Is it possible to develop variable coeffcient solver based on Trixi.jl framework?

[mathboylinlin]

Hello everyone. Could someone tell me is it possible to develop a solver for solving equations with solution dependent coefficinets or coordinate dependent coefficients? For example, in the heat transfer problem, the thermal conductivity is not always a constant but dependent on temperature which is an independent variable in the heat transfer equations. I would like to know whether Trixi.jl can deal with this problem. Thanks in advance.

[ranocha]

Coefficients that depend on the solution itself mean that you have to deal with a nonlinear problem. This is the focus of Trixi.jl, so it is widely supported. See for example https://trixi-framework.github.io/Trixi.jl/stable/tutorials/adding_new_scalar_equations/ for a simple tutorial describing a nonlinear scalar conservation law.
Coefficients depending on the space coordinates are less supported. Right now, we typically introduce the space coordinates as additional degrees of freedom as described in https://trixi-framework.github.io/Trixi.jl/stable/tutorials/adding_nonconservative_equation/ to handle this. This is suboptimal and should be changed at some point, but we did not have the resources to do so so far. See #358