An H-Adaptive Unstructured Mesh Refinement Strategy for Unsteady Problems

Abstract

An h-adaptive unstructured mesh refinement strategy to solve unsteady problems by the finite element method is presented. The maximum level of refinement for the mesh is prescribed beforehand. The core operation of the strategy, namely the refinement of the elements, is described in detail. It is shown through numerical tests that one of the advantages of the chosen refinement procedure is to keep bounded the mesh quality. The type of element is not changed and no transition templates are used, therefore hanging nodes appear in the adapted mesh. The 1-irregular nodes refinement constraint is applied and the refinement process driven by this criterion is recursive. Both the strength and weakness of the adaptivity algorithm are mentioned, based on clock time measures and implementation issues. To show the proper working of the strategy, an axisymmetric, compressible non-viscous starting flow in a bell-shaped nozzle is solved over an unstructured mesh of hexahedra.