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.
Keywords : Roe’s flux-difference splitting scheme, entropy fix, shock wave
