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

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  • Patil, D.V.

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.

Suggested Citation

  • Patil, D.V., 2013. "Chapman–Enskog analysis for finite-volume formulation of lattice Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2701-2712.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:12:p:2701-2712
    DOI: 10.1016/j.physa.2013.02.016
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    References listed on IDEAS

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    1. Ansumali, Santosh & Karlin, Iliya V. & Succi, Sauro, 2004. "Kinetic theory of turbulence modeling: smallness parameter, scaling and microscopic derivation of Smagorinsky model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 379-394.
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