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 Heyu Wang}, 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 & Heyu Wang 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 KW - kinetic/hydrodynamic coupling KW - 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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