Enhancement of the stability of lattice Boltzmann methods by dissipation control

A.N. Gorban and D.J. Packwood

Physica A: Statistical Mechanics and its Applications, 2014, vol. 414, issue C, 285-299

Abstract: Artificial dissipation is a well known tool for the improvement of stability of numerical algorithms. However, the use of this technique affects the accuracy of the computation. We analyse various approaches proposed for enhancement of the Lattice Boltzmann Methods’ (LBM) stability. In addition to some previously known methods, the Multiple Relaxation Time (MRT) models, the entropic lattice Boltzmann method (ELBM), and filtering (including entropic median filtering), we develop and analyse new filtering techniques with independent filtering of different modes. All these methods affect dissipation in the system and may adversely affect the reproduction of the proper physics. To analyse the effect of dissipation on accuracy and to prepare practical recommendations, we test the enhanced LBM methods on the standard benchmark, the 2D lid driven cavity on a coarse grid (101×101 nodes). The accuracy was estimated by the position of the first Hopf bifurcation points in these systems. We find that two techniques, MRT and median filtering, succeed in yielding a reasonable value of the Reynolds number for the first bifurcation point. The newly created limiters, which filter the modes independently, also pick a reasonable value of the Reynolds number for the first bifurcation.

Keywords: Lattice gas; Numerical stability; Critical Reynolds number; Entropy; Relaxation time; Hopf bifurcation (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:414:y:2014:i:c:p:285-299

DOI: 10.1016/j.physa.2014.07.052

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