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At least 703 records · Page 39Linked to original sources
arXiv1993

Elimination of Nonlinear Deviations in Thermal Lattice BGK Models

Abstracet: We present a new thermal lattice BGK model in D-dimensional space for the numerical calculation of fluid dynamics. This model uses a higher order expansion of equilibrium distribution in Maxwellian type. In the mean time the lattice symmetry is upgraded to ensure the isotropy of 6th order tensor. These manipulations lead to macroscopic equations free from nonlinear deviations. We demonstrate the improvements by conducting classical Chapman-Enskog analysis and by numerical simulation of shear wave flow. The transport coefficients are measured numerically, too.

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arXiv1993

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.

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arXiv1994

A Lattice Boltzmann Subgrid Model for High Reynolds Number Flows

A subgrid turbulence model for the lattice Boltzmann method is proposed for high Reynolds number fluid flow applications. The method, based on the standard Smagorinsky subgrid model and a single-time relaxation lattice Boltzmann method, incorporates the advantages of the lattice Boltzmann method for handling arbitrary boundaries and is easily implemented on parallel machines. The method is applied to a two-dimensional driven cavity flow for studying dynamics and the Reynolds number dependence of the flow structures. The substitution of other subgrid models, such as the dynamic subgrid model, in the framework of the LB method is discussed.

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arXiv1994

Estimating Functions of Probability Distributions from a Finite Set of Samples, Part 1: Bayes Estimators and the Shannon Entropy

We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint distribution, we present finite sample estimators for the mutual information, covariance, and chi-squared functions of that probability distribution.

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arXiv1994

Estimating Functions of Distributions from A Finite Set of Samples, Part 2: Bayes Estimators for Mutual Information, Chi-Squared, Covariance and other Statistics

We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint distribution, we present finite sample estimators for the mutual information, covariance, and chi-squared functions of that probability distribution.

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arXiv1994

A Lattice-Gas with Long-Range Interactions Coupled to a Heat Bath

Introduced is a lattice-gas with long-range 2-body interactions. An effective inter-particle force is mediated by momentum exchanges. There exists the possibility of having both attractive and repulsive interactions using finite impact parameter collisions. There also exists an interesting possibility of coupling these long-range interactions to a heat bath. A fixed temperature heat bath induces a permanent net attractive interparticle potential, but at the expense of reversibility. Thus the long-range dynamics is a kind of a Monte Carlo Kawasaki updating scheme. The model has a $PρT$ equation of state. Presented are analytical and numerical results for the a lattice-gas fluid governed by a nonideal equation of state. The model's complexity is not much beyond that of the FHP lattice-gas. It is suitable for massively parallel processing and may be used to study critical phenomena in large systems.

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arXiv1994

Lattice-Gas Automata Fluids on Parallel Supercomputers

A condensed history and theoretical development of lattice-gas automata in the Boltzmann limit is presented. This is provided as background to set up the context for understanding the implementation of the lattice-gas method on two parallel supercomputers: the MIT cellular automata machine CAM-8 and the Connection Machine CM-5. The macroscopic limit of two-dimensional fluids is tested by simulating the Rayleigh-Bénard convective instability, Kelvin-Helmholtz shear instability, and the Von Karman vortex shedding instability. Performance of the two machines in terms of both site update rate and maximum problem size are comparable. The CAM-8, being a low-cost desktop machine, demonstrates the potential of special-purpose digital hardware.

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arXiv1994

Application of Complex Daubechies' Wavelets to Numerical Simulation of a Nonlinear Signal Propagation Model

We report the first application of complex symmetric wavelets to the numerical simulation of a nonlinear signal propagation model. This model is the so-called nonlinear Schrodinger equation that describes, for instance, the evolution of the electric field amplitude in nonlinear optical fibers. We propose and study a new way to implement a global space-time adaptive grid, based on interpolation properties of higher-order scaling functions.

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arXiv1994

Lattice Gas Automata: a discrete model for simulation of continuous transport phenomena in packages of agricultural products

A Lattice Boltzmann scheme has been applied to the problem of heat and mass transport in packagings of cut flowers. The LB scheme, simulating convection-diffusion processes and heat and mass transfer between flowers and air flow, is described in detail. The objective of the research programme is to optimize the packaging design for improved flower quality. Comparison of experimental results and simulation results show that the LB-scheme is a promising simulation technique for achieving the research objective.

