A node-pair finite element/volume mesh adaptation technique for compressible flows based on a hierarchical approach

A grid adaptation technique for two-dimensional unstructured grids of triangles and quadrilaterals is presented. The error estimation procedure is formulated in terms of a node pair-based data structure that allows for a unified description of the finite element and finite volume schemes. The adaptation algorithm is based on a strategy of hierarchical corrections, where a suitable number of intermediate adapted grids are generated and successively corrected by employing a simple node insertion technique at the midpoint of the element edges. Coarsening of the grid is obtained in an implicit fashion by avoiding the insertion of new nodes during the correction phase. The adaptation history, from the initial to the current grid, including all intermediate grids, is stored and updated through the whole process. No intermediate grid is therefore required to be stored explicitly. The adapted grid is anisotropic, thanks to the adoption of both regular triangular and quadrilateral elements with high aspect ratio that are gathered in, for example, boundary layer or wake regions. Numerical experiments of steady compressible flows, including both inviscid and viscous flows, are presented to support the suitability of the adaptation technique.