Basic heat and wave equation solver for node and the browser


A simple solver of the heat/diffusion equation and wave equation meant for driving visualizations not for performing exacting scientific analysis. The forward Euler step is employed for simplicity and speed, as well as further simplifying the discrete equations with the convolution operator.

It solves the pde on an nxm square grid with n and m being defined by the setResolution method.

io = require('socket.io').listen(6543)
engine = require('pdeEngine')
field = engine( {
    dt: 0.1
  , gamma: 0.02
  , eqn: "wave"
field.setResolution(80, 100)
io.sockets.on('connection', function (socket) {
  socket.on('addSource', function(data) {
    field.addSource(data.row, data.col, mag)
setInterval( function () {
  var coeffs = field.update( {
      dt: 0.1
    , eqn: "diffusion"
    , alpha: 0.5
  // Render coeffs // 
} , 50 )

Of course you can employ any means of adding sources. The addSource method specifies the location of the source at that particular timestep with magnitude mag. Right now it emplaces a hard-coded Gaussian source centred at (row, col), with boundary cases already implemented.

The following are possible configuration options. If configs are omitted defaults will be used. The defaults are given after the ||:

   dt = spec.dt || 0.1
 , dx = spec.dx || 1
 , gamma = spec.gamma || 0.02   // wave decay factor 
 , vel = spec.vel || 2          // wave velocity 
 , alpha = spec.alpha || 1      // diffusion paramter 
 , eqn = spec.eqn || 'wave'

This is an early but fully working physics engine. Future releases may optimize algorithms or add new methods/configs, but this basic API should remain stable.

Tests will be coming I have them already for my own purposes. Just need to refactor and include.