Adaptive mesh refinement in binary black holes simulations

Understand

We discuss refinement criteria for the Berger-Rigoutsos (block-based) refinement algorithm in our numerical relativity code GR-Athena++ in the context of binary black hole merger simulations.

• We compare three different strategies: the "box-in-box" approach, the "sphere-in-sphere" approach and a local criterion for refinement based on the estimation of truncation error of the finite difference scheme.
• We extract and compare gravitational waveforms using the three different mesh refinement methods and compare their accuracy against a calibration waveform and demonstrate that the sphere-in-sphere approach provides the best strategy overall when considering computational cost and the waveform accuracy.
• Ultimately, we demonstrate the capability of each mesh refinement method in accurately simulating gravitational waves from binary black hole systems -- a crucial aspect for their application in next-generation detectors.