Lattice Gas Method Research Articles

Discrete modeling of water and pesticide movement in soil

Simulations of water and pesticide movement are presented for the unsaturated zone. Water movement is studied with a two‐dimensional Monte Carlo technique, where particles hop between the sites of a square lattice according to probabilistic rules. We developed this lattice gas method for two‐dimensional simulations of water flow in inhomogeneous media. Generalization to three dimensions is straightforward. The dynamics of the pesticide is simulated by particle tracking. After presenting the underlying discrete algorithms we emphasize calibration of the system. A soil is divided into homogeneous horizons, and our model is compared with the conventional one‐dimensional model PESTLA. We observe good agreement for both water content profile and pesticide distribution. The random elements in our algorithms cause moderate fluctuations in the results. As an example of two‐dimensional simulation, spatiotemporal pesticide patterns under a ridge are compared with the distribution under a flat soil surface.

Miscible displacement between two parallel plates: BGK lattice gas simulations

We study the displacement of miscible fluids between two parallel plates, for different values of the Péclet number Pe and of the viscosity ratio M. The full Navier–Stokes problem is addressed. As an alternative to the conventional finite difference methods, we use the BGK lattice gas method, which is well suited to miscible fluids and allows us to incorporate molecular diffusion at the microscopic scale of the lattice. This numerical experiment leads to a symmetric concentration profile about the middle of the gap between the plates; its shape is determined as a function of the Péclet number and the viscosity ratio. At Pe of the order of 1, mixing involves diffusion and advection in the flow direction. At large Pe, the fluids do not mix and an interface between them can be defined. Moreover, above M∼10, the interface becomes a well-defined finger, the reduced width of which tends to λ∞=0.56 at large values of M. Assuming that miscible fluids at high Pe are similar to immiscible fluids at high capillary numbers, we find the analytical shape of that finger, using an extrapolation of the Reinelt–Saffman calculations for a Stokes immiscible flow. Surprisingly, the result is that our finger can be deduced from the famous Saffman–Taylor one, obtained in a potential flow, by a stretching in the flow direction by a factor of 2.12.

Determination of elastic properties of very heterogeneous media with cellular automata

A cellular automaton is used to calculate the elastic properties of very heterogeneous media. The lattice gas method (designed to model viscous flow) is applied to elastic problems through the correspondence between the steady state velocity field in an incompressible Newtonian fluid at low Reynolds number and the displacement field in an incompressible elastic solid. The cellular automaton is applied to determine the elastic properties of a matrix containing randomly distributed hard inclusions. Because the equations of equilibrium are locally solved for any distribution of the inclusion phase, the method provides a means to estimate the influence of stress field perturbations on the macroscopic properties of heterogeneous systems. The effective elastic shear modulus is calculated as a function of the concentration C of the inclusion phase (0≤C≤1) for different values of R, the rheological contrast between the inclusion and the matrix. The numerical results are compared with those obtained by various micromechanical models. Estimates given by the cellular automaton agree with the analytical solution for a double periodic triangular system of discs. However, the effective shear modulus for the cellular automaton fluid does not fall within the limits of Hashin and Shtrikman. It follows the same trend as that of the lower bound but stays below the lower bound for all concentrations. Likewise, the shear modulus for a cellular automaton fluid is also systematically lower than that predicted by the differential method, although the trends are similar.

Efficient biased random bit generation for parallel lattice gas simulations

Lattice gas methods are often used to model the kinetics of a variety of diffusive systems. One of the main advantages of these methods is the ease at which they can be parallelized using simple bit vector operations. However, to describe the kinetics of the lattice gas in a randomly biased fashion, it is necessary to efficiently generate a randomly biased bit vector. If one generates a random floating point number per bit, then this is very costly. In this paper, an efficient algorithm is developed that leads to a fully bit vector implementation of a lattice gas automation while significantly reducing the amount of needed generated random floating point numbers. The bit vector algorithm using the new random biased bit vector algorithm is tested on a lattice gas method whose solution is modeled by the solution of the 1-D Burgers' equation. This new lattice gas method is then implemented on the BBN TC2200 and CRAY 90 parallel processors.

COMPUTING AERODYNAMICALLY GENERATED NOISE

▪ Abstract In contrast to computational aerodynamics, which has advanced to a fairly mature state, computational aeroacoustics (CAA) has only recently emerged as a separate area of study. Following a discussion of the classical field of aeroacoustics as introduced by Lighthill, the paper provides an overview and analysis of the problems associated with utilizing standard computational aerodynamics procedures for acoustic computations. Numerical aspects of computing sound-wave propagation are considered, including assessments of several schemes for spatial and temporal differencing. Issues of particular concern in computing aerodynamically generated noise, such as implementing surface and radiation boundary conditions and algorithms for predicting nonlinear steepening and shocks, are discussed. In addition, the paper briefly reviews alternatives to the conventional finite-difference schemes, such as boundary-element and spectral methods and the uncommon lattice-gas method.

