Fokker-Planck equation

[ignace-computing]

Hello.
Could someone please comment on the ease of using Trixi for the simulation of a multidimensional Fokker-Planck equation (for particle distributions)? In essence, I want to simulate an advection-diffusion equation with a nonconstant advection coefficient.
Thank you!
PS: sorry if this is not the right place for such questions.

[sloede]

PS: sorry if this is not the right place for such questions.

Hi @ignace-computing! Thank you for this issue - this is exactly the right place for such questions!

TL;DR

I am sorry to say this, but at the moment, advection-diffusion problems with variable advection coefficients are not supported in Trixi.

Longer explanation

Let me split your question into two separate issues:

• support for advection-diffusion equations
• support for variable coefficients

Support for advection-diffusion equations

At the moment we only support purely hyperbolic problems, thus with the current Trixi release it is not possible to simulate advection-diffusion problems out of the box. There is an open PR (#378), which will hopefully be merged soon (~April), that will add support for parabolic and hyperbolic-parabolic problems. However, the initial implementation is going to be very experimental and not fully thought out, so I'd not yet depend on it for longer-term projects.

Variable coefficient problems

Right now, we have no first-class support for variable coefficient problems in Trixi. Having said that, we do have an equation system AcousticPerturbationEquations2D that uses variable coefficients by storing them as extra state variables that are ignored during the time step evolution. It is not the most efficient approach, but it is easy to set up and it works. We have some ideas how to add proper support for variable coefficients, which is tracked in #358 (see specifically #358 (comment)), but there is no timeline on when this will be tackled yet. To conclude, I'd say you can have variable coefficients in Trixi, if you are willing to accept a certain amount of ugliness in the implementation :-)