An improved Roe solver for high order reconstruction schemes

Abstract Roe solver is one of the most popular upwind schemes in computational fluid dynamics which is first-order accurate in space. However, the amount of numerical dissipation gets larger than necessary for high order numerical schemes and then becomes the dominant term of the numerical error. This paper proposes a modified Roe solver that can use high order schemes with high stability based on splitting of the upwind term. The novel algorithm is proposed to compute the dissipation term of Roe flux function using low and high reconstruction schemes for computing acoustic and entropy waves information, respectively. It changes the original Roe solver dissipation term to improve the level of accuracy. The third-order WENO-Z and MUSCL schemes are adopted as high reconstruction schemes. Finite difference approach is used to simulate Euler equations with the original and modified Roe solvers. The results of four shock tube problems of Sod, Lax, Mach 3, and supersonic test cases are compared with the exact solution of the Riemann problem. It is found that the proposed Roe solver increases the accuracy and robustness of the original Roe solver, especially around the expansion waves, contact discontinuities, and shock waves.