Flux‐difference splitting scheme with modified multidimensional dissipation on unstructured meshes

Abstract

A flux‐difference splitting scheme with a modified multidimensional dissipation for high‐speed compressible flow analysis on unstructured meshes is presented. The scheme eliminates unphysical flow behaviors such as a spurious bump of the carbuncle phenomenon that occurs on the bow shock from flow over a blunt body, and the expansion shock generated from flow over a forward facing step. The switching function suggested by Quirk is implemented as a choice to detect the vicinity of strong shock. The proposed scheme is further extended to obtain higher‐order spatial and temporal solution accuracy. The scheme is, in addition, combined with an adaptive meshing technique that generates unstructured triangular meshes to resemble the flow phenomena for reducing computational effort. The entire procedure is evaluated by solving several benchmarks as well as steady‐state and transient high‐speed compressible flow problems.