Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics

Oleg Ilyin
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Oleg Ilyin: Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Vavilova-40, 119333 Moscow, Russia

Mathematics, 2021, vol. 9, issue 9, 1-14

Abstract: In this paper, we consider the development of the two-dimensional discrete velocity Boltzmann model on a nine-velocity lattice. Compared to the conventional lattice Boltzmann approach for the present model, the collision rules for the interacting particles are formulated explicitly. The collisions are tailored in such a way that mass, momentum and energy are conserved and the H -theorem is fulfilled. By applying the Chapman–Enskog expansion, we show that the model recovers quasi-incompressible hydrodynamic equations for small Mach number limit and we derive the closed expression for the viscosity, depending on the collision cross-sections. In addition, the numerical implementation of the model with the on-lattice streaming and local collision step is proposed. As test problems, the shear wave decay and Taylor–Green vortex are considered, and a comparison of the numerical simulations with the analytical solutions is presented.

Keywords: discrete velocity method; lattice Boltzmann method; computational fluid dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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