Two-dimensional thermal model of the finite-difference lattice Boltzmann method with high spatial isotropy

Abstract

The existing lattice Boltzmann method multispeed thermal models show a limited accuracy. This paper proposes a two-dimensional multispeed thermal model for the finite-difference lattice Boltzmann method (FDLBM). To recover correct fluid equations, up to fourth orders of local flow velocity should be retained in the local equilibrium distribution function and tensors of particle velocities should have up to seventh rank isotropy. In the FDLBM, particle velocities can be selected independently from the lattice configuration. Therefore, particle velocities of octagonal directions, which have up to seventh rank isotropic tensors, are adopted. The proposed model was verified by two simulations. The model showed excellent numerical stability in addition to strict accuracy.

The Design and Application of English Online Learning System Based on Bs

“…In the development of LB for NavierStokes systems, another way is referred to as the finite differencelattice Boltzmann method (FDLBM) [10][11][12]. The one byWatari-Tsutahara (WT) is typical [11]. The same idea wasthen extended to binary compressible flows [12].…”

“…The same idea wasthen extended to binary compressible flows [12]. FDLBM [11,12] breaks the binding of discretizations of space andtime and makes the particle speeds more flexible. But similar to previous LB models, the numerical stability problemremains one of the few blocks for its practical simulation to high Mach number flows.…”

“…Alexander, et al [4] presented a model where the sound speedis selectable; Yan, et al [5] proposed a compressible LB model with three-speed-threeenergy-level for the Eulersystem; Yu and Zhao [6] composed a model for compressible flows by introducing an attractive force to soften soundspeed; Sun [7][8][9] contributed a locally adaptive semi-discrete LB model, where the set of particle speed is chosenaccording to the local fluid velocity and internal energy so that the fluid velocity is no longer limited by the particlespeed set. In the development of LB for NavierStokes systems, another way is referred to as the finite differencelattice Boltzmann method (FDLBM) [10][11][12]. The one byWatari-Tsutahara (WT) is typical [11].…”

FFT-LB Modeling of Thermal Liquid-Vapor System

“…This model is a further development of the one originally proposed by Watari and Tsutahara (WT) [9] and then developed by Gonnella, Lamura and Sofonea (GLS) [44]. The original WT model works only for ideal gas.…”

“…During the past two decades, the lattice Boltzmann (LB) method has been developed rapidly and has been successfully applied to various fields [1], ranging from magnetohydrodynamics [2,3,4], to flows of suspensions [5,6], flows through porous media [7,8], compressible fluid dynamics [9,10,11,12,13,14], wave propagation [15,16], etc. Apart from the fields listed above, this versatile method is particularly promising in the area of multiphase systems [17,18,19,20,21,22,23].…”