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 [00:13<?, ?it/s]
  0%|          | 0.004/10.0 [00:13<9:14:36, 3328.98s/it]
  0%|          | 0.018/10.0 [00:13<2:03:04, 739.82s/it]
  5%|▍         | 0.499/10.0 [00:13<04:13, 26.71s/it]
 47%|████▋     | 4.724/10.0 [00:13<00:14,  2.84s/it]
 47%|████▋     | 4.724/10.0 [00:13<00:15,  2.87s/it]
100%|██████████| 10.0/10.0 [00:13<00:00,  1.36s/it]
100%|██████████| 10.0/10.0 [00:13<00:00,  1.36s/it]

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()