Prandtl number of lattice Bhatnagar–Gross–Krook fluid

Abstract

The lattice Bhatnagar-Gross-Krook modeled uid has an unchangeable unit Prandtl number. A simple method is introduced in this letter to formulate a exible Prandtl number for the modeled uid. The eectiveness was demonstrated by numerical simulations of the Couette ow.

Digital Physics Approach to Computational Fluid Dynamics: Some Basic Theoretical Features

“…The higher order distributions do not contribute to these hydrodynamic quantities. Substituting the above expanded forms into (16) and then separating the resulting equation into a set of equations corresponding to different powers of , we obtain…”

“…It has been directly verified that, using the BGK operator form, the form of N eq ij which gives the correct ideal order hydrodynamics also produces the correct dissipative order terms without any further assumptions or approximations. [14][15][16] However, for the more generalized linearized collision operator form of (15), calculations can be rather complicated and may not automatically lead to the correct dissipative forms. 4,5,19 Fortunately, it has been realized that the correct dissipative hydrodynamics is still guaranteed by the above chosen equilibrium distributions as long as the collision matrix admits the following eigenvalue relations,…”

Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition

“…However, whereas LBE techniques shine for the simulation of isothermal, quasi-incompressible flows in complex geometries, and LBM has been shown to be useful in applications involving interfacial dynamics and complex boundaries (see, for example, the recent works of Nie et al [6], Lim et al [7], Nguyen et al [8], Hoekstra et al [9], Facin et al [10], Inamuro et al [11] and Dupuis et al [12]), the application to fluid flow coupled with non negligible heat Nomenclature c i = (c ix , c iy ) discrete particle speeds c = dx/dt minimum speed on the lattice c s lattice sound speed dt time increment dx = dy lattice spacing T = T h − T c temperature difference between hot and cold wall e internal energy density e counter-slip internal energy density used in the thermal boundary conditions f , g continuous single-particle distribution functions for density-momentum and internal energy-heat flux fields f ,g modified continuous single-particle distribution functions for density-momentum and internal energy-heat flux fields f i , g i discrete distribution functions f i ,g i modified discrete distribution functions f e i , g e i equilibrium discrete distribution functions G 1 = βg(T − T ) buoyancy force per unit mass transfer turned out to be much more difficult (see, for example, Chen et al [13] and [14], Mc Namara et al [15], Chen [16], Vahala et al [17], Karlin et al [18], Luo [19], Succi et al [20] and Lallemand and Luo [21]). …”

Implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model with flux limiters

“…The value Pr=1 is uniquely defined in single relaxation time LB models like the thermal model of Watari and Tsutahara since both transport coefficients (viscosity g and heat conducibility j) are proportional to the relaxation time s. LB models that allow to control the value of Pr were recently proposed in the literature and rely on various schemes like multiple relaxation times or adjusted collision terms [33,[50][51][52][53][54][55][56][57]. In the case of the LB model used in this paper, the control of Pr may be achieved by introducing a force term I ki [43] in the evolution Eq.…”