Anisotropic Patch-Based Adaptive Mesh Refinement for Finite-Volume Methods

We propose an anisotropic, patch-based adaptive mesh refinement algorithm for the finite-volume method solving partial differential equations on Cartesian and mapped grids. For large flow gradients, such as shock waves and flame fronts, that are aligned with one grid direction, anisotropic refinement can provide a similar reduction in error using much less grid cells compared to isotropic refinement. To enable anisotropic refinement, additional logistics are needed to track anisotropic patches, and new operations for transferring data between patches of anisotropic refinement 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 refinement and modifications to the Berger-Rigoutsos grid generation algorithm are considered. The savings in cell count are expected to more than offset the extra program logistics. Validation of the anisotropic algorithm is achieved by comparison to the existing isotropic algorithm for an unsteady shock problem.