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 [00:10<?, ?it/s]
  0%|          | 0.004/10.0 [00:10<7:35:28, 2733.93s/it]
  0%|          | 0.018/10.0 [00:10<1:41:04, 607.58s/it]
  6%|▌         | 0.598/10.0 [00:10<02:52, 18.31s/it]
 56%|█████▋    | 5.64/10.0 [00:11<00:08,  1.96s/it]
 56%|█████▋    | 5.64/10.0 [00:11<00:08,  1.98s/it]
100%|██████████| 10.0/10.0 [00:11<00:00,  1.12s/it]
100%|██████████| 10.0/10.0 [00:11<00:00,  1.12s/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()