Quasiequilibrium lattice Boltzmann models with tunable bulk viscosity for enhancing stability

Pietro Asinari and Ilya V. Karlin
Phys. Rev. E 81, 016702 – Published 12 January 2010

Abstract

Taking advantage of a closed-form generalized Maxwell distribution function [P. Asinari and I. V. Karlin, Phys. Rev. E 79, 036703 (2009)] and splitting the relaxation to the equilibrium in two steps, an entropic quasiequilibrium (EQE) kinetic model is proposed for the simulation of low Mach number flows, which enjoys both the H theorem and a free-tunable parameter for controlling the bulk viscosity in such a way as to enhance numerical stability in the incompressible flow limit. Moreover, the proposed model admits a simplification based on a proper expansion in the low Mach number limit (LQE model). The lattice Boltzmann implementation of both the EQE and LQE is as simple as that of the standard lattice Bhatnagar-Gross-Krook (LBGK) method, and practical details are reported. Extensive numerical testing with the lid driven cavity flow in two dimensions is presented in order to verify the enhancement of the stability region. The proposed models achieve the same accuracy as the LBGK method with much rougher meshes, leading to an effective computational speed-up of almost three times for EQE and of more than four times for the LQE. Three-dimensional extension of EQE and LQE is also discussed.

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  • Received 12 June 2009

DOI:https://doi.org/10.1103/PhysRevE.81.016702

©2010 American Physical Society

Authors & Affiliations

Pietro Asinari1,* and Ilya V. Karlin2,3,†

  • 1Department of Energetics, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy
  • 2Institute of Energy Technology, ETH Zurich, 8092 Zurich, Switzerland
  • 3School of Engineering Sciences, University of Southampton, SO17 1BJ Southampton, United Kingdom

  • *pietro.asinari@polito.it
  • karlin@lav.mavt.ethz.ch

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Vol. 81, Iss. 1 — January 2010

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