Asymptotic analysis of extrapolation boundary conditions for LBM

Authors:
Maddu Shankar;S. Sundar
Affiliations:
Department of Mathematics, Indian Institute of Technology Madras, Chennai - 600036, India;Department of Mathematics, Indian Institute of Technology Madras, Chennai - 600036, India
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

We present an investigation of extrapolation boundary conditions for lattice Boltzmann method (LBM) using asymptotic analysis. Equilibrium and non-equilibrium extrapolation methods for velocity and pressure boundary conditions proposed in the literature were tested numerically in specific cases. We analyse these boundary conditions using asymptotic expansion techniques and show an improvement in the accuracy of the lattice Boltzmann solution. We also present few numerical examples and simulate fluid flow across an unsymmetrically placed stationary cylinder in a channel with steady and unsteady flow conditions. Thus the article demonstrates application of asymptotic analysis to understand properties of extrapolation boundary conditions for LBM and show the flexibility of these boundary conditions for complex fluid flow applications.