An unstructured block-based adaptive mesh refinement approach for discontinuous Galerkin method

This paper presents an adaptive mesh refinement (AMR) approach specifically designed for the discontinuous Galerkin (DG) method for conservation laws. Our approach employs block-based AMR to keep local data structures simple and computationally efficient, while supporting an unstructured topology of the initial root blocks through a forest representation to handle complex geometries. We introduce inter-block communication via guard cells to simplify flux computations between cells at same and different refinement levels. To preserve geometric fidelity of the computational domain with smooth boundaries during refinement, boundary nodes are projected onto either user-provided analytic surface functions or automatically reconstructed NURBS surfaces. The implementation includes MPI parallelization with dynamic load balancing using two alternatives: space-filling curve partitioning and graph partitioning. Numerical tests in 2D and 3D demonstrate the method’s expected order of accuracy, effective dynamic refinement control, and good parallel efficiency.