A new adaptive mesh refinement method in the GR-Athena++ code

It is barely feasible to find the analytical solution to astrophysically cataclysmic events, such as the merger of a binary black hole system. As such, the numerical relativity community has developed various techniques and infrastructures (codes) to find the answer and get insight into the physics of these astrophysical systems. Due to the lack of efficiency and the limited computational resources, numerical relativity codes refrain from using a monolithic and uniformly resolved mesh. Instead, an adaptive mesh refinement (AMR) is utilized in which the mesh adaptively uses different patches with a proportional resolution to resolve physical features of interest wherever necessary. Therefore, deciding what regions of the computational grid should be refined requires an appropriate criterion for the AMR. 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-refining of a region takes place according to this error. One of the advantages of this method is that the knowledge of the apparent horizons or the location of the punctures is not required. In other words, the refinement is smart enough to automatically resolve the region around the punctures, where it is needed most. Furthermore, this method ensures the magnitude of error is more or less uniform across the computational grid, i.e., unnecessary refinement is not taking place. Here, after a short introduction to GR-Athena++ code, we present some preliminary results of this new AMR method for an evolution of a binary black hole system.