Modified kinetic flux vector splitting schemes for compressible flows

作者：Chen Yibing^*; Jiang Song

来源：Journal of Computational Physics, 2009, 228(10): 3582-3604.

DOI：10.1016/j.jcp.2009.01.035

• KFVS scheme
• First-and second-order modified KFVS schemes
• BGK scheme
• Nonoscillatory
• Contact discontinuities
• Multi-fluids

We investigate the traditional kinetic flux vector splitting (KFVS) and BGK schemes for the compressible Euler equations. First, based on a careful study of the behavior of the discrete physical variables across the contact discontinuity, we analyze quantitatively the mechanism of inducing spurious oscillations of the velocity and pressure in the vicinity of the contact discontinuity for the first-order KFVS and BGK schemes. Then, with the help of this analysis, we propose a first-order modified KFVS (MKFVS) scheme which is oscillation-free in the vicinity of the contact discontinuity, provided certain consistent conditions are satisfied. Moreover, by using piecewise linear reconstruction and van Leer's limiter, the first-order MKFVS scheme is extended to a second-order one, consequently, a nonoscillatory second-order MKFVS scheme is constructed. Finally, by combing the MKFVS schemes with the gamma-model, we successfully extend the MKFVS schemes to multi-flows, and propose therefore a first- and second-order MKFVS schemes for multi-fluid computations, which are nonoscillatory across fluid interfaces. A number of numerical examples presented in this paper validate the theoretic analysis and demonstrate the good performance of the MKFVS schemes in simulation of contact discontinuities for both single- and multi-fluids.

• 出版日期2009-6-1
• 单位北京应用物理与计算数学研究所