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Galilean-invariant multi-speed entropic lattice Boltzmann models.
Boghosian, Bruce M.
Love, Peter J.
Yepez, J. (Jeffrey)
Coveney, Peter (Peter V.)
2004.
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Description
In recent work [Phys. Rev. E 68 (2003) 025103], it was shown that the requirement of Galilean invariance determined the form of the H function used in entropic lattice Boltzmann models for the incompressible Navier-Stokes equations in D dimensions. The form obtained was that of the Burg entropy for D=2, and the Tsallis entropy with q=1-2/D for D≠2. The conclusions obtained in that work were restricted
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to particles of a single-mass and speed on a Bravais lattice. In this work, we generalize the construction of such Galilean-invariant entropic lattice Boltzmann models by allowing for certain models with multiple masses and speeds. We show that the required H function for these models must be determined by solving a certain functional differential equation. Remarkably, the solutions to this equation also have the form of the Tsallis entropy, where q is determined by the solution to a certain transcendental equation, involving the dimension and symmetry properties of the lattice, as well as the masses and speeds of the particles. © 2004 Published by Elsevier B.V.
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Creator department
Tufts University. Department of Physics and Astronomy.
Tufts University. Department of Mathematics.
Subject
Statistical mechanics.
Permanent URL
http://hdl.handle.net/10427/014375
Citation
Boghosian, Bruce M., Peter J. Love, Jeffrey Yepez, and Peter V. Coveney. "Galilean-Invariant Multi-Speed Entropic Lattice Boltzmann Models." Physica D: Nonlinear Phenomena 193, no. 1-4 (June 2004): 169-181. doi:10.1016/j.physd.2004.01.018.
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v405sn77b
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