Removing Hanging Faces from Tree-Based Adaptive Meshes for Numerical Simulations

Abstract

Adaptive mesh refinement (AMR) suffers from the problem of hanging faces in regions where elements of different refinement levels are neighbored, restricting its applicability when numerical solvers or methods are only compatible with conformal meshes. In our work, we develop a new feature for the tree-based AMR library t8code, that post-processes adaptive meshes and removes their hanging faces. In particular, we consider 2-dimensional quadrilateral refinements and insert transition cells of triangular subelements to ensure a one-to-one correspondence of elements faces and neighbors. The resulting conformal mesh is then called a transitioned mesh. We ensure that our method can properly be used in the context of AMR, where the mesh is constantly adapted and thus the transitioned mesh is as well. Furthermore, the neighbor-finding process in t8code is efficiently implemented via the Morton SFC index. We develop an extension of this approach for transitioned meshes, such that neighbor elements can efficiently be identified here, too. Numerical tests have proven the efficiency of our implementations and their applicability in a simple Finite Volume setting for the linear advection equation. Recently, progress has been made to enable MPI for these new features as well.