A COMPARISON OF SINGLE-TIME RELAXATION LATTICE BOLTZMANN SCHEMES WITH ENHANCED STABILITY

Francesca Tosi (), Stefano Ubertini (), Sauro Succi (), Hudong Chen () and Ilya V. Karlin ()
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Francesca Tosi: Università degli studi di Firenze, Dip. di Matematica U. Dini, Viale Morgagni, 67a, 50134 Firenze, Italia
Stefano Ubertini: Università degli studi di Roma, Tor Vergata Dip. di Ing. Meccanica, Via del Politecnico, 1 0133 Roma, Italia
Sauro Succi: Istituto Applicazioni del Calcolo CNR, Via del Policlinico, 137 0161 Roma, Italia
Hudong Chen: Exa Corporation, 3 Burlington Woods Drive, Burlington, MA 01802, USA
Ilya V. Karlin: Aerothermochemistry and Combustion System Laboratory, Swiss Federal Institute of Technology, ETH-Zentrum, CH-8092, Zurich, Switzerland

International Journal of Modern Physics C (IJMPC), 2006, vol. 17, issue 10, 1375-1390

Abstract: In the recent years the entropic version of the lattice Boltzmann method (ELB) has made proof of significantly enhanced numerical stability as compared to the standard single-time relaxation form of the lattice Boltzmann equation. In this paper, we compare ELB with a more empirical procedure, based on the idea of modifying the value of the relaxation time in such a way as to enforce the positivity of the kinetic distribution function (fix-up method). The stability enhancement due to ELB and fix-up are compared for the case a two-dimensional lid-driven cavity flow. It is shown that ELBM offers higher stability at a moderate price in terms of computational overhead. On the other hand, even the simple fix-up procedure can provide significant savings over the standard single-time relaxation method, virtually cost-free in terms of computational requirements.

Keywords: Lattice Boltzmann method; stability; entropic; fix-up (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0129183106009163

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