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Numerical simulations of merging compact objects and their remnants form thetheoretical foundation for gravitational wave and multi-messenger astronomy.While Cartesian-coordinate-based adaptive mesh refinement is commonly used forsimulations, spherical-like coordinates are more suitable for nearly sphericalremnants and azimuthal flows due to lower numerical dissipation in theevolution of fluid angular momentum, as well as requiring fewer numbers ofcomputational cells. However, the use of spherical coordinates to numericallysolve hyperbolic partial differential equations can result in severeCourant-Friedrichs-Lewy (CFL) stability condition timestep limitations, whichcan make simulations prohibitively expensive. This paper addresses this issuefor the numerical solution of coupled spacetime and general relativisticmagnetohydrodynamics evolutions by introducing a double FFT filter andimplementing it within the fully MPI-parallelized SphericalNR framework in theEinstein Toolkit. We demonstrate the effectiveness and robustness of thefiltering algorithm by applying it to a number of challenging code tests, andshow that it passes these tests effectively, demonstrating convergence whilealso increasing the timestep significantly compared to unfiltered simulations.

Ameliorating the Courant-Friedrichs-Lewy condition in spherical  coordinates: A double FFT filter method for general relativistic MHD in  dynamical spacetimes