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Comparison of Simulations of Convective Flows

Published online by Cambridge University Press:  03 June 2015

Pierre Lallemand  and
François Dubois
Pierre Lallemand
Affiliation:
Beijing Computational Science Research Center, Beijing Run Ze Jia Ye, China
François Dubois*
Affiliation:
Structural Mechanics and Coupled Systems Laboratory, Conservatoire National des Arts et Métiers, Paris, France Department of Mathematics, University Paris-Sud, Bât. 425, F-91405 Orsay Cedex, France
*
*Corresponding author. Email addresses: pierre.lallemand1@free.fr (P. Lallemand), francois.dubois@math.u-psud.fr (F. Dubois)
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Abstract

We show that a single particle distribution for the “energy-conserving” D2Q13 lattice Boltzmann scheme can simulate coupled effects involving advection and diffusion of velocity and temperature. We consider various test cases: non-linear waves with periodic boundary conditions, a test case with buoyancy, propagation of transverse waves, Couette and Poiseuille flows. We test various boundary conditions and propose to mix bounce-back and anti-bounce-back numerical boundary conditions to take into account velocity and temperature Dirichlet conditions. We present also first results for the de Vahl Davis heated cavity. Our results are compared with the coupled D2Q9-D2Q5 lattice Boltzmann approach for the Boussinesq system and with an elementary finite differences solver for the compressible Navier-Stokes equations. Our main experimental result is the loss of symmetry in the de Vahl Davis cavity computed with the single D2Q13 lattice Boltzmann model without the Boussinesq hypothesis. This result is confirmed by a direct Navier Stokes simulation with finite differences.

Keywords

650576N1580A2082C20Bounce-backnatural convectionadiabatic wallde Vahl Davis
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 5 , May 2015 , pp. 1169 - 1184
Copyright
Copyright © Global-Science Press 2015 

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