Volume 4, Issue 6
A Moving Mesh Method for Kinetic/Hydrodynamic Coupling

Zhicheng Hu & Heyu Wang

Adv. Appl. Math. Mech., 4 (2012), pp. 685-702.

Published online: 2012-12

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  • Abstract

This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions. With some criteria, the domain is dynamically decomposed into three parts: kinetic regions where fluids are far from equilibrium, hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition. The Boltzmann-BGK equation is solved in kinetic regions, while Euler equations in hydrodynamic regions and both equations in buffer regions. By a well defined monitor function, our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions. In each moving mesh step, the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion. In such a framework, the evolution of the hybrid model and the moving mesh procedure can be implemented independently, therefore keep the advantages of both approaches. Numerical examples are presented to demonstrate the efficiency of the method.

  • Keywords

Moving mesh method, kinetic/hydrodynamic coupling, the Boltzmann-BGK equation.

  • AMS Subject Headings

65M50, 76P05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-685, author = {Zhicheng Hu , and Wang , Heyu}, title = {A Moving Mesh Method for Kinetic/Hydrodynamic Coupling}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {6}, pages = {685--702}, abstract = {

This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions. With some criteria, the domain is dynamically decomposed into three parts: kinetic regions where fluids are far from equilibrium, hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition. The Boltzmann-BGK equation is solved in kinetic regions, while Euler equations in hydrodynamic regions and both equations in buffer regions. By a well defined monitor function, our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions. In each moving mesh step, the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion. In such a framework, the evolution of the hybrid model and the moving mesh procedure can be implemented independently, therefore keep the advantages of both approaches. Numerical examples are presented to demonstrate the efficiency of the method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-12S01}, url = {http://global-sci.org/intro/article_detail/aamm/143.html} }
TY - JOUR T1 - A Moving Mesh Method for Kinetic/Hydrodynamic Coupling AU - Zhicheng Hu , AU - Wang , Heyu JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 685 EP - 702 PY - 2012 DA - 2012/12 SN - 4 DO - http://doi.org/10.4208/aamm.12-12S01 UR - https://global-sci.org/intro/article_detail/aamm/143.html KW - Moving mesh method, kinetic/hydrodynamic coupling, the Boltzmann-BGK equation. AB -

This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions. With some criteria, the domain is dynamically decomposed into three parts: kinetic regions where fluids are far from equilibrium, hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition. The Boltzmann-BGK equation is solved in kinetic regions, while Euler equations in hydrodynamic regions and both equations in buffer regions. By a well defined monitor function, our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions. In each moving mesh step, the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion. In such a framework, the evolution of the hybrid model and the moving mesh procedure can be implemented independently, therefore keep the advantages of both approaches. Numerical examples are presented to demonstrate the efficiency of the method.

Zhicheng Hu & Heyu Wang. (1970). A Moving Mesh Method for Kinetic/Hydrodynamic Coupling. Advances in Applied Mathematics and Mechanics. 4 (6). 685-702. doi:10.4208/aamm.12-12S01
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