Anisotropic Cartesian Grid Adaptation

Abstract

A three-dimensional grid adaptation method using the concept of anisotropic Cartesian grid has been developed to improve the efficiency of an existing Cartesian grid adaptation method by reducing the total number of cells needed to compute a flow field. The present grid adaptation is carried out by performing both grid coarsening and refinement in such a way that the cell aspect ratio can take an arbitrary value, keeping the grid smoothness. This flexibility necessitates the concept of unstructured approach. Two test cases: a cylinder in supersonic flow and an ONERA M6 wing in transonic flow show that the present method can well capture 2D and 3D flow features. In the cylinder case, the number of cells after the final adaptation cycle is one or two orders of magnitude less than that of the corresponding isotropic grid; in the ONERA M6 case it becomes about half as many. This remarkable saving in the 2D case is achieved because the spanwise domain is covered by only one cell in the present method, unlike conventional isotropic approaches. As a result of the decrease in the number of cells, the anisotropic grid requires less time to solve the flow and less amount of total memory, though the amount of memory per cell actually increases because of its unstructured property.