Ameliorating the Courant-Friedrichs-Lewy condition in spherical
coordinates: A double FFT filter method for general relativistic MHD in
dynamical spacetimes
Numerical simulations of merging compact objects and their remnants form the
theoretical foundation for gravitational wave and multi-messenger astronomy.
While Cartesian-coordinate-based adaptive mesh refinement is commonly used for
simulations, spherical-like coordinates are more suitable for nearly spherical
remnants and azimuthal flows due to lower numerical dissipation in the
evolution of fluid angular momentum, as well as requiring fewer numbers of
computational cells. However, the use of spherical coordinates to numerically
solve hyperbolic partial differential equations can result in severe
Courant-Friedrichs-Lewy (CFL) stability condition timestep limitations, which
can make simulations prohibitively expensive. This paper addresses this issue
for the numerical solution of coupled spacetime and general relativistic
magnetohydrodynamics evolutions by introducing a double FFT filter and
implementing it within the fully MPI-parallelized SphericalNR framework in the
Einstein Toolkit. We demonstrate the effectiveness and robustness of the
filtering algorithm by applying it to a number of challenging code tests, and
show that it passes these tests effectively, demonstrating convergence while
also increasing the
timestep significantly compared to unfiltered simulations.Comment: 15 pages, 13 figures, revtex4-