flux_lax_friedrichs should be specialized for equations with discontinuous parameter-as-variables

[jlchan]

Right now, if you have a bottom topography or another spatially dependent parameter in your solution, you need to store it as an additional variable in the solution.

Note that rhs! should return zero for any variables which are parameters but not true variables. However, if this additional variable is discontinuous, and your surface flux is flux_lax_friedrichs, the LxF penalization will be non-zero and enforce continuity during the ODE solve.

I noticed this issue with the quasi-1D SWE equations, as well as an incoming PR for the quasi-1D Euler equations. I'm not sure if it as issue for SWE too.

[andrewwinters5000]

That is true. This was first noticed by Lars for the AcousticPerturbationEquations2D so he wrote a special version of the Lax-Friedrichs dissipation term that zeros out the appropriate entries. Later we did the same for the ShallowWaterEquations in 1D and 2D as well as for the two-layer shallow water equations.

[ranocha]

The "correct" fix for it would be to treat space-dependent terms as first-class citizens, see #358

[andrewwinters5000]

Definitely, this issue and subsequent workarounds have been around for awhile.

[jlchan]

Great. I'll file a PR to fix it for the quasi-1D SWE and then it should be resolved for that equation too.

[jlchan]

Turns out the LxF dissipation was already implemented correctly for quasi-1D SWE. The issue was with flux for quasi-1D SWE instead (it included a non-conservative term). This will be fixed in #1731.