A Node-Pair Finite Element / Finite Volume Mesh Adaptation Technique for Compressible Flows

A grid adaptation technique for two-dimensional unstructured grids of triangles and quadrilaters is presented. The error estimation procedure, as well as the refinement / coarsening algorithms, are formulated in terms of a node-pair based data structure, that allows for a unified description of the finite element and finite volumes discretizations. The adaptation algorithm is based on a strategy of successive corrections, where a suitable number of intermediate adapted grids are generated and successively corrected employing only a nodes insertion technique. Coarsening of the grid is obtained in an implicit fashion avoiding the insertion of new nodes during the correction phase. The adaptation history, from the initial grid through the intermediate grids, and up to the final mesh is stored and updated through the whole process. No intermediate grid is therefore required to be stored explicitly. Since no explicit coarsening or nodes movement technique is employed here, the algorithm is very fast and robust. Numerical experiments of steady compressible flows are presented to support the description of the adaptation technique.