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] 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)
[x] Explicit time stepping, CFL-based step size control and error-based adaptive step sizes (#1116)
[x] DGMulti solver and mesh
[x] 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)
[x] Polynomial and nodal SBP approximation spaces
[x] "Esoteric" methods such as FD SBP, CGSEM via SummationByPartsOperators.jl, and GaussSBP
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:
TreeMesh
? or probably better creating a simple uniform 1D mesh type on the fly)TreeMesh
etc.)DGMulti
solver and meshexamples/dgmulti_2d/elixir_euler_triangulate_pkg_mesh.jl
for an example using a "ready-made" geometry from StartUpDG.jl)