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<6:08:11, 2210.08s/it]
  2%|▏         | 0.24/10.0 [00:08<05:59, 36.85s/it]
 48%|████▊     | 4.777/10.0 [00:08<00:09,  1.86s/it]
 48%|████▊     | 4.777/10.0 [00:08<00:09,  1.87s/it]
100%|██████████| 10.0/10.0 [00:08<00:00,  1.12it/s]
100%|██████████| 10.0/10.0 [00:08<00:00,  1.12it/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()