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

Abstract

The compressible gas flows 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 flows. 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 finite volume upwind computer code. This scheme is taylored to refine or coarsen the computational mesh where gradients of the flow properties are respectively high or low. The refinement 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 effectiveness of the scheme in reducing the computational time, while increasing the solution accuracy, is assessed. It is shown that the refinement procedure alone leads to a number of computational cells which is 20% larger than when alternate passes of refinement and coarsening are used. Accordingly, a reduction of computational time of the same order of magnitude is obtained. Mesh adaption procedures are frequently used to reduce the characteristic dimension of the computational cells in interesting regions of the flowfield, with the aim of yielding a better resolution of the simulated phenomena. Most often in computational fluid dynamics, such regions are those where the gradients of the flow properties are high or where the numerical solution exhibits a large error. Typical regions of high gradients are boundary and shear layers, chemical reaction fronts and shock waves. The exact position of these regions are not known a priori. In particular, shock waves are usually captured by the discretization schemes of the governing equations and span over two or three computational cells, even though the physical dimension of these waves is of order of a few mean free paths of the gas molecules. Successive refinements are usually necessary to achieve a good resolution of the regions of the flowfield where high gradients occurs. As a consequence, a significant increase of the number of mesh volumes may result, eventually leading to a concentration of refined volumes in regions of the flowfield where those volumes are no longer needed. Thus, mesh coarsening techniques are of interest with the aim of increasing the characteristic dimension of the computational mesh, ultimately leading to a reduction of the computational time. In this paper refinement and coarsening techniques taylored for unstructured meshes will be evaluated with respect to the gains in solution accuracy and computational time. During the past few years, several authors have developed mesh adaptation techniques in an unstructured mesh context. Hierarchical mesh adaptation techniques have been developed by Kallinderis and Viajayan, 1 and by Speares and Berzins 2 on three-dimensional unstructured meshes.The coarsening procedure acts only in regions previously