Document Type

Article

Publication Date

2007

DOI

http://dx.doi.org/10.1103/PhysRevE.75.036712

Publication Title

Physical Review E- Statistical, Nonlinear, and Soft Matter Physics

Volume

75

Issue

036712

Pages

1-11

Abstract

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.

Original Publication Citation

Keating, B., Vahala, G., Yepez, J., Soe, M., & Vahala, L. (2007). Entropic lattice Boltzmann representations required to recover Navier-Stokes flows. Physical Review E, 75(036712), 1-11. doi: 10.1103/PhysRevE.75.036712

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