Ameliorating the Courant Limitation on Vacuum and GRMHD Simulation in Spherical-Polar Coordinates:*

Spherical-like coordinates have many advantages when it comes to evolving systems that are approximately axially symmetric. This includes the remnants of compact-object mergers. However, the often severe Courant limitation associated with the origin and polar axis can make high-resolution simulations impractical. In this talk we describe two techniques for mitigating the Courant limitation using filtering algorithms