A new AMR method in GR-Athena++

Finding analytical solution of the coupled Einstein-Euler equations in highly nonlinear regimes, for instance, around the moment of merger of two compact objects, is infeasible. As such, numerical relativity codes, like, the GR-Athena++ code, among others, are required to find the answer and get insight into the physics of these astrophysical systems. Additionally, resolving more physical features in greater details are expected from these codes, owing to enhancements in sensitivity and advent of new detectors. However, the computational resources are limited; hence, during the solve, we must adaptively decide how well different regions of the computational domain should be resolved. In other words, a good criterion for adaptive mesh refinement (AMR) is desired in order to efficiently use the resources and resolve the physics of interest. To achieve this goal, we look at the truncation error of the finite difference derivative in the GR-Athena++ code. In this method, refinement or de-refinement of a region is taking place according to this error. Here, we present some preliminary results of the new AMR for a single black hole system.