Multi-dimensional Limiting Strategy for Robust, Accurate and Efficient Computations of Compressible Flows on Unstructured Meshes

Abstract

The present paper deals with the accurate and robust limiting procedure for the multi-dimensional flow analysis on unstructured meshes. The multi-dimensional limiting process (MLP) which was successfully proposed on structured grid system is extended to unstructured meshes. Based on MUSCL-type framework on unstructured meshes, the new slope limiter is devised to satisfy the MLP condition, which is quite effective to regulate the unwanted oscillations, especially on multiple dimensions. Considering the neighborhood based on the vertex of the cell, as well as the edge, this limiting strategy captures the multi-dimensional flow features very accurately with the proper stencils. From the various numerical results, these desirable characteristics of the proposed limiting strategy are clearly shown.