Lattice Boltzmann methods

Chen S and Doolen G D 1998 Lattice Boltzmann method for fluid flows Ann. Rev. Fluid Meoh. 30 329-64... 

Another numerical study of free-surface flow patterns in narrow channels was conducted by Yang et al. [185]. They considered the flow of bubbles of different size driven by body forces, for example the rising of bubbles in a narrow capillary due to buoyancy. The lattice Boltzmann method [186] was used as a numerical scheme... 

Rohde, M., Extending the Lattice-Boltzmann method—novel techniques for local grid refinement and boundary conditions , Ph.D. Thesis, Delft University of Technology, Delft, Netherlands (2004). 

Fio. 16. Snapshot of the 2D concentration field for reactive fluids. Reprinted from Chemical Engineering Science, Vol. 56, Zeiser et al, CFD-Calculation of Flow, Dispersion and Reaction in a Catalyst Filled Tube by the Lattice Boltzmann Method, pp. 1697-1704, Copyright (2001), with permission from Elsevier. 

The flow resistance behavior of the reconstructed medium can now be examined by performing 3D flow simulations with the Lattice Boltzmann method (Chen and Doolen, 1998), and obtaining the permeability of the material (Konstandopoulos, 2003). Figure 8(a) depicts a visualization of 3D flow tubes and flow velocity distributions at different cross sections in a reconstructed filter material. Figure 8(b) shows the comparison of computer simulated and experimental permeabilities obtained with the experimental protocol described in Konstandopoulos (2003). 

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... 

R.A. Escobar, S.S. Ghai, M.S. Jhon, and C. Amon, Time-dependent simulations of subcontinuum heat generation effects in electronic devices using the lattice-Boltzmann method,... 

Direct numerical solution using finite-difference, finite-element, and boundary-element methods have played important roles in porous-media research. During the last decade, the lattice-Boltzmann method has emerged as a preferred method for many applications, particularly in the hydrology literature. Significant advantages include relatively simple... 

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. 

Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Aimu Rev Fluid Mech 30 329-364... 

Sectional and class methods for the solution of the collisional KE are generally called discrete-velocity methods (DVM). These methods are based on the simple idea of discretizing the velocity space into a grid constituted by a finite number of points. The existing methods are characterized by different grid structures (Aristov, 2001). For example, lattice Boltzmann methods discretize the velocity space into a regular cubic lattice with a constant lattice size (Li-Shi, 2000), whereas other methods employ different discretization schemes (Monaco Preziosi, 1990). By using a similar approach to that used with PBE, it is possible to define A,- as the number density of the particles with velocity and the discretized KE becomes... 

Aidun, C. K. Clausen, J. R. 2010 Lattice-Boltzmann method for complex flows. Annual Review of Fluid Mechanics 42, 439 72. 

Lallemand, P. Luo, L.-S. 2003 Theory of the lattice Boltzmann method dispersion, dissipation, isotropy, Galilean invariance, and stability. Physical Review E 68,036706. 

Sankaranarayanan, K., Shan, X., Kevrekidis, I. G. Sundaresan, S. 2002 Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method. Journal ofEluid Mechanics 452, 61-96. 

Stockman et al. (1997) provide details on the practical problems and limitations of lattice gas and lattice Boltzmann methods in flow and transport simulation. In particular, they focus on errors associated with boundary conditions, the accuracy required for useful comparison with experimental data, programming, and problem size and run-time issues. For lattice gas methods, they find that averaging over a large number of time steps is sometimes needed to resolve the flow velocity field. This limits the applicability of lattice gas methods to flow simulation under steady state or slowly varying conditions. In contrast, dispersive processes alone can be adequately simulated with lattice gasses by averaging a much smaller number of time steps. Lattice Boltzmann methods do not require averaging. 

Stockman, H.W., C. Cooper, C. Li, and S.J. Perea-Reeves. 1997. Practical application of lattice-gas and lattice Boltzmann methods to dispersion problems. Int. J. Complex Sysl. Pup. 90. Available at http //www. wi/.ard.com/ hwstock/saltfing.htm. 

If one is interested in properties that vary on very long distance and time scales it is possible that a drastic simplification of the molecular dynamics will still provide a faithful representation of these properties. Hydrodynamic flows are a good example. As long as the dynamics preserves the basic conservation laws of mass, momentum and energy, on sufficiently long scales the system will be described by the Navier-Stokes equations. This observation is the basis for the construction of a variety of particle-based methods for simulating hydrodynamic flows and reaction-diffusion dynamics. (There are other phase space methods that are widely used to simulate hydrodynamic flows which are not particle-based, e.g. the lattice Boltzmann method [125], which fall outside the scope of this account of MD simulation.)... 

A further theme is the development of techniques to bridge the length and time scales between truly molecular-scale simulations and more coarse-grained descriptions. T q)ical examples are dissipative particle dynamics [226] and the lattice-Boltzmann method [227]. Part of the motivation for this is the recognition that... 

A lattice scheme which does capture hydrodynamic behaviour is the lattice Boltzmann method [M, M, M and... 

Abe Takashi. 1997. Derivation of the lattice Boltzmann method by means of the discrete ordinate method for the Boltzmann equation. Journal of Computational Physics. 131 (1). 

Horbach, J. Frenkel, D. Lattice-Boltzmann Method for the Simulation of... 

---