Stabilized Roe-FDS Scheme for Solving Shock Wave Instabilities Problems on Triangular Grids

Abstract

Abstract

This paper study the numerical instability of Roe's flux-difference splitting scheme on triangular grids. The
scheme may sometimes lead to unphysical flow solutions in certain problems. These problems include the carbuncle
phenomenon that refers to a spurious bump on the bow shock near the flow center line ahead the blunt body or an
unrealistic perturbation that occurs from a moving shock along odd-even grid perturbation in a straight duct. The new idea
of entropy fix for unstructured triangular grids is presented to improve the computed shock wave resolution. The
proposed scheme is further extended to obtain higher-order spatial and temporal solution accuracy. The solution accuracy
is further improved by coupling an error estimation procedure to an adaptive remeshing algorithm. Efficiency of the
combined procedure is evaluated by analyzing supersonic shocks and shock propagation behaviors for both the steady and unsteady high-speed compressible flows.