We show that discrete lattice effects must be considered in the introduction of a force into Boltzmann equation. A representation forcing term is then proposed. With representation, Navier-Stokes equation derived from through Chapman-Enskog expansion. Several other existing treatments are also examined.

In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is decompose distribution function at node into its equilibrium and non-equilibrium parts then approximate part with first-order extrapolation of neighbouring fluid node. Schemes for velocity pressure are constructed based on method. resulting schemes second-order accuracy. Numerical tests show that numerical solutions LBM together present excellent agreement...

A boundary treatment for curved walls in lattice Boltzmann method is proposed. The distribution function at a wall node who has link across the physical decomposed into its equilibrium and nonequilibrium parts. part then approximated with fictitious one where condition enforced, using first-order extrapolation based on of neighboring fluid node. Numerical results show that present second-order accuracy, well-behaved stability characteristics.

In this paper a lattice Boltzmann model is proposed for isothermal incompressible flow in porous media. The key point to include the porosity into equilibrium distribution, and add force term evolution equation account linear nonlinear drag forces of medium (the Darcy's Forcheimer's term). Through Chapman-Enskog procedure, generalized Navier-Stokes equations media are derived from present model. two-dimensional Poiseuille flow, Couette lid-driven cavity simulated using It found numerical...

Abstract In this paper, a thermal lattice BGK model is developed for the Boussinesq incompressible fluids. The basic idea to solve velocity field and temperature using two independent equations, respectively, then combine them into one coupled whole system. porous plate problem two‐dimensional natural convection flow in square cavity with Pr=0.71 various of Rayleigh numbers are simulated model. numerical results found be good agreement analytical solutions or those previous studies....

Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS finite-volume with discretization of particle velocity space. After introduction two auxiliary distribution functions inclusion collision effect, becomes fully explicit update function. Furthermore, an asymptotic preserving method, where time step only determined by Courant-Friedricks-Lewy condition continuum limit....

In this paper, a general bounce-back scheme is proposed to implement concentration or thermal boundary conditions of convection-diffusion equation with the lattice Boltzmann method (LBM). Using scheme, conditions, i.e., ${b}_{1}\frac{\ensuremath{\partial}{C}_{w}}{\ensuremath{\partial}n}+{b}_{2}{C}_{w}={b}_{3}$, can be easily implemented at boundaries complex geometry structure like that in porous media. The numerical results obtained using present are excellent agreement analytical solutions...

This paper is a continuation of our earlier work [Z.L. Guo {\it et al.}, Phys. Rev. E {\bf 88}, 033305 (2013)] where multiscale numerical scheme based on kinetic model was developed for low speed isothermal flows with arbitrary Knudsen numbers. In this work, discrete unified gas-kinetic (DUGKS) compressible the consideration heat transfer and shock discontinuity Shakhov an adjustable Prandtl number. The method explicit finite-volume transport collision processes are coupled in evaluation...

In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is proposed for incompressible multiphase flow systems. model, one distribution function used to solve the Chan-Hilliard equation and other adopted Navier-Stokes equations. Unlike previous LB models, proper source term incorporated in interfacial evolution such that can be derived exactly also pressure designed recover correct hydrodynamic Furthermore, velocity fields calculated explicitly. A series of...

ABSTRACT A lattice Boltzmann model for convection heat transfer in porous media is proposed. In this model, a new distribution function introduced to simulate the temperature field addition density velocity field. The macroscopic equations are recovered from through Chapman-Enskog procedure. validated by several benchmark problems, and it found that numerical results good agreement with well-documented literature.

A lattice Boltzmann model is proposed for solving low Mach number thermal flows with viscous dissipation and compression work in the double-distribution-function framework. distribution function representing total energy defined based on a single velocity function, its evolution equation derived from continuous equation. clear physics simple structure then obtained kinetic decoupled hydrodynamic equations. The tested by simulating Poiseuille flow natural convection square cavity, it found...

A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The can be applied to the common real complex-valued evolutionary equations, such as Schr\"odinger equation, complex Ginzburg-Landau Burgers-Fisher heat conduction sine-Gordon by using a relaxation time. Detailed simulations of these equations are performed, it found that numerical results agree well...

AbstractIn this work, we apply the lattice Boltzmann equation (LBE) with multiple relaxation times (MRTs) to simulate Poiseuille flow in slip regime. We analyse detail discrete diffusive and combined bounce-back-specular-reflection boundary conditions for LBE, effects at boundary, determinations of In particular, implement second-order MRT–LBE model validate our numerical results Knudsen number Kn ≤ 0.2 by using analytic solution. Our analysis shows that Bhatnagar–Gross–Krook (BGK) cannot...

The standard lattice Boltzmann equation (LBE) is inadequate for simulating gas flows with a large Knudsen number. In this paper we propose generalized effective relaxation times based on recently developed Navier-Stokes constitution [Guo, Europhys Lett. 80, 24001 (2007)] nonequilibrium flows. A kinetic boundary condition corresponding to second-order slip scheme also designed the model. LBE model and are analyzed unidirectional flow, it found that in order obtain equations, must be properly...

In this paper, we study systematically the physical symmetry, spatial accuracy, and relaxation time of lattice Boltzmann equation (LBE) for microgas flows in both slip transition regimes. We show that symmetry accuracy existing LBE models are inadequate simulating regime. Our analysis further indicates a flow, channel wall confinement exerts nonlinear effect on time, which should be considered modeling flows.

Outflow boundary condition (OBC) is a critical issue in computational fluid dynamics. As type of numerical method for flows, the lattice Boltzmann equation (LBE) has gained much success variety complex and certain OBCs have been suggested LBE simulating simple single-phase flows. However, very few discussions on made two-phase method. In this work, three types that are widely used i.e., Neumann condition, convective extrapolation extended to their performances investigated. The comprehensive...

The capability of modeling and simulating complex interfacial dynamics multiphase flows has been recognized as one the main advantages lattice Boltzmann equation (LBE). A basic feature two-phase LBE models, i.e., force balance condition at discrete level LBE, is investigated in this work. An explicit force-balance formulation derived for a flat interface by analyzing two-dimensional nine-velocity (D2Q9) model without invoking Chapman-Enskog expansion. result suggests that generally between...