Add tests using other real types

We should check whether everything works using

• Float32
• Float64 (current default)
• Types from MultiFloats.jl or Quadmath.jl

It would also be nice to see the impact on performance.

Tasks

• Convert 0.5 * or 1/2 * to 0.5f0 *
• Use oftype and convert in initial conditions, source terms etc.
• Implement ln_mean and other math.jl functions for Float32 (https://github.com/trixi-framework/Trixi.jl/pull/2048)
• Make mesh types flexible enough (for solve)
  • Fix TreeMesh, hardocded to Float64 https://github.com/trixi-framework/Trixi.jl/blob/345f53acf3b2c1d80431b2a330d16fdca7638728/src/meshes/tree_mesh.jl#L102-L104
  • StructuredMesh
  • UnstructuredMesh2D
  • P4estMesh
  • Fix T8codeMesh, hardcoded to Float64 https://github.com/trixi-framework/Trixi.jl/blob/345f53acf3b2c1d80431b2a330d16fdca7638728/src/meshes/t8code_mesh.jl#L34
  • Fix DGMulti, hardcoded in several places https://github.com/trixi-framework/Trixi.jl/blob/345f53acf3b2c1d80431b2a330d16fdca7638728/src/solvers/dgmulti/shock_capturing.jl#L32
• Check/fix initialization of mesh types
• Volume terms
  • weak form
  • flux differencing
  • shock capturing (typically uses EC fluxes with ln_mean)
  • strong form
  • upwind FDSBP
• Callbacks
  • StepsizeCallback
  • AnalysisCallback
  • SaveSolutionCallback
  • ...
• Add unit tests for numerical fluxes
• Add new tests for full elixirs
  • Be aware of trigonometric functions! See https://github.com/trixi-framework/Trixi.jl/pull/2048