Related papers: Appendix: Chapman-Enskog Expansion in the Lattice …
The Boltzmann equation becomes invalid as the size of gas molecules is comparable with the average intermolecular distance. A better description is provided by the Enskog collision operator, which takes into account the finite size of gas…
The free-energy lattice Boltzmann (LB) model is one of the major multiphase models in the LB community. The present study is focused on a class of free-energy LB models in which the divergence of thermodynamic pressure tensor or its…
Four different kinds of laminar flows between two parallel plates are investigated using the Lattice Boltzmann Method (LBM). The LBM accuracy is estimated in two cases using numerical fits of the parabolic velocity profiles and the kinetic…
Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is…
We use the Boltzmann equation in the relaxation time approximation to study the expansion of a dilute Fermi gas at unitarity. We focus, in particular, on the approach to the hydrodynamic limit. Our main finding are: i) In the regime that…
We present a general methodology for constructing lattice Boltzmann models of hydrodynamics with certain desired features of statistical physics and kinetic theory. We show how a methodology of linear programming theory, known as…
Discrete Boltzmann model (DBM) is a type of coarse-grained mesoscale kinetic model derived from the Boltzmann equation. Physically, it is roughly equivalent to a hydrodynamic model supplemented by a coarse-grained model for the relevant…
Solving the Stefan problem, also referred as the heat conduction problem with phase change, is a necessary step to solve phase change problems with convection. In this article, we are interested in using the Lattice Boltzmann Method (LBM)…
A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the…
We analyze one-dimensional classical and quantum microscopic lattice-gas models governed by a lattice Boltzmann equation at the mesoscopic scale, achieved by ensemble averaging over microscopic realizations. The models are governed by the…
The recent development of the lattice gas automata method and its extension to the lattice Boltzmann method have provided new computational schemes for solving a variety of partial differential equations and modeling chemically reacting…
A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice…
It is proposed a dimensional Lattice Boltzmann Method (LBM) of wide application for simulating fluid flow and heat transfer problems. The proposed LBM consists in the numerical solution of the discrete lattice Boltzmann equation (LBE) using…
The Lattice Boltzmann Method (LBM) is widely recognized as an efficient algorithm for simulating fluid flows in both single-phase and multi-phase scenarios. In this research, a quantum Carleman Linearization formulation of the Lattice…
In this paper, a lattice Boltzmann model with the single-relaxation-time model for the Cahn-Hilliard equation (CHE) is proposed. The discrete source term is redesigned through a third-order Chapman-Enskog analysis. By coupling the…
In this article, we present a detailed asymptotic analysis of the lattice Boltzmann method with two different collision mechanisms of BGK-type on the D2Q9-lattice for generalized Newtonian fluids. Unlike that based on the Chapman-Enskog…
In this paper, we propose a lattice Boltzmann (LB) model to solve the coupled Cahn-Hilliard-Navier-Stokes equations. Differently from previous efforts, the LB equation for the fluid velocity is decomposed in a space of non-orthogonal…
We develop a unified multi-relaxation-time lattice Boltzmann (MRT-LB) framework based on discrete Hermite polynomials (Hermite matrices) for the Navier-Stokes equations (NSEs) and nonlinear convection-diffusion equations (NCDEs), using…
Recently, Murthy et al. [2017] and Escande et al. [2020] adopted the Lattice Boltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropic solids. The LBM is attractive as an elastodynamic solver because it can be…
A truncated Hilbert expansion with multiple scales is used to construct asymptotic solution of the linearized one-dimensional Boltzmann equation with small Knudsen number. The freedom ganed by introducing new independent time variables is…