variable bathymetry Serre-Green-Naghdi equations

[ranocha]

This is the next step of #129

[codecov]

Codecov Report

Attention: Patch coverage is 99.66887% with 1 line in your changes missing coverage. Please review.

Project coverage is 97.57%. Comparing base (8fcba88) to head (d4f9dd6).
Report is 1 commits behind head on main.

Files	Patch %	Lines
src/equations/serre_green_naghdi_1d.jl	99.64%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #135      +/-   ##
==========================================
+ Coverage   97.00%   97.57%   +0.57%     
==========================================
  Files          18       20       +2     
  Lines        1369     1569     +200     
==========================================
+ Hits         1328     1531     +203     
+ Misses         41       38       -3     

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[JoshuaLampert]

Only a preliminary review with a question regarding the use of eta and h.

[JoshuaLampert]

Another question, which just came into my mind: What do we do if you pass bathymetry_flat to the equation, but then set a non-constant bathymetry in the initial condition. I haven't thought about that before. Should this raise a warning or an error or nothing?

[JoshuaLampert]

Can you please also add a well-balancedness test?

[ranocha]

Another question, which just came into my mind: What do we do if you pass bathymetry_flat to the equation, but then set a non-constant bathymetry in the initial condition. I haven't thought about that before. Should this raise a warning or an error or nothing?

Where could we add such a check? My first idea was to look at create_cache, but that doesn't have the initial condition

[JoshuaLampert]

Another question, which just came into my mind: What do we do if you pass bathymetry_flat to the equation, but then set a non-constant bathymetry in the initial condition. I haven't thought about that before. Should this raise a warning or an error or nothing?

Where could we add such a check? My first idea was to look at create_cache, but that doesn't have the initial condition

It could live in Semidiscretization, but then I would only add such a check when all equations have a field bathymetry (or bathymetry_type), i.e. after finishing #130.

[JoshuaLampert]

Now we have a bunch of conflicts to solve... 🙄

[ranocha]

Now we have a bunch of conflicts to solve... 🙄

Done

[JoshuaLampert]

Thanks!

[ranocha]

In general we have some code duplication. Would it be possible and wise to put some recurring patterns into functions, e.g., thing like

        if equations.bathymetry_type isa BathymetryMildSlope
            factor = 0.75
        else # equations.bathymetry_type isa BathymetryVariable
            factor = 1.0
        end

Done in c7ff29a and 0062720

[JoshuaLampert]

Final iteration. This looks already very nice!

[JoshuaLampert]

LGTM! Thanks a lot!

[JoshuaLampert]

Now we only have this nasty codecov error on MacOS. But since it seems to fail consistently, I would like to find a fix before merging this PR.

[JoshuaLampert]

Thanks!