Add tests using other real types · trixi-framework/Trixi.jl#591

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We should check whether everything works using

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

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

Research direction: Focus on converting Float64 specific literals to generic types using `oftype` and `convert`, and check for hardcoded Float64 in mesh files.
Tech stack: None
Domain: testingperformance
Issue type: Test
Difficulty: 3
Estimated time: Half day
Activity status: Active
Clarity: Clear
Prerequisites: GitJulia
Newbie friendliness: 75