A high-order gas-kinetic Navier-Stokes flow solver
A high-order gas-kinetic Navier-Stokes flow solver
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高阶气体动力学纳维-斯托克斯流动求解器
DOI：
10.1016/j.jcp.2010.05.019
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发表时间：
2010-09
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现代可压缩流动解算器的发展基础是基于无粘欧拉方程的Riemann解。高阶格式基本上与高阶空间内插或重建有关。为了克服Riemann解引起的低阶波动相互作用机制，可以通过Runge-Kutta方法来提高格式的时间精度，其中通过Runge-Kutta过程中的分步空间重构来缓解一阶Riemann解中的动力学缺陷。由于空间和时间的解耦，原始非线性控制方程的时空演化之间的紧密耦合似乎被削弱了。最近发展起来的许多高阶方法在分段不连续的高阶初始重构下都需要一个Navier-Stokes通量函数。然而，分段间断初值与Navier-Stokes方程的双曲-抛物线性质在数学上似乎是不一致的，例如由于初始间断导致粘性项和导热项的发散。本文从玻耳兹曼方程出发，从高阶不连续重构出发，给出了一个随时间变化的通量函数。这种方法的理论基础是由于Boltzmann方程对初始数据的光滑性没有特别的要求，而动力学方程具有在大于颗粒碰撞时间的时间尺度上从初始不连续流动条件开始构造耗散波结构的机制。目前的高阶通量计算方法是求解N-S方程的二阶气体动力学BGK格式(BGK-NS)的推广。从二阶到高阶的简单扩展的新奇之处在于微观水平上简单的粒子输运和碰撞机制。本文将提出一种构造这种高阶方法的层次结构。通过粘性流动计算格式的数值表现，可以清楚地看出在通量计算中非线性耦合时空演变的必要性。
The foundation for the development of modern compressible flow solver is based on the Riemann solution of the inviscid Euler equations. The high-order schemes are basically related to high-order spatial interpolation or reconstruction. In order to overcome the low-order wave interaction mechanism due to the Riemann solution, the temporal accuracy of the scheme can be improved through the Runge–Kutta method, where the dynamic deficiencies in the first-order Riemann solution is alleviated through the sub-step spatial reconstruction in the Runge–Kutta process. The close coupling between the spatial and temporal evolution in the original nonlinear governing equations seems weakened due to its spatial and temporal decoupling. Many recently developed high-order methods require a Navier–Stokes flux function under piece-wise discontinuous high-order initial reconstruction. However, the piece-wise discontinuous initial data and the hyperbolic-parabolic nature of the Navier–Stokes equations seem inconsistent mathematically, such as the divergence of the viscous and heat conducting terms due to initial discontinuity. In this paper, based on the Boltzmann equation, we are going to present a time-dependent flux function from a high-order discontinuous reconstruction. The theoretical basis for such an approach is due to the fact that the Boltzmann equation has no specific requirement on the smoothness of the initial data and the kinetic equation has the mechanism to construct a dissipative wave structure starting from an initially discontinuous flow condition on a time scale being larger than the particle collision time. The current high-order flux evaluation method is an extension of the second-order gas-kinetic BGK scheme for the Navier–Stokes equations (BGK-NS). The novelty for the easy extension from a second-order to a higher order is due to the simple particle transport and collision mechanism on the microscopic level. This paper will present a hierarchy to construct such a high-order method. The necessity to couple spatial and temporal evolution nonlinearly in the flux evaluation can be clearly observed through the numerical performance of the scheme for the viscous flow computations.
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DOI：
10.1002/bbpc.19660700827
发表时间：
1966-11
期刊：
Berichte der Bunsengesellschaft für physikalische Chemie
影响因子：
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作者：
H. Wagner
通讯作者：
H. Wagner
影响因子：
4.1
作者：
HARTEN, A;ENGQUIST, B;CHAKRAVARTHY, SR
通讯作者：
CHAKRAVARTHY, SR
影响因子：
4.1
作者：
Jiang, GS;Shu, CW
通讯作者：
Shu, CW
影响因子：
12.8
作者：
W. Vincenti;C. Kruger;T. Teichmann
通讯作者：
W. Vincenti;C. Kruger;T. Teichmann
影响因子：
2.5
作者：
Li, QB;Fu, S;Xu, K
通讯作者：
Xu, K