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%|          | 0.00334/10.0 [00:08<7:26:46, 2681.53s/it]
  2%|▏         | 0.17025/10.0 [00:08<08:37, 52.61s/it]
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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()