Initial condition for parabolic terms requires defining `diffusivity` as global function

Yeah, this is one of the open issues with parabolic terms in Trixi.jl.

The initial condition (and thus the analysis routines) dispatch on the hyperbolic equation type. However, this makes it impossible to pass in parabolic parameters. Thus, if the exact solution is stored in the `initial_condition` but depends on parabolic parameters we can't access them. As a workaround, we create a global `diffusivity() = ...` function that can be called from within `initial_condition`.

I tried working around this in https://github.com/trixi-framework/Trixi.jl/pull/1160 by introducing a combined equation type, but it was a bit messy.

_Originally posted by @jlchan in https://github.com/trixi-framework/Trixi.jl/pull/1490#discussion_r1213212418_