MHD implementation details and discussions

Random bits and pieces

• Reuse parts of Harm3D
• Used Harm3d as a reference, but the only parts of Harm3d directly included were for the Con2PrimM routines.

Conventions / Variable names etc.

• Principally follow the Valencia formulation as out-lined in Anton et al. (2006)
• HydroBase's Bvec[1-3] GF will be identified with Valencia's B^i vector
• Bvec[] will be used both as an evolved quantity and a primitive variable
• During the Carpet workshop, we concluded it is easier to define B^i to be the undensitized magnetic field; this requires some care, since psi^6 B^i is the quantity that appears in the evolution equation, but simplifies the rest of the code
• Only use locally calculated "comoving magnetic tensor" b^a when needed
• In general, but especially for MHD, it seems worthwhile to promote sqrt(gamma)=psi^6 to an independent gridfunction
• See Josh Faber's notes here [1], or check out the code (still a work in progress!!!) here [2].
• Josh Faber will commit has committed the routines mentioned in these notes soon.
• Scott Noble and Josh Faber worked on Con2PrimM and have committed.

Subprojects

Task	Main people	Notes	Status
Riemann Problem	Faber		HLLE done
Con2Prim	Noble, Faber	from Harm3D	done, except for general EOS
Constraint transport	?	from Harm3D	still on drawing board
Reconstruction	Faber, Mundim		done
Failure Recovery Procedure	?		just using old tools for now
Carpet Refluxing	Erik Schnetter		Finished?
EMF Restriction/Prolongation	?	Needed for CT only
Constraint Damping?	Faber, Mundim, Noble	SR case done	GR derived, not implemented yet
Tests and debugging	Mundim, Faber, Noble		In progress

During the Cactus workshop, some progress was made on implementing MHD within GRHydro by reimplementing various subroutines with alternate versions for MHD and calling them out with the MHD flag in the scheduler. Basically, instead of GRHydro_filename.F90, we will have GRHydro_filenameM.F90.

Most of these *M.F90 files have generated and are part of ET already.

Notes on the derivation of the GR divergence cleaning equations:
File:Rel cleaning new.pdf
File:Rel cleaning new.tex