Added Shu-Osher initialization for 1D compressible Euler with Gauss nodes

[mleprovost]

@jlchan I have added an example with the Shu-Osher initialization for the 1D compressible Euler with Gauss nodes (GaussSBP()).

I have slightly modified the initialization to avoid positivity issues.

The implementation uses a shock capturing. The time solver is SSPRK43 with adaptive time stepping.

For future work, add the ability to pass a positivity preserving limiter, e.g, PositivityPreservingLimiterZhangShu, for Gauss nodes to time-stepper SSPRK43?

[github-actions[bot]]

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Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 96.15%. Comparing base (fadfb3a) to head (4a923a2). Report is 1 commits behind head on main.

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[sloede]

The new elixir should be used in at least one test, to ensure that future changes to our API will not accidentally break it without anyone noticing.

[JoshuaLampert]

It looks like you have run the formatter with a different version than we use in our CI tests. Could you please rerun the formatter again with JuliaFormatter v1.0.45?

[ranocha]

It looks like some tests fail. Could you please check what's going on?

[mleprovost]

I fixed an error w.r.t the values of l2 and linf in the Shu Osher setting.

[jlchan]

That's odd. The DGMulti tests are still failing - and the failures appear to be due to real differences in the computed norms.

I wonder if it's related to https://github.com/trixi-framework/Trixi.jl/issues/881?

[jlchan]

There shouldn't be, but I'll double check tonight.

[mleprovost]

I realized that (Trixi)> test doesn't run all the tests, and I forgot to remove some stochasticity that I introduced in the initial condition as I was playing with the solver.