A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations | |
Liu C; Xu K; Sun QH(孙泉华); Cai QD; Xu, K (reprint author), Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China.; Xu, K (reprint author), Hong Kong Univ Sci & Technol, Dept Mech & Aerosp Engn, Kowloon, Hong Kong, Peoples R China. | |
Source Publication | JOURNAL OF COMPUTATIONAL PHYSICS |
2016 | |
Volume | 314Pages:305-340 |
ISSN | 0021-9991 |
Abstract | Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the NavierStokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well. (C) 2016 Elsevier Inc. All rights reserved. |
Keyword | Direct Modeling Unified Gas Kinetic Scheme Boltzmann Equation Kinetic Collision Model Asymptotic Preserving |
DOI | 10.1016/j.jcp.2016.03.014 |
URL | 查看原文 |
Indexed By | SCI |
Language | 英语 |
WOS ID | WOS:000374122100018 |
WOS Keyword | Direct modeling ; Unified gas kinetic scheme ; Boltzmann equation ; Kinetic collision model ; Asymptotic preserving |
WOS Research Area | Computer Science ; Physics |
WOS Subject | Computer Science, Interdisciplinary Applications ; Physics, Mathematical |
Funding Organization | The authors would like thank all reviewers for their valuable comments, Prof. S. Jin for his constructive discussion on the stability analysis, and Dr. S.Z. Chen and Dr. L. Wu for their help on numerical discretization of the full Boltzmann collision term. The work was supported by Hong Kong research grant council (620813, 16211014, 16207715) and NSFC-91330203, and was partially supported by the open fund of state key laboratory of high-temperature gas dynamics, China (No. 2013KF03). |
Department | LHD微尺度和非平衡流动 |
Classification | 一类 |
Ranking | False |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://dspace.imech.ac.cn/handle/311007/59544 |
Collection | 高温气体动力学国家重点实验室 |
Corresponding Author | Xu, K (reprint author), Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China.; Xu, K (reprint author), Hong Kong Univ Sci & Technol, Dept Mech & Aerosp Engn, Kowloon, Hong Kong, Peoples R China. |
Recommended Citation GB/T 7714 | Liu C,Xu K,Sun QH,et al. A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2016,314:305-340. |
APA | Liu C,Xu K,孙泉华,Cai QD,Xu, K ,&Xu, K .(2016).A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations.JOURNAL OF COMPUTATIONAL PHYSICS,314,305-340. |
MLA | Liu C,et al."A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations".JOURNAL OF COMPUTATIONAL PHYSICS 314(2016):305-340. |
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