On the Stability of the Finite Difference based Lattice Boltzmann Method

Mohamed El-Amin, Shuyu Sun, Amgad Salama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
Original languageEnglish (US)
Title of host publicationProcedia Computer Science
PublisherElsevier BV
Pages2101-2108
Number of pages8
DOIs
StatePublished - Jun 1 2013

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