Modified kinetic flux vector splitting schemes for compressible flows
Modified kinetic flux vector splitting schemes for compressible flows
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可压缩流的改进动通量矢量分裂方案
DOI：
10.1016/j.jcp.2009.01.035
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发表时间：
2009-06
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影响因子：
--
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中科院分区：
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--
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本文研究了可压缩欧拉方程的传统的动量矢通量分裂（KFVS）和BGK格式。首先，在仔细研究离散物理量在接触间断处的行为的基础上，定量分析了一阶KFVS和BGK格式在接触间断附近引起速度和压力虚假振荡的机制。然后，在此分析的帮助下，我们提出了一阶修正KFVS（MKFVS）格式，只要满足某些一致性条件，该格式在接触不连续附近是无振荡的。利用分段线性重构和货车Leer限制器，将一阶MKFVS格式推广到二阶，从而构造了一个无振荡的二阶MKFVS格式.最后，通过将MKFVS格式与γ模型相结合，我们成功地将MKFVS格式推广到多流体问题，并由此提出了一阶和二阶跨流体界面无振荡的多流体计算MKFVS格式。本文给出的数值算例验证了理论分析，并证明了MKFVS格式在模拟单流体和多流体接触不连续性方面的良好性能。
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 γ-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.
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