Evaluation of Adaptive Mesh Refinement and Coarsening for the Computation of Compressible Flows on Unstructured Meshes

Abstract

SUMMARYThe compressible gas ows of interest to aerospace applications often involve situations where shock and expansion waves are present. Decreasing the characteristic dimension of the computational cells in the vicinity of shock waves improves the quality of the computed ows. This reduction in size may be accomplished by the use of mesh adaption procedures. In this paper an analysis is presented of an adaptive mesh scheme developed for an unstructured mesh ÿnite volume upwind computer code. This scheme is tailored to reÿne or coarsen the computational mesh where gradients of the ow properties are respectively high or low. The reÿnement and coarsening procedures are applied to the classical gas dynamic problems of the stabilization of shock waves by solid bodies. In particular, situations where oblique shock waves interact with an expansion fan and where bow shocks arise around solid bodies are considered. The e ectiveness of the scheme in reducing the computational time, while increasing the solution accuracy, is assessed. It is shown that the reÿnement procedure alone leads to a number of computational cells which is 20% larger than when alternate passes of reÿnement and coarsening are used. Accordingly, a reduction of computational time of the same order of magnitude is obtained.

Adaptive mesh refinement for high‐resolution finite element schemes

“…The basic idea is to contract edges and consolidate the two adjacent nodes. In general, di erent strategies [48] exist for positioning the newly created vertex which can be combined to improve the geometric quality of the resulting mesh. For an AFC scheme, the new vertices should be positioned so as to improve the algebraic properties of the discretization.…”