We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

Lattice boltzmann method for fluid flows

With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.

Lattice-Boltzmann Method for Complex Flows

In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models.

Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.

/pdf/lattice-gas-cellular-automata-and-lattice-boltzmann-models-2kkc77jjx8.pdf

Lattice-Gas Cellular Automata and Lattice Boltzmann Models

Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction

A lattice Boltzmann equation method for simulating multiphase immiscible fluid flows with variation of density and viscosity, based on the model proposed by Gunstensen et al. for two‐component immiscible fluids [Phys. Rev. A 43, 4320 (1991)] is developed. The numerical measurements of surface tension and viscosity agree well with theoretical predictions. Several basic numerical tests, including spinodal decomposition, two‐phase fluid flows in two‐dimensional channels, and two‐phase viscous fingering, are shown in agreement of experiments and analytical solutions.

A lattice Boltzmann model for multiphase fluid flows

/pdf/toward-improved-prediction-of-reservoir-flow-performance-1r1uh37lgt.pdf

Toward Improved Prediction of Reservoir Flow Performance

Calculating flow and transport in porous/fractured media using the cellular automata approach

Lattice gas automata for flow through porous media

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Papers

A lattice Boltzmann model for multiphase fluid flows

Toward Improved Prediction of Reservoir Flow Performance

Calculating flow and transport in porous/fractured media using the cellular automata approach

Lattice gas automata for flow through porous media