Kinetic-theory-based low diffusion flux vector splitting scheme

Abstract

Flux vector splitting (FVS) schemes are simple and robust. These two advantages are very attractive for large engineering application CFD softwares. However, traditional FVS schemes often introduce over diffusions and cannot give satisfied solutions for the contact discontinuities and rarefaction waves. In this article, following the idea of Toro-Vazquez, we firstly divide the flux into two parts: convective terms and pressure terms. Then the flux vector splitting kinetic scheme is used to construct the numerical scheme for both terms. Upwind scheme is chosen to discretize the convective terms to improve the resolution near the contact discontinuities. NOK scheme is utilized to discretize the pressure terms, and the collision terms are also added to improve the accuracy. Finally, a new low diffusion kinetic (LDK) flux vector splitting scheme is obtained. This new scheme is simple and robust, and has higher resolution near the contact discontinuities and higher accuracy near the rarefaction waves compared with the traditonal FVS. Numerical tests shows the comparisons between some current numerical schemes and the new scheme, and demonstrate that this new scheme behaves well in all the test cases.