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Improve documentation #144

@JoshuaLampert

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@JoshuaLampert

Up to now we only have one overview page in the documentation, which tries to cover everything in the package. I think it would be nice to split this up in several parts focusing on different aspects (e.g. pages about more theoretical aspects and more tutorial-like pages). Ideas for tutorials:

  • Basic introductory example
  • Compare different SBP solvers: Especially upwind vs central (upwind leads to higher resolution), but also FD vs. DG vs. CG vs. Fourier: Maybe make this two separate tutorials? (also explain about SBP operators)
  • Dispersion
  • Explain influence of using relaxation (exact preservation of nonlinear invariant, quadratic vs. linear error growth)
  • Compare different equations with experimental data from Dingemans setup, see Add comparison with experimental data to docs #238
  • Make more experimental data available for comparisons (can be done last)

In addition, it would be nice to have a page explaining the implementation strategy and the interplay between different building blocks (mesh, equations, solver, semidiscretization, ODE solver, callbacks), maybe similar to the diagram in https://trixi-framework.github.io/Trixi.jl/stable/overview/#overview-semidiscretizations.

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