MHD development

MHD Development Agenda

List of Potential Topics

• Vector Potential implementation
• Combining constraint transport and divergence cleaning
• Divergence cleaning and mesh refinement

Vector Potential

Evolving the vector potential allows for better conservation across refinement level boundaries and better control of the B-field divergence. Evolving the vector potential is also better behaved surrounding puncture BHs. As this feature changes one of the base evolved variables with a non-local connection to the variables currently used in pointwise MHD routines, though, an efficient toggle system to switch evolution schemes could use further discussion.

Current State

This was partially implemented in the last development workshop, though this has been removed again from the development version. We had agreed to implement the algebraic gauge first, but ultimately need the Lorenz gauge. Initial implementation had been of cell-centered vector potential, though we should now be able to support staggered grid vector potential.

Matters to Discuss

• Staggered vs unstaggered A^i
• Prolongation operators given the location on the cell ( for staggered A only )
• Scheduling for reconstructing B from the vector potential

Coding Tasks

As this workshop will take place during the pre-release phase, this development should take place in Zelmani.

• Storage and evolution (simpler now that E^i has been implemented and tested for the constraint transport)
• B-field construction from A^mu
• Initial Prim2Con support for A^mu
• Reconstruction support for A^mu
• Riemannsolver support for A^mu
• Recovery point-wise support for A^mu

Con2Prim Inverter

• add code to transition into force-free inversion (no force free evolution) if magnetic pressure starts to dominate gas pressure (done in SpEC, seems robust)