We have investigated the feasibility of the hybrid-type method of lattice Boltzmann and Brownian dynamics as a simulation technique for a magnetic particle suspension. To do so, we have addressed aggregation phenomena in thermodynamic equilibrium and have compared the present results with those of Monte Carlo method and the previous lattice Boltzmann method based on fluctuation hydrodynamics (F...

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second-order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also invest...

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of e...

The particles model, the collision model, the polynomial development used for the equilibrium distribution, the time discretization and the velocity discretization are factors that let the lattice Boltzmann framework (LBM) far away from its conceptual support: the continuous Boltzmann equation (BE). Most collision models are based on the BGK, single parameter, relaxation-term leading to constan...

A finite difference lattice Boltzmann method based on the Bhatnagar–Gross–Krook-type modeled Boltzmann equation is proposed. Themethod relies on a different lattice equilibriumparticle distribution function and the use of a splitting method to solve the modeled lattice Boltzmann equation. The splitting technique permits the boundary conditions for the lattice Boltzmann equation to be set as con...

Due to its computational efficiency, the kinetic-based lattice Boltzmann method has recently been used to model nonequilibrium gas dynamics. With appropriate boundary conditions, lattice Boltzmann models have been able to capture both velocity slip and temperature jump at a solid surface. To enable these models to simulate flows in the transition regime, both high-order and modified lattice Bol...

We consider the problem of “energy conserving” lattice Boltzmann models. A major difficulty observed in previous studies is the coupling between the viscous and thermal waves even at moderate wave numbers. We propose a theoretical framework based on the knowledge of the partial equivalent equations of the lattice Boltzmann scheme at several orders of precision. With the help of linearized model...

The Lattice Boltzmann Method (LBM) has numerous computational advantages, such as the simplicity of programming, the ability to incorporate microscopic interactions, and the easy parallelization of algorithms. The traditional lattice Boltzmann model has a constraint of small mach number(the velocity of fluid must be less than 0.3 mach). This paper presents a novel lattice Boltzmann method to si...

We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete vel...

The lattice Boltzmann equation was introduced about 20 years ago as a new paradigm for computational fluid dynamics. In this paper, we revisit the main formulation of the lattice Boltzmann collision integral (matrix model) and introduce a new two-parametric family of collision operators, which permits us to combine enhanced stability and accuracy of matrix models with the outstanding simplicity...