Stability investigation of the two-dimensional nine-vectors model of the lattice Boltzmann method for fluid flows in a square cavity

Abstract

In this paper we consider the stability of the two-dimensional nine-vectors model of the lattice Boltzmann method which used to model fluid flows in a square lid-driven cavity. Obtained numerical solutions were compared with the results of the numerical experiments by the finite element method. We investigate the influence of Reynolds and Mach numbers on method`s stability. Shown the dependence between the kinematic viscosity of the modeling liquid and cell`s size. Have been shown the advantages and disadvantages of this computational method.