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DG and Trixi tutorial in the docs

Open ranocha opened this issue 3 years ago • 0 comments

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

ranocha avatar Oct 07 '20 08:10 ranocha