Rotating magnetohydrodynamic flow solver

The repository is meant to act as a source code control and back up of the project.

Milestones:

• Incompressible Navier-Stokes equations
• Convective flow (Incompressible Navier-Stokes equations with bouyancy term + heat equation)
• Rotational convective flow (Incompressible Navier-Stokes equations with bouyancy term and coriolis term + heat equation)
• Rotational magnetohydrodynamic flow (Incompressible Navier-Stokes equations with bouyancy term and coriolis term + heat equation + induction equation )

which are to be tested with the following benchmarks

1. Taylor-Green Vortex: https://en.wikipedia.org/wiki/Taylor%E2%80%93Green_vortex, Schaefer et. al (1996) and Guermond (2006) test
2. Christon, Gresho und Sutton (2002)
3. Christensen et. al (2000), Case 0
4. Christensen et. al (2000), Case 1 and Jackson et. al (2014)

To do list

• Removing the bug in the adaptive mesh refinement branch
• High Peclet number test and interpretation of the result
• Remove hard-coded absolute tolerance
• Adding the buoyancy to the Navier-Stokes solver
• Interfacing of the entities and the solvers
• Restructure the assembly scratch and copy structs and instance the FEValues in the Navier-Stokes solver with a Mapping
• Reduce global communication and do not compute extrapolated values using vectors
• Neumann boundary conditions in the incremental pressure projection scheme (Navier-Stokes solver)
• Restructure the parameters of the solvers
• Algebraic multigrid preconditioning in both solvers
• Implement a proper reset method in the NavierStokesProjection solver to make sure that the Poisson pre-step is done on each cycle of a temporal test
• Python or bash script for running convergence tests
• Adaptive timestepping
• Initialization from analytical solution
• Restart from numerical solution

Questions

• High Reynolds number tests and inspection of the solution w.r.t. instabilities
• Stabilizitation of convectivion dominated flows?!