
state.impulse_bz(0, 0, 1.0/consts::C);
//state.impulse_ey(0, 0, 1.0);
state.impulse_ey(0, 0, 1.0);
state.impulse_bz(7, 0, 1.0/consts::C);
//state.impulse_ey(7, 0, 1.0);
state.impulse_ey(7, 2, 1.0);
state.impulse_bz(15, 0, 1.0/consts::C);
//state.impulse_ey(15, 0, 1.0);
state.impulse_ey(15, 0, 1.0);
loop {
NumericTermRenderer.render(&state);
state.step();

26
src/lib.rs
View File

@@ -21,6 +21,10 @@ pub mod consts {
/// Also equal to 1/sqrt(epsilon_0 mu_0)
pub const C: f32 = 299792458f32;
// pub const Z0: f32 = 376.73031366857f32;
// Vacuum Permeability
// pub const Mu0: f32 = 1.2566370621219e-6; // H/m
// Vacuum Permittivity
// pub const Eps0: f32 = 8.854187812813e-12 // F⋅m−1
}
#[derive(Default)]
@@ -36,8 +40,7 @@ impl SimState {
}
pub fn step(&mut self) {
let mut working_cells = self.cells.clone();
//let mut working_cells = vec![Cell::default(); self.cells.len()];
let mut working_cells = Array2::default((self.height(), self.width()));
// first advance all the magnetic fields
for down_y in 1..self.height() {
for right_x in 1..self.width() {
@@ -94,7 +97,7 @@ impl SimState {
/// | |
/// +-------.-------+
///
/// Where the right hand rule indicates that positive Bz is pointing out of the page, towards the
/// Where the right hand rule indicates that positive Bz is pointing into the page, away from the
/// reader.
///
/// The dot on bottom is Ex of the cell at (x, y+1) and the dot on the right is the Ey of the cell at
@@ -123,11 +126,12 @@ impl Cell {
// Rearrange: dB_z/dt = dE_x/dy - dE_y/dx
// Discretize: (delta B_z)/(delta t) = (delta E_x)/(delta y) - (delta E_y)/(delta x)
//
// light travels C meters per second, therefore (delta x)/(delta t) = (delta y)/(delta t) = c if we use SI units.
// Simplify: delta B_z = (delta E_x)/c - (delta E_y)/c
// light travels C meters per second, and it we're only stepping half a timestep here (the other half when we advance E),
// therefore (delta x)/(2 delta t) = (delta y)/(2 delta t) = c if we use SI units.
// Simplify: delta B_z = (delta E_x)/(2c) - (delta E_y)/(2c)
let delta_ex = down.ex - self.ex;
let delta_ey = right.ey - self.ey;
let delta_bz = (delta_ex - delta_ey) / consts::C;
let delta_bz = (delta_ex - delta_ey) / (2f32*consts::C);
Cell {
ex: self.ex,
ey: self.ey,
@@ -142,15 +146,15 @@ impl Cell {
// Expand: dE_x/dt = c^2 dB_z/dy (1); dE_y/dt = -c^2 dB_z/dx (2)
//
// Discretize (1): (delta E_x)/(delta t) = c^2 (delta B_z)/(delta y)
// Recall: (delta y)/(delta t) = c, as from step_b
// Substitute: (delta E_x) = c (delta B_z,y)
// Recall: (delta y)/(delta t) = 2c, as from step_b
// Substitute: (delta E_x) = c/2 (delta B_z,y)
//
// Discretize (2): (delta E_y)/(delta t) = -c^2 (delta B_z)/(delta x)
// Substitute c: (delta E_y) = -c (delta B_z,x)
// Substitute c: (delta E_y) = -c/2 (delta B_z,x)
let delta_bz_y = self.bz - up.bz;
let delta_ex = consts::C * delta_bz_y;
let delta_ex = (0.5f32*consts::C) * delta_bz_y;
let delta_bz_x = self.bz - left.bz;
let delta_ey = consts::C * delta_bz_x;
let delta_ey = -(0.5f32*consts::C) * delta_bz_x;
Cell {
ex: self.ex + delta_ex,
ey: self.ey + delta_ey,