Estimates of wave speeds

[ranocha]

Often, we need some estimates of the wave speeds, e.g.

• for CFL-based time step control

• for numerical fluxes like local Lax-Friedrichs, Harten-Lax-van Leer

  In principle, multiple estimate of the wave speeds can be used, e.g.

• "naive" values based on the local wave speeds of one or two nodes

• exact value from the solutions of the corresponding Riemann problem (if available)

• some estimates from the literature

~Can/shall we try to create some unified interface for these estimates?~ We created a unified interface for wave speed estimates in #493. Now, we shall to add more sophisticated wave speed estimates, e.g.

• [ ] Euler euations
  • Guermond and Popov (2016) Fast Estimation from above of the maximum wave speed in the Riemann problem for the Euler equations, Journal of Computational Physics 321, pp. 908-926
  • Chen and Shu (2017) Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws, Journal of Computational Physics 345, pp. 427-461

[gregorgassner]

1.) I wonder if we should relate this to making scalar nodal functions (e.g. pressure), and one could be to compute the maximum wave speeds.

In general, I prefer to encapsulate the equation of state...as this would in theory allow us to change to another EOS a bit simpler...

2.) In general I like the idea to play around with the wave speeds. Especially for the Riemann solvers there is an impact in the choice of the wave speeds, e.g. the HLL or HLLC ones. However, I am not sure how immediate this problem is right now, or maybe something to keep for future experiments with a possible FV solver in Trixi.

[ranocha]

Sounds good to me. From my point of view, there are more important things to do right now (MPI, Taal), so we will keep this on our radar and come back to it later.

[DanielDoehring]

See PRs #1545 and https://github.com/trixi-framework/Trixi.jl/pull/1561