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Lattice Boltzmann Simulation of Microstructures
Published in Shyam S. Sablani, M. Shafiur Rahman, Ashim K. Datta, Arun S. Mujumdar, Handbook of Food and Bioprocess Modeling Techniques, 2006
The lattice Boltzmann method is a recently developed computer modeling methodology that is gaining attention in the academic world, especially for the simulation of complex fluid phenomena at the mesoscopic scale.1,2 The mesoscop ic scale lies between the molecular (micro) scale, and the macroscopic scale, where physical quantities are assumed to be continuous. Somewhere between the micro and macroscale, the continuum approach breaks down and some parts of physical systems cannot be assumed to be continuous. Examples of these mesoscale systems are emulsions, colloidal suspensions, flow in porous media, and polymer solutions.
Introduction
Published in Mohamed Gad-el-Hak, MEMS, 2005
Thus, three essential ingredients in the development of a lattice Boltzmann method for a single physics or multiphysics fluid-flow problem must be completely specified: (1) a discrete lattice on which the fluid particles reside, (2) a set of discrete velocities ei to represent particle advection from one node of the lattice to its nearest neighbor, and (3) a set of rules for the redistribution of particles on a node to mimic collision processes in the fluid. These rules are provided by the distribution functions fi of the particles; the evolution of distribution functions in time (for a discrete time step Δt ) is obtained by solving the LBGK equation. The LBGK equation for fi requires the knowledge of the equilibrium distribution function fi(0). The discrete velocities ei are determined so that the macroscopic density and momentum satisfy the constraints ρ=∑ifi and ρV=∑ifiei respectively, where V is the macroscopic-averaged fluid velocity. Therefore, the determination of appropriate equilibrium particle distribution function for a given fluid flow problem is essential for solving the problem by LBM.
Non-circular particle treatment in smoothed profile method: a case study of elliptical particles sedimentation using lattice Boltzmann method
Published in Journal of Dispersion Science and Technology, 2020
Akbar Kohestani, Mohammad Rahnama, Saeed Jafari, Ebrahim Jahanshahi Javaran
The Lattice Boltzmann Method is a mesoscopic computational approach with its roots in the kinetic theory; it is based on resolving the evolution of statistical distribution functions on lattices. The method involves a relatively straightforward implementation; it is inherently suited for parallelization, and is applicable to complex flows with complex geometries or multiple inter-particle interactions. LBM is a numerical procedure to solve the Boltzmann equation. As a main concept in LBM, density distribution function is obtained from the discretized Boltzmann equation, which can be expressed as follows:[39]
Three-Dimensional Lattice Boltzmann Model for Acoustic Waves Emitted by a Source
Published in International Journal of Computational Fluid Dynamics, 2021
Jaouad Benhamou, Salaheddine Channouf, Mohammed Jami, Ahmed Mezrhab, Daniel Henry, Valéry Botton
The lattice Boltzmann method is an open-source alternative numerical method for simulating different types of fluid flows. Contrary to the usual approach based on Navier-Stokes equations, the LBM aims at discretizing the Boltzmann equation, corresponding to statistical modelling of the dynamics of the particles forming the fluid. The origin of LBM generally derives from cellular automata and lattice-gas automata (Frisch, Hasslacher, and Pomeau 1986; McNamara and Zanetti 1988; He and Luo 1997), and its theory is inspired by statistical physics and the kinetic theory of gases (Mohamad 2011; Huang, Sukop, and Lu 2015; Timm et al. 2017).