Trixi.jl
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DG and Trixi tutorial in the docs
It would be nice to have a brief explanation of DG methods and their implementation in Trixi.jl in the docs. That part is different from https://github.com/trixi-framework/Trixi.jl/issues/169, since it should contain an introduction to the mathematical parts of the algorithms instead of "just" the combination of Trixi's API components to run something. Here is a preliminary list of topics to be covered:
- [x] Simple and clear scalar linear advection example in 1D (#943)
- Describe basics of weak form DG
- Implement a simple weak form DG specialized to scalar linear advection in 1D on a uniform mesh (maybe using the
TreeMesh
? or probably better creating a simple uniform 1D mesh type on the fly) - Use OrdinaryDiffEq.jl with adaptive time stepping (simple and easy to use)
- Show how to write the same example using Trixi's capabilities (
TreeMesh
etc.)
- [x] Flux differencing aka split form DG: Compressible Euler equations based on existing elixirs, EC flux of Ranocha and split form of Shima et al. or Kennedy & Gruber (#1002)
- [x] Shock capturing with flux differencing based on an existing elixir (#1024)
- [x] Stage limiter (positivity preserving limiter of Zhang & Shu) (#1024)
- [x] Adaptive mesh refinement based on an existing elixir (#1025)
- [x] Non-periodic boundary conditions based on existing elixirs (Dirichlet BC, wall BC) (#1059)
- [x] Structured mesh with mapping, e.g., 2D flow with compressible Euler equations (flow around a cylinder?) (#1084)
- [x] Mention KPP elixir introduced in #1035 in "Adding a new equation" (#1025)
- [ ] Explicit time stepping, CFL-based step size control and error-based adaptive step sizes (#1116)
- [ ]
DGMulti
solver and mesh- [ ] Triangular meshes with DG (see
examples/dgmulti_2d/elixir_euler_triangulate_pkg_mesh.jl
for an example using a "ready-made" geometry from StartUpDG.jl) - [ ] Polynomial and nodal SBP approximation spaces
- [ ] "Esoteric" methods such as FD SBP, CGSEM via SummationByPartsOperators.jl, and GaussSBP
- [ ] Triangular meshes with DG (see