Comparison of Simulations of Convective Flows

Pierre Lallemand (1) , François Dubois (2, 3)

1 CSRC - Beijing Computational Science Research Center [Beijing]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés

We show that a single particle distribution for the 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.

Keywords: bounce-back; natural convection; adiabatic wall; de Vahl Davis; de Vahl Davis AMS classification: 6505; 76N15; 80A20; 82C20 *

Domains: Numerical Analysis [math.NA]

Pierre Lallemand, François Dubois. Comparison of Simulations of Convective Flows. Communications in Computational Physics, 2013, 17 (05), pp.1169 - 1184. ⟨10.4208/cicp.2014.m400⟩. ⟨hal-00922901v2⟩