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]
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  0%|          | 0.004/10.0 [00:08<5:47:09, 2083.79s/it]
  3%|▎         | 0.255/10.0 [00:08<05:18, 32.70s/it]
 49%|████▉     | 4.927/10.0 [00:08<00:08,  1.70s/it]
 49%|████▉     | 4.927/10.0 [00:08<00:08,  1.71s/it]
100%|██████████| 10.0/10.0 [00:08<00:00,  1.18it/s]
100%|██████████| 10.0/10.0 [00:08<00:00,  1.18it/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()