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]
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  0%|          | 0.004/10.0 [00:10<7:22:57, 2658.85s/it]
  0%|          | 0.018/10.0 [00:10<1:38:18, 590.89s/it]
  6%|▌         | 0.607/10.0 [00:10<02:44, 17.54s/it]
 57%|█████▋    | 5.723/10.0 [00:10<00:08,  1.88s/it]
 57%|█████▋    | 5.723/10.0 [00:10<00:08,  1.90s/it]
100%|██████████| 10.0/10.0 [00:10<00:00,  1.09s/it]
100%|██████████| 10.0/10.0 [00:10<00:00,  1.09s/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()