A single-relaxation-time lattice Boltzmann model for anisotropic advection-diffusion equation based on the diffusion velocity flux formulation

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Abstract

In this paper, we describe a single-relaxation-time (SRT) lattice Boltzmann formulation, which can be effectively applied to anisotropic advection-dispersion equations (AADE). The formulation can be applied to space and time variable anisotropic hydrodynamic dispersion tensor. The approach utilizes diffusion velocity lattice Boltzmann formulation which in the case of AADE can represent anisotropic diagonal and off-diagonal elements of the dispersion matrix by the coupling of advective and diffusive fluxes in equilibrium function. With this approach, AADE can be applied to the SRT lattice Boltzmann formulation using the same equilibrium function and without any changes to collision step nor in the application of boundary conditions. The approach shows good stability even for highly anisotropic dispersion tensor and is tested on selected illustrative examples which demonstrate the accuracy and applicability of the proposed method.

Details

Original languageEnglish
Pages (from-to)1423-1432
Number of pages10
JournalComputational Geosciences
Volume22
Issue number6
DOIs
StatePublished - 1 Dec 2018

Keywords

  • Lattice Boltzmann method, Anisotropic advection-dispersion equation, Single relaxation time, Diffusion velocity flux

ID: 4788682