Solution Adaptive Isotropic And Anisotropic Mesh Refinement Using General Elements

Abstract

Two refinement techniques to generate solution adaptive meshes have been developed. Both techniques utilize arbitrary polyhedra (general elements) to constrain the propagation of refinement. A face-based approach that produces isotropic refinement and a combined element- and edge-based approach that produces anisotropic refinement are presented. Refinement is triggered through sensors that use a shock detection algorithm or error estimation based on the smoothness of the reconstructed solution variables. The basic algorithms as well as specific implementation issues are presented. The advantages and disadvantages of the different methods are discussed and illustrated through a set of synthetic and realistic test cases. It is shown that general elements can be employed effectively in solution adaptive meshes generated using refinement