Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

Patil, DV (2013) Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation. In: Physica A: Statistical Mechanics and its Applications, 392 (12). pp. 2701-2712.

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Abstract

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

Item Type:	Journal Article
Publication:	Physica A: Statistical Mechanics and its Applications
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Lattice Boltzmann Method; Chapman-Enskog Expansion; Finite Volume; Apparent Viscosity
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	21 Jun 2013 05:31
Last Modified:	21 Jun 2013 05:31
URI:	http://eprints.iisc.ac.in/id/eprint/46682

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