MEHCscheme

A mass, energy, and helicty conserving dual-field Galerkin finite element discretization of the incompressible Navier-Stokes problem based on this paper https://arxiv.org/abs/2104.13023 implemented in MFEM, see https://mfem.org/

CMake and Make

TODO (basically download and unpack mfem and glvis into the extern folder, then install it there as described on mfem.org; then run the build.sh file to cmake, the compile.sh file to make, the run.sh file to run and the clean.sh file to delete the mesh and solution files afterwards)

folder structure

• /build will contain all files produced by cmake
• /extern contains the mfem (v4.5) and glvis (v4.2) library
• /out contains plots and data outputs
• /scripts contains some files necessary for plotting etc
• /src contains the cpp files that implement the mehc scheme
• .sh are all shell scripts, that contain some handy commands for building, compiling, running and cleaning

run the scheme:

1. select the cpp file in src/CMakeLists.txt :
   • periodic-conv.cpp
   • periodic-cons.cpp
   • dirichlet-[placeholder].cpp
2. run ./build.sh
3. run ./compilerun.sh
4. produce a visualization using scripts/plots_[placeholder].ipynb
5. find the visualizsations in out/plots
6. find the raw data in out/rawdata