Anisotropic Patch-Based Adaptive Mesh Re nement for Finite-Volume Method

We propose an anisotropic, patch-based adaptive mesh re nement algorithm for the nite-volume method solving partial di erential equations on Cartesian and mapped grids. For large ow gradients, such as shock waves and ame fronts, that are aligned with one grid direction, anisotropic re nement can provide a similar reduction in error using much less grid cells compared to isotropic re nement. To enable anisotropic re nement, additional logistics are needed to track anisotropic patches, and new operations for transferring data between patches of anisotropic re nement are introduced. In this study, we focus on developing these new operators associated with a single-level grid and explore the solutions to issues associated with the operators across grid levels. For example, methods for tagging regions for anisotropic re nement and modi cations to the Berger-Rigoutsos grid generation algorithm are considered. The savings in cell count are expected to more than o set the extra program logistics. Validation of the anisotropic algorithm is achieved by comparison to the existing isotropic algorithm for an unsteady shock problem.