2.5 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 [00:09<?, ?it/s]
  0%|          | 0.004/10.0 [00:09<6:21:32, 2290.14s/it]
  2%|▏         | 0.175/10.0 [00:09<08:34, 52.37s/it]
 30%|███       | 3.041/10.0 [00:09<00:21,  3.03s/it]
 30%|███       | 3.041/10.0 [00:09<00:21,  3.08s/it]
100%|██████████| 10.0/10.0 [00:09<00:00,  1.07it/s]
100%|██████████| 10.0/10.0 [00:09<00:00,  1.07it/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()