Fluid flow across mass fractals and self-affine surfaces

We use a lattice-gas method to simulate the slow flow of a fluid in systems with fractal surfaces and volumes. Two systems are studied. One is flow in a single three-dimensional fracture with self-affine surfaces. The other is flow across a three-dimensional diffusion-limited aggregate. In both cases, significant deviations from classical results are observed.

THE LATTICE GAS METHOD AND INTERACTION WITH AN ELASTIC SOLID

The aim of this paper is to illustrate the possibility of simulating fluid-structure interactions by a lattice gas method. After a brief review of lattice gas hydrodynamics, this paper presents a method for evaluating the displacement of the nodes of the structure, the flow, and the technique used to link the two descriptions. The realization of the kinematics condition at the moving interface is explained in detail. The paper is concluded by two examples: free vibrations of a beam in a closed box filled with a fluid, and free vibrations of a beam in a channel flow.

Simulations of viscous flows of complex fluids with a Bhatnagar, Gross, and Krook lattice gas

We address the question of using a lattice gas method to study flows of complex fluids, such as non-Newtonian or miscible fluids. A Bhatnagar, Gross, and Krook lattice technique provides a tool to simulate the flow of one fluid and the diffusion of a tracer in that fluid. We extend the technique to flows in which the viscosity is space and time dependent. This approach is suitable for non-Newtonian fluids (shear dependent viscosity) and miscible fluids (concentration dependent viscosity). The modified scheme is tested on physical flow situations, analytically tractable for the sake of comparison.

Lattice-gas crystallization

This paper presents a new lattice-gas method for molecular dynamics modeling. A mean-field treatment is given and is applied to a linear stability analysis. Exact numerical simulations of the solid-phase crystallization are presented, as is a finite-temperature multiphase liquid-gas system. The lattice-gas method, a discrete dynamical method, is therefore capable of representing a variety of collective phenomena in multiple regimes from the hydrodynamic scale down to a molecular dynamics scale.

A hybrid computer simulation approach to shock propagation in fluid through porous media

An interacting lattice gas method is introduced to study the shock propagation through fluid in a porous medium. this approach incorporates the collision between the fluid particles as in direct simulation methods and interactions among the particles by the Metropolis algorithms to hop the fluid particles. We consider a two dimensional discrete lattice with a line of shock in a porous medium generated by a random distribution of fixed barriers at the pore boundaries. The velocity gradient caused by the shock drives the fluid. We find that the shock fronts drift in high porosity and propagate nondiffusively as the shock-driven flow field competes with the pore barriers, especially at low porosity (i.e. high ramification). The magnitude of the fluid velocity at the shock front decays with time nonlinearly. The shock depletes the fluid density as it propagates into the lattice. Damping of the shock profile is enhanced on reducing the porosity.

Lattice methods and their applications to reacting systems

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 systems. The lattice gas method, regarded as the simplest microscopic and kinetic approach which generates meaningful macroscopic dynamics, is fully parallel and can, as a result, be easily programmed on parallel machines. In this paper, we introduce the basic principles of the lattice gas method and the lattice Boltzmann method, their numerical implementations and applications to chemically reacting systems. Comparisons of the lattice Boltzmann method with the lattice gas technique and other traditional numerical schemes, including the finite difference scheme and the pseudo-spectral method, for solving the Navier-Stokes hydrodynamic fluid flows will be discussed. Recent developments of the lattice gas and the lattice Boltzmann method and their applications to pattern formation in chemical reaction-diffusion systems, multiphase fluid flows and polymeric dynamics will be presented.

Lattice methods and their applications to reacting systems

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 systems. The lattice gas method, regarded as the simplest microscopic and kinetic approach which generates meaningful macroscopic dynamics, is fully parallel and can, as a result, be easily programmed on parallel machines. In this paper, we introduce the basic principles of the lattice gas method and the lattice Boltzmann method, their numerical implementations and applications to chemically reacting systems. Comparisons of the lattice Boltzmann method with the lattice gas technique and other traditional numerical schemes, including the finite difference scheme and the pseudo-spectral method, for solving the Navier-Stokes hydrodynamic fluid flows will be discussed. Recent developments of the lattice gas and the lattice Boltzmann method and their applications to pattern formation in chemical reaction-diffusion systems, multiphase fluid flows and polymeric dynamics will be presented.

