Fokker-Planck diffusion equation

[chmin333]

Dear Dr. Zwicker,
Thanks for this wonderful package! I really appreciate your work, but I just have several questions about the package.

I want to solve this fokker-planck diffusion equation where
P = P(x,y,t) probability density function,
D = Diffusion coefficient,
V = (dx/dt, dy/dt) external drift velocity vector, which is my custom vector field in the form of numpy array

Is there any way to include custom vector field into the PDE?
Also how can I include vector term in the PDE? I could not find example codes that include vector term.
Can you show demonstration code?
Thank you!

[david-zwicker]

This is certainly possible. Here is a little example that might get you on track:

grid = pde.UnitGrid([32, 32], periodic=True)
field = pde.VectorField.random_uniform(grid)

velocity = pde.VectorField(grid, data=field.data)  # set velocity field from numpy array
state = pde.ScalarField.random_normal(grid)  # set initial state 

D = 0.5
eq = pde.PDE({'P': f'-divergence(P * V) + {D}/2 * laplace(P)'}, consts={'V': velocity})

result = eq.solve(state, t_range=1e2, dt=1e-4, tracker=['progress', 'plot'])

[chmin333]

Thank you for the quick reply! It was really helpful!