In the late 90's and early 2000's the concept of a discrete H theorem and Lyapunov
functionals as a way to ensure stability of lattice Boltzmann solvers was a shift of paradigm in …

In the last decade, minimal kinetic models, and primarily the lattice Boltzmann equation,
have met with significant success in the simulation of complex hydrodynamic phenomena …

Derivation of the lattice Boltzmann method from the continuous kinetic theory [X. He and LS
Luo, Phys. Rev. E 55, R6333 (1997); X. Shan and X. He, Phys. Rev. Lett. 80, 65 (1998)] is …

We derive minimal discrete models of the Boltzmann equation consistent with equilibrium
thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A new …

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In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB)
models for multiphase flow are presented. In contrast to the Bhatnagar–Gross–Krook (BGK) …

In this paper, we review the construction of low-dimensional manifolds of reduced
description for equations of chemical kinetics from the standpoint of the method of invariant …

In this paper, we study systematically the physical symmetry, spatial accuracy, and
relaxation time of the lattice Boltzmann equation (LBE) for microgas flows in both the slip …

The lattice Boltzmann method is developed to study gaseous slip flow in microchannels. An
approach relating the Knudsen number with the relaxation time in the lattice Boltzmann …

A recently introduced theory of higher-order lattice Boltzmann models [Chikatamarla and
Karlin, Phys. Rev. Lett. 97, 190601 (2006)] is elaborated in detail. A general theory of the …