Divergence-Free Magnetohydrodynamics on Conformally Moving, Adaptive Meshes Using a Vector Potential Method

Understand

We present a new method for evolving the equations of magnetohydrodynamics (both Newtonian and relativistic) that is capable of maintaining a divergence-free magnetic field ($\nabla \cdot \mathbf{B} = 0$) on adaptively refined, conformally moving meshes.

• The method relies on evolving the magnetic vector potential and then using it to reconstruct the magnetic fields.
• The advantage of this approach is that the vector potential is not subject to a constraint equation in the same way the magnetic field is, and so can be refined and moved in a straightforward way.
• We test this new method against a wide array of problems from simple Alfven waves on a uniform grid to general relativistic MHD simulations of black hole accretion on a nested, spherical-polar grid.