A one-stage high-order gas-kinetic scheme for multi-component flows with interface-sharpening technique

Abstract

We propose a one-stage high-order gas-kinetic scheme (GKS) with interface-sharpening technique for the 4-equations model of compressible multi-component stiffened-gas flows. The scheme is constructed based on the framework of a one-stage efficient high-order GKS (EHGKS), which can achieve uniform high-order accuracy in both space and time. The main idea in the construction of the new scheme consists of three parts. Firstly, different from the original EHGKS, the non-oscillatory kinetic (NOK) flux is introduced to compute the leading term and the related flux evaluations, which enables the modified EHGKS suitable for stiffened gases, together with no pressure and velocity oscillations across the contact discontinuities. Then the modified scheme is utilized to discrete the conservative parts of the 4-equations model. Secondly, in order to avoid the oscillations across material interfaces, a high-order GKS is derived to solve the non-conservative parts of the 4-equations model following the idea of Abgrall [1]. Finally, to further reduce the over diffusion near a material interface, a simple interface-sharpening technique is developed, which combines the idea of interface construction and downwind scheme. The numerical results demonstrate that the proposed scheme can not only achieve the designed uniform accuracy in both space and time, but also sharply capture material interfaces.