Analysis and boundary condition of the lattice Boltzmann BGK model with two velocity components

Biophysics Group; Dept. of Math.; Kansas State University; KS 66506); Los Alamos; Los Alamos National Lab; Los Alamos National Lab); Manhattan; NM 87545; Qisu Zou (Theoretical Division

arxiv: comp-gas/9507002 · v1 · pith:IDHOF5BPnew · submitted 1995-07-22 · comp-gas · nlin.CG

Analysis and boundary condition of the lattice Boltzmann BGK model with two velocity components

Xiaoyi He (Center for Nonlinear Studies , Los Alamos National Lab , Los Alamos , NM 87545 , Theoretical Biology , Biophysics Group , Los Alamos National Lab) , Qisu Zou (Theoretical Division

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Dept. of Math. Kansas State University Manhattan KS 66506)

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classification comp-gas nlin.CG

keywords boundaryanalysisvelocityboltzmannboundariesconditionflowlattice

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In this paper, we study the two dimensional lattice Boltzmann BGK model (LBGK) by analytically solving a simple flow in a 2~-D channel. The flow is driven by the movement of upper boundary with vertical injection fluid at the porous boundaries. The velocity profile is shown to satisfy a second-order finite-difference form of the simplified incompressible Navier-Stokes equation. With the analysis, different boundary conditions can be studied theoretically. A momentum exchange principle is also revealed at the boundaries. A general boundary condition for any given velocity boundary is proposed based on the analysis.

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Analysis and boundary condition of the lattice Boltzmann BGK model with two velocity components

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