Volume 17, Issue 5
Comparison of Simulations of Convective Flows

Pierre Lallemand & François Dubois

Commun. Comput. Phys., 17 (2015), pp. 1169-1184.

Published online: 2018-04

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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.

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@Article{CiCP-17-1169, author = {Pierre Lallemand , and François Dubois , }, title = {Comparison of Simulations of Convective Flows}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {5}, pages = {1169--1184}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2014.m400}, url = {http://global-sci.org/intro/article_detail/cicp/11007.html} }
TY - JOUR T1 - Comparison of Simulations of Convective Flows AU - Pierre Lallemand , AU - François Dubois , JO - Communications in Computational Physics VL - 5 SP - 1169 EP - 1184 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.2014.m400 UR - https://global-sci.org/intro/article_detail/cicp/11007.html KW - AB -

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.

Pierre Lallemand & François Dubois. (2020). Comparison of Simulations of Convective Flows. Communications in Computational Physics. 17 (5). 1169-1184. doi:10.4208/cicp.2014.m400
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