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arXiv1994

Nonlinear Analysis of Experimental Noisy Time Series in Fluidized Bed Systems

The paper describes the application of some numerical techniques to analyze and to characterize the observed dynamical behaviour of fluidized bed systems. The preliminary results showed clearly that the dynamics of the considered process can be nonrecurrent and governed by chaotic deterministic rules rather than by stochastic ones. This significant conclusion was allowed by the application of a proper filtering procedure which was able to reduce the unwanted influence of significant broadband noise detected in the sampled experimental data.

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arXiv1994

Recognition of Temporal Sequences of Patterns

Using an asymmetric associative network with synchronous updating, it is possible to recall a sequence of patterns. To obtain a stable sequence generation with a large storage capacity, we introduce a threshold that eliminates the contribution of weakly correlated patterns. For this system we find a set of evolution equations for the overlaps of the states with the patterns to be recognized. We solve these equations in the limit of the stationary cycle, and obtain the critical value of the capacity as a function of the threshold and temperature. Finally, a numerical simulation is made, confirming the theoretical results.

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arXiv1994

Renormalization of Lattice Gas Transport Coefficients

A method is described for calculating corrections to the Boltzmann/Chapman-Enskog analysis of lattice gases due to the buildup of correlations. It is shown that renormalized transport coefficients can be calculated perturbatively by summing terms in an infinite series. A diagrammatic notation for the terms in this series is given, in analogy with the Feynman diagrams of quantum field theory. This theory is applied to an example lattice gas and shown to correctly predict experimental deviation from the Boltzmann prediction.

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arXiv1995

Algebraic Spatial Correlations and Non-Gibbsian Equilibrium States

Non-Gibbsian stationary states occur in dissipative non-equilibrium systems. They are closely connected with the lack of detailed balance and the absence of a fluctuation-dissipation theorem. These states exhibit spatial correlations that are long ranged under generic conditions, even in systems with short range interactions, provided the system has slow modes and some degree of spatial anisotropy. In this paper we present a theory for static pair correlations in lattice gas automata violating detailed balance, and we show that the spatially uniform non-Gibbsian equilibrium state exhibits long range correlations, even in the absence of an external driving field.

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arXiv1995

A Method for Near-Equilibrium Discrete-Velocity Gas Flows

We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the resultant scheme strongly resembles the original processes. The kinetic nature of the scheme and the modeling of the {\em infinite collision rate} limit, result in a small value of the coefficient of (numerical)-viscosity, the behavior of which is remarkably physical [18]. A first order method, and two second order methods using the total variation diminishing principle are developed and an example application presented. Given the same computer resources, it is expected that with this approach, much higher Reynold's number will be achievable than presently possible with either lattice gas automata or lattice Boltzmann approaches. The ideas being general, the scheme is applicable to any discrete-velocity model, and to lattice gases as well.

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arXiv1995

Plane Waves in a Multispeed Discrete-Velocity Gas

A kinetic flux-splitting procedure used in conjunction with local thermodynamic equilibrium in a finite volume allows us to investigate numerically discrete-velocity gas flows. The procedure, outlined for a general discrete-velocity gas, is used to simulate flows of the nine-velocity gas, a simple two dimensional multiple-speed discrete-velocity gas, wherein a multiplicity of speeds ensures nontrivial thermodynamics. After verifying the linear wave limit and the non-linear steepening of wavefronts, the stability and propagation of planar discontinuities in that model gas is studied. The supersonic-subsonic requirement for the stable propagation of a discontinuity, being kinematic in nature is the same in the model gas, as e.g., in a perfect gas. However, the finiteness of the velocity space in the model gas does not allow a translation of the above kinematic condition to the thermodynamic requirement of increasing entropy across a compressive shock: a case of an entropy decreasing compressive shock in the model gas is presented. Finally, the interaction of various types of waves--shock waves, rarefactions and contact surfaces--in the model gas are shown in a simulation of the shock tube problem.

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arXiv1995

Lattice Boltzmann Model For Magnetic Fluids

A lattice Boltzmann model with interacting particles was developed in order to simulate the magneto-rheological characteristics of magnetic fluids. In the frame of this model, $6\, +\,1$ species of particles are allowed to move across a $2D$ triangular lattice. Among these species, $6$ of them carry an individual magnetic dipole moment and interact themselves not only as a result oflocal collisions, as in current Lattice Boltzmann models, but also as a result of nearest neighbours magnetic dipole-dipole interaction. The relative distribution of the individual magnetic moments is determined by the intensity of an external static magnetic field acting on the whole system. This model exhibits some relevant characteristics of real magnetic fluids, i.e., anisotropic structure formation as a result of magnetic field induced gas-liquid phase transition and magnetic field dependence of the sound velocity and the attenuation coefficient.

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