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Finite Volume Lattice Boltzmann Method for Nearly Incompressible Flows on Arbitrary Unstructured Meshes

Part of: Basic methods in fluid mechanics Time-dependent statistical mechanics (dynamic and nonequilibrium) Incompressible viscous fluids

Published online by Cambridge University Press:  21 July 2016

Weidong Li  and
Li-Shi Luo
Weidong Li*
Affiliation:
Department of Mathematics & Statistics, Old Dominion University, Norfolk, Virginia 23529, USA Computational Science Research Center, Beijing 100193, China
Li-Shi Luo*
Affiliation:
Department of Mathematics & Statistics, Old Dominion University, Norfolk, Virginia 23529, USA Computational Science Research Center, Beijing 100193, China
*
*Corresponding author. Email addresses:lwd_1982.4.8@163.com (W. D. Li), lluo@odu.edu, lluo@csrc.ac.cn (L.-S. Luo)
*Corresponding author. Email addresses:lwd_1982.4.8@163.com (W. D. Li), lluo@odu.edu, lluo@csrc.ac.cn (L.-S. Luo)
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Abstract

A genuine finite volume method based on the lattice Boltzmann equation (LBE) for nearly incompressible flows is developed. The proposed finite volume lattice Boltzmann method (FV-LBM) is grid-transparent, i.e., it requires no knowledge of cell topology, thus it can be implemented on arbitrary unstructured meshes for effective and efficient treatment of complex geometries. Due to the linear advection term in the LBE, it is easy to construct multi-dimensional schemes. In addition, inviscid and viscous fluxes are computed in one step in the LBE, as opposed to in two separate steps for the traditional finite-volume discretization of the Navier-Stokes equations. Because of its conservation constraints, the collision term of the kinetic equation can be treated implicitly without linearization or any other approximation, thus the computational efficiency is enhanced. The collision with multiple-relaxation-time (MRT) model is used in the LBE. The developed FV-LBM is of second-order convergence. The proposed FV-LBM is validated with three test cases in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the Blasius boundary layer; and (c) the steady flow past a cylinder at the Reynolds numbers Re=10, 20, and 40. The results verify the designed accuracy and efficacy of the proposed FV-LBM.

Keywords

Finite volume methodlattice Boltzmann equationarbitrary unstructured meshcomplex geometrymulti-dimensional scheme

MSC classification

Secondary: 76M12: Finite volume methods 76M28: Particle methods and lattice-gas methods 76D05: Navier-Stokes equations 82C40: Kinetic theory of gases
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 2 , August 2016 , pp. 301 - 324
Copyright
Copyright © Global-Science Press 2016 

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