Lattice Gas Method Research Articles

Integer lattice gas with a sampling collision operator for the fluctuating diffusion equation.

We developed an integer lattice gas method for the fluctuating diffusion equation. Such a method is unconditionally stable and able to recover the Poisson distribution for the microscopic densities. A key advance for integer lattice gases introduced in this paper is a sampling collision operator that replaces particle collisions with sampling from an equilibrium distribution. This can increase the efficiency of our integer lattice gas by several orders of magnitude.

Validity of the molecular-dynamics-lattice-gas global equilibrium distribution function

The molecular-dynamics-lattice-gas (MDLG) method establishes a direct link between a lattice-gas method and the coarse-graining of a molecular dynamics (MD) approach. Due to its connection to MD, the MDLG rigorously recovers the hydrodynamics and allows to validate the behavior of the lattice-gas or lattice-Boltzmann methods directly without using the standard kinetic theory approach. In this paper, we show that the analytical definition of the equilibrium distribution function remains valid even for very high volume fractions.

2.2 量子格子ガス法による二重障壁構造の共鳴トンネル効果の動特性の計算

2.2 量子格子ガス法による二重障壁構造の共鳴トンネル効果の動特性の計算

111 固気混相流の格子気体シミュレーションにおける粒子境界条件の検討(流体工学(混相流2))

111 固気混相流の格子気体シミュレーションにおける粒子境界条件の検討(流体工学(混相流2))

Numerical study of unstable reaction-diffusion fronts in porous media

Numerical simulations using a lattice-gas method (FHP-III) were performed. The method was modified for simulating two miscible fluids into a rectangular cell with obstacles (porous medium) and without obstacles (Hele-Shaw cell). An external force can be applied to each fluid. A suitable combination of this force and initial conditions can develop an unstable interface front (Rayleigh-Taylor instability). A chemical reaction between the fluids was also introduced, with a parameter that controls the reaction rate. The influence of the parameters that control the force and the chemical reaction on the development of the instability was studied.

Relativistic Path Integral as a Lattice-based Quantum Algorithm

We demonstrate the equivalence of two representations of many-body relativistic quantum mechanics: the quantum lattice-gas method and the path integral method. The former serves as an efficient lattice-based quantum algorithm to simulate the space-time dynamics of a system of Dirac particles.

Lattice gas models derived from effective field theory

We start from a low-energy effective field theory for interacting fermions on the lattice and expand in the hopping parameter to derive the nearest-neighbor interactions for a lattice gas model. In this model, the renormalization of couplings for different lattice spacings is inherited from the effective field theory, systematic errors can be estimated a priori, and the breakdown of the lattice gas model description at low temperatures can be understood quantitatively. We apply the lattice gas method to neutron matter and compare with results from a recent quantum simulation.

Numerical investigations of passive and reactive flow through generic single fractures with heterogeneous permeability

Numerical investigations of the relationship between permeability distributions representing fracture apertures and the transport of inert and reactive solutes have been carried out. To model reactive transport, a lattice gas method for fluid flow was coupled to a finite-difference solution to the advection–dispersion equation with the inclusion of mineral dissolution and precipitation reactions. This enabled us to model reactive flow in heterogeneous media with a feedback between geochemical alteration and the flow regime. We modelled the transport of both inert tracers and reactive solutes through several realisations of different permeability distributions. The numerically simulated distributions were generated to represent transport through a fracture of 150 m×50 m area. The mean of a contaminant plume moved sublinearly through the distribution with the mean velocity decreasing through time. The standard deviation of a contaminant plume throughout the medium scales as σ∼tβ. We have found that β ranges from 0.5 to 0.9 for different distributions, for Gaussian transport β=0.5. The introduction of reactive solutes changes the flow and transport properties. Quartz dissolution, for example, increases the permeability and creates channels which focus the flow and increase the dissolution to create a positive feedback until the solution reaches saturation. The roughness of the dissolution pattern is dependent on the initial geometry and the Damköhler number.

The use of lattice gas method in explaining architectural acoustics principles

Many concepts in architectural acoustics are based on physical phenomena, such as sound propagation, reflection, etc. In explaining those phenomena, it is necessary to employ the principles of physical acoustics. Unfortunately, the methods of physical acoustics are not easily approachable unless one is familiar with mathematical physics techniques, partial differential equations, for example. The lattice gas method, based on the cellular automata concept, can be an alternative to avoid the use of complicated mathematical equations. A relatively simple code can be used to generate computer simulations. The existing models for sound propagation by Sudo and Sparrow, are examined. Models for other phenomena involving architectural acoustics are suggested.

217 実数格子ガス法を用いたコロイド流動系の数値解析

217 実数格子ガス法を用いたコロイド流動系の数値解析

LATTICE-GAS AUTOMATA FOR THE PROBLEM OF KINETIC THEORY OF GAS DURING FREE EXPANSION

The lattice-gas method has been applied to solve the problem of kinetic theory of gas in the Gay–Lussac–Joule experiment. Numerical experiments for a two-dimensional gas were carried out to determine the number of molecules in one vessel (Nr), the ratio between the mean square values of the components of molecule velocity [Formula: see text], and the change in internal energy (ΔU) as a function of time during free expansion. These experiments were repeated for different sizes of an aperture in the partition between the two vessels. After puncturing the partition, the curve for the particle number in one vessel shows a damped oscillation for about half of the total number. The oscillations do not vanish after a sampling over different initial configurations. The system is in nonequilibrium due to the pressure equilibration, and here the flow is actually compressible. The equilibration time (in time steps) decreases with decreased size of aperture in the partition. For very small apertures (equal or less than [Formula: see text] lattice units), the number of molecules in one vessel changes with time in a smooth way until it reaches half of the total number; their curves obey the analytical solution for quasi-static processes. The calculations on [Formula: see text] and ΔU also support the results that the equilibration time decreases with decreased size of aperture in the partition.

