Issues in adaptive mesh refinement

In this paper, we present an approach for a patch-based adaptive mesh refinement (AMR) for multi-physics simulations. The approach consists of clustering, symmetry preserving, mesh continuity, flux correction, communications, management of patches, and dynamical load balance. Among the special features of this patch-based AMR are symmetry preserving, efficiency of refinement, special implementation of flux correction, and patch management in parallel computing environments. Here, higher efficiency of refinement means less unnecessarily refined cells for a given set of cells to be refined. To demonstrate the capability of the AMR framework, hydrodynamics simulations with many levels of refinement are shown in both two- and three-dimensions.