Numerical Transport Process of Splitting Kinetic Schemes in the Navier–Stokes–Fourier Limit

IF 1.1 4区工程技术 Q4 MECHANICS

International Journal of Computational Fluid Dynamics Pub Date : 2021-09-14 DOI:10.1080/10618562.2021.2023737

Yajun Zhu, Chengwen Zhong, K. Xu

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引用次数: 2

Abstract

The Boltzmann equation is the fundamental governing equation in rarefied gas dynamics. Due to the complexity of Boltzmann collision term, operator splitting treatment is commonly adopted, where the Boltzmann equation is split into a convection equation for particles' free transport and an ordinary differential equation for particles' collision. However, this split treatment will introduce numerical error proportional to the time step, which may contaminate the physical solution in the near continuum regime. Therefore, for a multiscale kinetic method, the asymptotic preserving property to obtain the Navier–Stokes–Fourier (NSF) solution in the hydrodynamic limit is very important. In this paper, we analyse the effective relaxation time from different evolution processes of several kinetic schemes and investigate their capabilities to recover the NSF solution. The general requirement on a splitting kinetic method for the NSF solution has been presented. Numerical validation has been carried out, which shows good agreement with the theoretical analysis.

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Navier-Stokes-Fourier极限下分裂动力学格式的数值输运过程

玻尔兹曼方程是稀薄气体动力学的基本控制方程。由于玻尔兹曼碰撞项的复杂性，通常采用算子分裂处理，将玻尔兹曼方程拆分为粒子自由输运的对流方程和粒子碰撞的常微分方程。然而，这种分裂处理将引入与时间步长成正比的数值误差，这可能会污染近连续统状态下的物理溶液。因此，对于多尺度动力学方法，在水动力极限下获得Navier-Stokes-Fourier (NSF)解的渐近保持性质是非常重要的。本文分析了几种动力学方案在不同演化过程中的有效松弛时间，并研究了它们恢复NSF解的能力。给出了NSF解的分裂动力学方法的一般要求。数值验证结果与理论分析吻合较好。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Computational Fluid Dynamics 物理-力学

CiteScore

2.70

自引率

7.70%

发文量

审稿时长

3 months

期刊介绍： The International Journal of Computational Fluid Dynamics publishes innovative CFD research, both fundamental and applied, with applications in a wide variety of fields. The Journal emphasizes accurate predictive tools for 3D flow analysis and design, and those promoting a deeper understanding of the physics of 3D fluid motion. Relevant and innovative practical and industrial 3D applications, as well as those of an interdisciplinary nature, are encouraged.