Explicit formulations of gas-kinetic flux solver for simulation of incompressible and compressible viscous flows
Explicit formulations of gas-kinetic flux solver for simulation of incompressible and compressible viscous flows
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DOI：
10.1016/j.jcp.2015.07.060
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发表时间：
2015-11
期刊：
影响因子：
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通讯作者：
Y. Sun;C. Shu;C. Teo;Yan Wang;Liming Yang
中科院分区：
文献类型：
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作者：
Y. Sun;C. Shu;C. Teo;Yan Wang;Liming Yang
本文提出了一种用于模拟不可压缩和可压缩粘性流动的气体动力通量求解器（GKFS）。在该求解器中，有限体积法被应用到离散的Navier-Stokes方程。在界面处的无粘和粘性通量同时通过气体动力学方案，局部重建连续玻尔兹曼方程的解。与传统的气体动力学BGK格式不同，本文提出了一种计算非平衡态分布函数的简单方法，即用胞间及其周围点的平衡态分布函数之差计算非平衡态分布函数。作为一个结果，显式公式计算保守的流量变量和通量简单地推导出来。特别是，提出了三个具体的计划，并通过几个不可压缩和可压缩的测试例子进行验证。数值结果表明，这三种格式都能对不可压流动提供精确的数值结果。另一方面，方案III在可压缩流动的模拟中更加稳定和一致。
In this paper, a gas-kinetic flux solver (GKFS) is presented for the simulation of incompressible and compressible viscous flows. In this solver, the finite volume method is applied to discretize the Navier–Stokes equations. The inviscid and viscous fluxes at the interface are obtained simultaneously via the gas-kinetic scheme, which locally reconstruct the solution for the continuous Boltzmann equation. Different from the conventional gas-kinetic BGK scheme [1], a simple way is presented in this work to evaluate the non-equilibrium distribution function, which is calculated by the difference of equilibrium distribution functions at the cell interface and its surrounding points. As a consequence, explicit formulations for computing the conservative flow variables and fluxes are simply derived. In particular, three specific schemes are proposed and validated via several incompressible and compressible test examples. Numerical results show that all three schemes can provide accurate numerical results for incompressible flows. On the other hand, Scheme III is much more stable and consistent in simulation of compressible flows.