Lattice-Boltzmann method/models

The mesoscopic modeling approach consists of a stochastic reconstruction method for the generation of the CL and GDL microstructures, and a two-phase lattice Boltzmann method for studying liquid water transport and flooding phenomena in the reconstructed microstructures. 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

Only a few LES simulations have been reported describing the turbulent flow in single phase stirred tanks (e.g., [20, 77, 18]). The lattice-Boltzmann method is used in the more recent publications since this scheme is considered to be an efficient Navier-Stokes solver. Nevertheless, the computational requirements of these models are still prohibitive, therefore the application of this approach is restricted to academic research. No direct simulations of these vessels have been performed yet. 

Inamuro, T., N. Konishi, and F. Ogino. A Galilean Invariant Model of the Lattice Boltzmann Method for Multiphase Huid Flows Using Free-Energy Approach. Comput. Phys. Commun. 129 32-45 (2000). 

Luo, L.-S. Theory of the Lattice Boltzmann Method Lattice Boltzmann Models for Nonideal Gases. Phys. Rev. E 62 4982-4996 (2000). 

Sbragaglia, M., R. Benzi, L. Biferale, S. Sued, K. Sugiyama, and F. Toschi. Generalized Lattice Boltzmann Method with Multirange Pseudopotential. Phys. Rev. E 75 026702 (2007). Shan, X. and H. Chen. Lattice Boltzmann Model of Simulating Flows with Multiple Phases and Components. Phys. Rev. E 47 1815-1819 (1993). 

The flow field between the spheres can be solved for instance by the lattice Boltzmann method. The detailed gas-particle interaction (in the form of drag force) obtained from this microscopic level lattice Boltzmann method simulation will be appfied to higher level models instead of the conventional empirical correlations, which are only valid for spatially homogeneous flows. 

The lattice Boltzmann method is a mesoscopic simulation method for complex fluid systems. The fluid is modeled as fictitious particles, and they propagate and coUide over a discrete lattice domain at discrete time steps. Macroscopic continuum equations can be obtained from this propagation-colhsion dynamics through a mathematical analysis. The particulate nature and local d3mamics also provide advantages for complex boundaries, multiphase/multicomponent flows, and parallel computation. 

The lattice Boltzmann method (LBM) is a relatively new simulation technique for complex fluid systems and has attracted great interests from researchers in computational physics and engineering. Unlike traditional computation fluid dynamics (CFD) methods to numerically solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy), LBM models the fluid as fictitious particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh. Due to its particulate nature and local dynamics, LBM has several advantages over conventional CFD methods, especially in dealing with complex boundaries, incorporation of microscopic interactions, and parallel computation [1, 2]. 

Zhang J (2011) Lattice Boltzmann method for microfluidics models and applications. Microfluid Nanofluid 10 1-28... 

He XY, Chen SY, Doolen GD (1998) A novel thermal model for the lattice Boltzmann method in incompressible limit. J Comput Phys 42(146) 282-300... 

Maxwell B. J. (1997). Lattice Boltzmann methods in interjacial wave modelling. PhD Thesis, University of Edinburgh. 

Many of the mixing simulations described in the previous section deal with the modeling of mass transfer between miscible fluids [33, 70-77]. These are the simulations which require a solution of the convection-difliision equation for the concentration fields. For the most part, the transport of a dilute species with a typical diSusion coeflEcient 10 m s between two miscible fluids with equal physical properties is simulated. It has already been mentioned that due to the discretization of the convection-diffusion equation and the typically small diffusion coefficients for liquids, these simulations are prone to numerical diffiision, which may result in an over-prediction of mass transfer efficiency. Using a lattice Boltzmann method, however, Sullivan et al. [77] successfully simulated not only the diffusion of a passive tracer but also that of an active tracer, whereby two miscible fluids of different viscosities are mixed. In particular, they used a coupled hydrodynamic/mass transfer model, which enabled the effects of the tracer concentration on the local viscosity to be taken into account. 

A relatively new approach to the resolution of the fluid dynamics problem is the lattice Boltzmann method (LBM). LBM models the fluid flow as a movement of imaginary particles interacting with the obstacles (fibres)... 

Nabovati A, Llewellin E W and Sousa ACM (2009), A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method . Comp PartAiAppl Sci Manuf, 40(6-7), 860-869. 

Karra, S. Modeling electrospinning process and a numerical scheme using lattice Boltzmann method to simulate viscoelastic fluid flows, in Mechanical Engineering. Indian Institute of Technology Madras, Chennai, p. 60 (2007). 

D analysis, modeling and simulation of transport processes in fibrous microstmctures using the lattice Boltzmann method, in Proceedings of the International Symposium on Transport in Porous Materials and in Networked Microstmctures, with Special Focus on the Link Between Microscopy and Modelling, Villigen. 

Particle-based simulation techniques include atomistic MD and coarse-grained molecular dynamics (CG-MD). Accelerated dynamics methods, such as hyperdynamics and replica exchange molecular dynamics (REMD), are very promising for circumventing the timescale problem characteristic of atomistic simulations. Structure and dynamics at the mesoscale level can be described within the framework of coarse-grained particle-based models using such methods as stochastic dynamics (SD), dissipative particle dynamics (DPD), smoothed-particle hydrodynamics (SPH), lattice molecular dynamics (LMD), lattice Boltzmann method (IBM), multiparticle collision dynamics (MPCD), and event-driven molecular dynamics (EDMD), also referred to as collision-driven molecular dynamics or discrete molecular dynamics (DMD). 

Tabe, Y, Lee, Y, Chikahisa, T. Kozakai, M. Numerical simulation of liquid water and gas flow in a channel and a simplified gas diffusion layer model of polymer electrolyte membrane fuel-cells using the lattice Boltzmann method. J. Power Sources 193 (2009b), pp. 24-31. 

The Lattice Boltzmann method involves simulating a Boltzmann distribution of velocities on each site of a lattice. The distribution functions are allowed to evolve on a lattice to an equilibrium chosen to satisfy given conservation laws. On sufficiently large length- and time-scales, the macroscopic hydro-dynamic equations are obeyed. The method is thus suitable for modelling complex flows induced by shear, as well as diffusive processes such as phase separation. 

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