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Mathematical Problems in Engineering
Volume 2015, Article ID 159418, 12 pages
Research Article

Downstream-Conditioned Maximum Entropy Method for Exit Boundary Conditions in the Lattice Boltzmann Method

1CONICET, Avenida Rivadavia 1917, 1033 Buenos Aires, Argentina
2National University of Central Buenos Aires, Pinto 399, 7000 Tandil, Argentina
3CNEA-CONICET, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina

Received 18 March 2015; Revised 15 June 2015; Accepted 6 July 2015

Academic Editor: Seungik Baek

Copyright © 2015 Javier A. Dottori et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM) based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.