Using three-dimensional reconstructed microstructures for predicting intrinsic permeability of reservoir rocks based on a Boolean lattice gas method

This paper presents a method for predicting the intrinsic permeability of porous media based on the integration of the local velocity field. Three-dimensional representations of the porous structure are reconstructed from two-dimensional binary images, after segmentation of digital images acquired from thin plates, commonly used in microscopy. Velocity field is calculated on these three-dimensional representations using a Boolean lattice gas method (LGA). Reconstruction is based on a Gaussian stochastic simulation. Mercury-intrusion results furnish auxiliary data that are used for the estimation of a critical percolation diameter and to establish a necessary condition for the binary source images to give accurate predictions of permeability, considering the intrinsic limitations of the reconstruction process. Reconstruction method and connection loss, resolution factor, adherence conditions and the effects of Boolean noise in the calculation of permeability are fully discussed. The method is used to simulate flows through several petroleum reservoir rocks, leading to intrinsic permeability prediction. Simulation is compared with experimental results. Considered as an intrinsic permeability prediction method based on the geometrical information that is possible to recovery from microscopy thin plates, three-dimensional reconstruction appears to be the most critical step in present simulation scheme.

Three-dimensional analyses of fluids with surfactants using the real-coded lattice gas method

We established a simulation model for the fluid-surfactant system, by introducing dumbbell-structured particles into the Real-Coded Lattice Gas (RLG), an efficient particle-based model for fluctuating hydrodynamics. Numerical simulations in 3D geometries were carried out. In particular, we successfully reproduced the spontaneous assembling of spherical micelles in an aqueous environment and the formation of bicontinuous phase in a water/oil/surfactant ternary fluid.

Development of a simulation model for solid objects suspended in a fluctuating fluid

We have been developing a new lattice gas model, a Real-coded Lattice Gas (RLG) method, in order to study complex fluid flows. In this study, we extend the RLG method in order to perform of the simulation of blood flows with individual descriptions of red blood cells. These topics are strongly related to clinical and medical engineering problems.

Simulation of Convective Detonation Waves in a Porous Medium by the Lattice Gas Method

“Gas—film” convective detonation in a rigid porous medium is considered. The motion of the gas phase is described by a discrete stochastic lattice gas model taking into account the real laws of friction and heat exchange between the phases. The reaction kinetics was specified so that the characteristic time of combustion corresponded to experiment. The model simulates the main characteristics of the phenomenon: a nonflat (irregular) wave front, smooth increase in the pressure averaged over the charge cross section, friction–dominated mean flow, slow cooling of combustion products after completion of the reaction.

F08-1 格子ガス法による熱流動および複雑流体解析(F08 格子ガス法・格子ボルツマン法による熱流動および複雑流体のシミュレーションの現状と課題)(フォーラム)

F08-1 格子ガス法による熱流動および複雑流体解析(F08 格子ガス法・格子ボルツマン法による熱流動および複雑流体のシミュレーションの現状と課題)(フォーラム)

Immiscible real-coded lattice gas

The real-coded lattice gas method was proposed by Malevanets (1997). In this new lattice gas model, particles have continuous velocity distributions, which would yield to Maxwell–Boltzmann distribution in the equilibrium state. Furthermore, collision and streaming schemes do not depend on the explicit lattice structure. Extension to the three-dimensional calculation becomes straightforward both conceptually and practically. We extended this innovative model to the modeling of immiscible binary fluids by introducing colored particles and their interactions. Benchmark calculations show that Laplace law is satisfied in both 2D and 3D spaces. Simulations of phenomena occurring in the realistic immiscible binary fluids were carried out successfully. The model worked stably, and the qualitative agreement with the well-known droplet behavior has been observed.

界面活性剤を含む多相系の実数速度格子ガスモデル

We have developed an extended version of the Real-Coded Lattice Gas Method, in order to simulate behaviors of multi-phase systems with surfactants. We characterized surfactants by dumbbell-shaped particles, composed by sets of hydrophilic ends and hydrophobic ends connected by rigid rods. By adopting our model, we conducted simulations of micelle formations by surfactants in an aqueous environment. In the simulations, our model provided significant results which reflect some of the properties of actual micelle structures.

Droplet Dynamics Using the Lattice-Gas Method

We apply the lattice-gas method to study droplet behavior. The ascending velocity and deformation of a drop under buoyancy are numerically analyzed. We develop an algorithm to adjust surface tension by changing collision rules, and deformation of a droplet is calculated with different surface tensions. The deformation of a drop driven by the pressure gradient under gravity is also investigated.

Fingering in 2D Parallel Viscous Flow

We study the displacement of miscible fluids of different viscosities (viscosity ratio AI) between two parallel plates, using the BGK lattice gas method. At high Peclet numbers, a symmetric interface develops in the gap between the plates. Above M +J 10, the interface becomes a well-defined finger, the reduced width of which tends to A~n = 0.56 at large AI. Assuming that a miscible displacement at high Peclet numbers is equivalent to an immiscible displacement at high capillary numbers, we extend the calculations of Reinelt & Saffman for immiscible fluids, and find the analytical shape of the finger. The result is compared to the celebrated Saffman-Taylor finger.