Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation

Reis, Timothy ORCID: https://orcid.org/0000-0003-2671-416X and Phillips, Timothy Nigel ORCID: https://orcid.org/0000-0001-6455-1205 2008. Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation. Physical Review -Series e- 77 (2) , 026702. 10.1103/PhysRevE.77.026702

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Abstract

The simplest and most efficient lattice Boltzmann model that is able to recover the Navier-Stokes equations is based on a single-parameter scattering matrix, where the parameter is the first nonzero eigenvalue of the collision matrix. This simple model, based on a single relaxation time, has many shortcomings. Among these is the lack of freedom to extend the model to complex fluids whose stress tensors are characterized by more complicated constitutive relations. The lattice Boltzmann methodology may be generalized by considering the full collision matrix and tuning the matrix elements to obtain the desired macroscopic properties. The generalized hydrodynamics of a generalized lattice Boltzmann equation (LBE) was studied by Lallemand and Luo Phys. Rev. E 61 6546 (2000)] by solving the dispersion equation of the linearized LBE. In this paper, an alternative approach to solving the dispersion equation based on a formal perturbation analysis is described. The methodology outlined is systematic, can be readily applied to other lattices, and does not require the reciprocals of the relaxation times to be small.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	8 pages.
Publisher:	American Physical Society
ISSN:	1539-3755
Last Modified:	11 May 2023 14:02
URI:	https://orca.cardiff.ac.uk/id/eprint/18427

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