Grid Refinement Criterion for GRMHD Simulations

Numerical simulations of astrophysical flows around compact objects such as black holes demand high accuracy in regions of sharp gradients, turbulence, and discontinuities, while also requiring computational efficiency over large domains. Adaptive mesh refinement (AMR) provides a powerful tool to achieve this balance; however, the success of AMR hinges on the quality of the refinement and de-refinement criteria. In this work, we explore a grid refinement strategy inspired by the smoothness of fourth-order derivatives. We implement this method in the GPU-parallelized code AthenaK and evaluate its effectiveness on several problems that test the numerical accuracy and efficiency of the method. We find that the criterion can effectively track discontinuities without over refining smooth regions while nicely coarsening the grid structure over smooth regions. This approach has promising applications to general relativistic magneto-hydrodynamic (GRMHD) simulations of accretion flows and jet launching, where capturing small-scale physics as well as computational efficiency is crucial. This work takes a step towards a physically informed refinement strategy that could enable faster and more accurate simulations of extreme astrophysical phenomena.