2.2.3 Simple diffusion equation

This example solves a simple diffusion equation in two dimensions.

  0%|          | 0/10.0 [00:00<?, ?it/s]
Initializing:   0%|          | 0/10.0 [00:00<?, ?it/s]
  0%|          | 0/10.0 [00:06<?, ?it/s]
  0%|          | 0.004/10.0 [00:06<4:32:00, 1632.71s/it]
  2%|▏         | 0.216/10.0 [00:06<04:55, 30.25s/it]
 36%|███▌      | 3.596/10.0 [00:06<00:11,  1.83s/it]
 36%|███▌      | 3.596/10.0 [00:06<00:11,  1.87s/it]
100%|██████████| 10.0/10.0 [00:06<00:00,  1.49it/s]
100%|██████████| 10.0/10.0 [00:06<00:00,  1.49it/s]

from pde import DiffusionPDE, ScalarField, UnitGrid

grid = UnitGrid([64, 64])  # generate grid
state = ScalarField.random_uniform(grid, 0.2, 0.3)  # generate initial condition

eq = DiffusionPDE(diffusivity=0.1)  # define the pde
result = eq.solve(state, t_range=10)
result.plot()