Efficient Delaunay-based solution adaptation for three-dimensional unstructured meshes

Abstract

Solution-based mesh adaptation is a subject of great significance to the practical application of unstructured grid CFD methods. Much of the work done in this area has either been limited to two-dimensional studies or has employed cell/edge-splitting strategies. The edge- splitting technique is rather inefficient, producing a 2:1 refinement with each adaptation, and does not readily allow for a coarsening of the mesh where flow gradients are negligible. With a recent shift to unstructured methods emphasizing mixed-element meshes, adaptation methods for hybrid tetrahedral/prismatic grids are needed. In this work, an efficient solution-adaptive procedure is developed for three-dimensional mixed-element unstructured meshes. For the interior tetrahedra, a Delaunay cavity reconstruction and circumcenter point placement strategy ensures the quality of the adapted mesh. Coarsening of the mesh is accomplished by collapsing edges from the grid. Refinement and coarsening techniques for the boundary mesh and boundary layer prism cells are developed as well. Of paramount importance is the development of a flow feature sensor that detects the relevant viscous and inviscid regions of the domain where coarsening and refinement are required. The method is shown to be effective for aerodynamic applications, detecting regions of interest and modifying the mesh accordingly.