An unstructured block-based adaptive mesh refinement approach for explicit discontinuous Galerkin method (2502.12620v1)

Abstract: In the present paper, we present an adaptive mesh refinement(AMR) approach designed for the discontinuous Galerkin method for conservation laws. The block-based AMR is adopted to ensure the local data structure simplicity and the efficiency, while the unstructured topology of the initial blocks is supported by the forest concept such that the complex geometry of the computational domain can be easily treated. The inter-block communication through guardcells is introduced to avoid the direct treatment of flux computing between cells at different refinement levels. The sharp corners and creases generated during direct refinement can be avoided by projecting the boundary nodes to either the user-defined boundary surface function or the auto-generated NURBs. High-level MPI parallelization is implemented with dynamic load balancing through a space curve filling procedure. Some test cases are presented. As a result, ideal accuracy order and versatility in tracing and controlling the dynamic refinement are observed. Also, good parallelization efficiency is demonstrated.