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]
  0%|          | 0/10.0 [00:11<?, ?it/s]
  0%|          | 0.00316/10.0 [00:11<10:01:49, 3612.05s/it]
  2%|▏         | 0.1541/10.0 [00:11<12:09, 74.07s/it]
 80%|███████▉  | 7.99595/10.0 [00:11<00:02,  1.43s/it]
 80%|███████▉  | 7.99595/10.0 [00:11<00:02,  1.43s/it]
100%|██████████| 10.0/10.0 [00:11<00:00,  1.14s/it]
100%|██████████| 10.0/10.0 [00:11<00:00,  1.14s/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()