格子気体法における圧力場の検討

Recently, the lattice gas method has been widely used to simulate fluid motions. Many researchers have computed the velocity fields of various flows by this method, and have already confirmed that the results agree well with the experiments. However, the pressure field has not been examined. In this paper, in order to verify the pressure field of the lattice gas method, we will present a method to compute the pressure field, and apply it to a flow around a plate and that around a rotating wing which is a model of the Weis-Fogh mechanism. The drag and the lift coefficients obtained by this method agree reasonably well with experimental values, and the validity of the pressure fields by the lattice gas method was confirmed.

Modeling water infiltration in unsaturated porous media by interacting lattice gas‐cellular automata

A two‐dimensional lattice gas‐cellular automaton fluid model with long‐range interactions (Appert and Zaleski, 1990) is used to simulate saturated and unsaturated water infiltration in porous media. Water and gas within the porous medium are simulated by applying the dense and the light phase, respectively, of the cellular automaton fluid. Various wetting properties can be modeled when adjusting the corresponding solid‐liquid interactions. The lattice gas rules include a gravity force step to allow buoyancy‐driven flow. The model handles with ease complex geometries of the solid, and an algorithm for generating random porous media is presented. The results of four types of simulation experiments are presented: (1) We verified Poiseuille's law for steady and saturated flow between two parallel plates. (2) We analyzed transient water infiltration between two parallel plates of varying degrees of saturation and various apertures. (3) Philip's infiltration equation was adequately simulated in an unsaturated porous medium. (4) Infiltration into an aggregated medium containing one vertical parallel crack was simulated. Further applications of this lattice gas method for studying unsaturated flow in porous media are discussed.

Gas dynamics of cellular automata (review)

The goal of the review is to acquaint experts in combustion and explosion with the method of cellular automata, also called the lattice-gas method, a comparatively new approach to modeling of gas-dynamic processes. The motion of a continuous medium is modeled directly by calculating the evolution of a special microworld of particles, which move in a fixed two- or three-dimensional lattice and collide with each other at the lattice sites. In essence, what is involved is the most simplified version of molecular dynamics. Examples are given of application to various problems, including calculation of reacting flows, unstable problems, and flows in a complex geometry. Possible applications of the method in the physics of combustion and explosion are discussed.

Nucleation, domain growth, and fluctuations in a bistable chemical system

Phase separation and nucleation processes are investigated for a bistable chemical system. The study utilizes a reactive lattice-gas cellular automaton model to provide a mesoscopic description of the dynamics. Simulations of steady-state structure, wave propagation, and critical nucleus size using this model are compared with results based on the deterministic equations of motion. The dynamic structure factor is computed for evolution from the unstable state and the effects of correlations are examined for early and late times. The study provides insight into these processes in a fluctuating, extended medium and also provides a test of the ability of the reactive lattice-gas method to describe the fluctuations in the system.

Spontaneous symmetry-breaking in the 3-D wake of a long cylinder simulated by the lattice gas method and drag coefficient measurements

Spontaneous symmetry-breaking in the 3-D wake of a long cylinder simulated by the lattice gas method and drag coefficient measurements

Lattice Boltzmann computations for reaction-diffusion equations

A lattice Boltzmann model for reaction-diffusion systems is developed. The method provides an efficient computational scheme for simulating a variety of problems described by the reaction-diffusion equations. Diffusion phenomena, the decay to a limit cycle, and the formation of Turing patterns are studied. The results of lattice Boltzmann calculations are compared with the lattice gas method and with theoretical predictions, showing quantitative agreement. The model is extended to include velocity convection in chemically reacting fluid flows.

29 O 03 Lattice gas method for suspensions

29 O 03 Lattice gas method for suspensions

Lattice Boltzmann computational fluid dynamics in three dimensions

The recent development of the lattice gas method and its extension to the lattice Boltzmann method have provided new computational schemes for fluid dynamics. Both methods are fully paralleled and can easily model many different physical problems, including flows with complicated boundary conditions. In this paper, basic principles of a lattice Boltzmann computational method are described and applied to several three-dimensional benchmark problems. In most previous lattice gas and lattice Boltzmann methods, a face-centered-hyper-cubic lattice in four-dimensional space was used to obtain an isotropic stress tensor. To conserve computer memory, we develop a model which requires 14 moving directions instead of the usual 24 directions. Lattice Boltzmann models, describing two-phase fluid flows and magnetohydrodynamics, can be developed based on this simpler 14-directional lattice. Comparisons between three-dimensional spectral code results and results using our method are given for simple periodic geometries. An important property of the lattice Boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency, while all other methods, including the spectral method, are unable to model complicated geometries efficiently.