Physica A 414 (2014) 285–299 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Enhancement of the stability of lattice Boltzmann methods by dissipation control A.N. Gorban a,∗ , D.J. Packwood b a Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK b Mathematics Institute, University of Warwick, Coventry, UK highlights • The stability problem arises for lattice Boltzmann methods in modelling of highly non-equilibrium fluxes. • Dissipation control is an efficient tool to improve stability but it affects accuracy. • We analyse the stability–accuracy problem for lattice Boltzmann methods with additional dissipation. • We compare various methods for dissipation control: Entropic filtering, Multirelaxation methods and Entropic collisions. • For numerical test we use the lid driven cavity; the accuracy was estimated by the position of the first Hopf bifurcation. article info Article history: Received 22 March 2014 Received in revised form 5 July 2014 Available online 23 July 2014 Keywords: Lattice gas Numerical stability Critical Reynolds number Entropy Relaxation time Hopf bifurcation abstract Artificial dissipation is a well known tool for the improvement of stability of numerical al- gorithms. 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 indepen- dent 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 dissi- pation 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 yield- ing 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. © 2014 Elsevier B.V. All rights reserved. 1. Introduction Lattice Boltzmann methods (LBMs) are a type of discrete algorithm which can be used to simulate fluid dynamics and more [1–4]. One of the nicest properties of an LB scheme is that the transport component of the algorithm, advection, is exact. All of the dissipation in the discrete system then occurs due to the relaxation operation. This dissipation occurs at different orders of the small parameter, the time step [5]. The first order gives an approximation to the Navier–Stokes equations (with ∗ Corresponding author. Tel.: +44 1162231433. E-mail addresses: ag153@le.ac.uk, gorbanster@gmail.com (A.N. Gorban), d.packwood@warwick.ac.uk (D.J. Packwood). http://dx.doi.org/10.1016/j.physa.2014.07.052 0378-4371/© 2014 Elsevier B.V. All rights reserved.