Acoustic Properties of Fontainebleau Samples by Lattice Models

Acoustic properties of dry or saturated porous media can be studied numerically by a combined use of lattice spring models and lattice Boltzmann models. The methodology is briefly described and it is systematically applied to a series of Fontainebleau sandstones whether they are dry or saturated with incompressible or compressible fluids. The velocities of compression and shear waves, as well as their attenuation, are determined. The simulation results are in good agreement compared with the existing methods and experimental data.

     

Improved Lattice Boltzmann Models for Precipitation and Dissolution

A challenge when modeling mineral growth inside the pore space of a porous media is to minimize the effect of the computational grid on the shape of the minerals being formed. Pore surface area and volume are important quantities in estimating upscaled permeability and effective rate equations, which emphasize the importance of models that minimize or completely eliminate grid effects. In this paper, we study how the initial orientation of the solid structure on the numerical grid affects the growth pattern due to precipitation in a lattice Boltzmann model. We have implemented a volume of fluid method to represent the solid interface, and we introduce a surface tension term that extensively reduces the dependency on the underlying numerical grid. We study both diffusion-limited and reaction-limited precipitation. In the diffusion-limited case, instabilities will develop on small scales. The surface tension term effectively introduces a short wavelength cut off which limits the unstable precipitation and reduces grid effects. We argue that the surface tension term is needed to obtain a growth pattern independent of the initial orientation on the underlying grid in the diffusion-limited case, and that simpler models can be used in the reaction-limited case.     

Strain rate dependency of uniaxial tensile strength in Gosford sandstone by the Distinct Lattice Spring Model with X-ray micro CT

Mechanisms causing strain rate dependency of the uniaxial tensile strength of Gosford sandstone are studied using the Distinct Lattice Spring Model (DLSM). The DLSM is built to have a microstructure which resembles aspects of the microstructure in a sample of the sandstone observed through 5 μm resolution X-ray micro CT scanning. Numerical dynamic uniaxial tensile tests on the sandstone are performed using both X-ray micro CT based and homogenous particle models. The results indicate that there is an only negligible strength increase with increasing strain rate for the homogenous particle model. However, a significant strength increase is observed with increasing strain rate for the X-ray micro CT based particle model. Therefore, it must be the microstructure that causes a strain rate dependency. Moreover, the influence of viscosity and rate dependency of springs are also studied. Results reveal that the rate dependency of the springs rather than their viscosity is also a main cause of the rate dependency.     

Diffusivity of Lattice Gases

We consider one-component lattice gases with local dynamics and a stationary product Bernoulli measure on ${\mathbb{Z}^d}$ . We study the scaling exponents of the space-time correlations of the system in equilibrium at a given density. We consider a variance-like quantity computed from the correlations called the diffusivity (connected to the Green–Kubo formula) and give rigorous upper and lower bounds on it that depend on the dimension and the local behavior of the macroscopic flux function. Our results identify the cases in which the system scales superdiffusively; these cases have been predicted before, using non-rigorous scaling arguments. Our main tool is the resolvent method: the estimates are the result of a careful analysis of a complicated variational problem.     

Lattice modelling of nematodynamics

The microstructures of textured nematics under shear are investigated by means of a director lattice model incorporating linear shear response as well as elastic interactions between neighbouring directors. The model can be understood as a lattice implementation of the so-called nematodynamics equation for a constant uniaxial order parameter. The dimensionless number governing the model is found to be a mesoscale Ericksen number, which scales with the square of the lattice cell size. It is shown that the predicted microstructure depends strongly on the scale of that number. In particular, disclination loops are found to grow for a range of mesoscale Ericksen numbers, while below or above that they disappear. We apply the model to investigate the director profiles of tumbling nematics. If the orientations are restricted to lying in the vorticity plane, we reproduce the director wind-up layers and distortion saturation predicted theoretically. In the full three-dimensional case an initially polydomain director field evolves to a vorticity-aligned state up to a critical Ericksen number, above which in-plane orientations with distortion saturation are found. The simulations hence reproduce the transition from log-rolling to flow aligning with increasing shear rate observed experimentally. Received: 9 March 1999 /Accepted: 26 July 1999     

Lattice Boltzmann model for nanofluids

A nanofluid is a particle suspension that consists of base liquids and nanoparticles and has great potential for heat transfer enhancement. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles, a lattice Boltzmann model is proposed for simulating flow and energy transport processes inside the nanofluids. First, we briefly introduce the conventional lattice Boltzmann model for multicomponent systems. Then, we discuss the irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids and describe a lattice Boltzmann model for simulating nanofluids. Finally, we conduct some calculations for the distribution of the suspended nanoparticles.     

Lattice approaches to packed column simulations

This work presents a review of the findings into the ability of a digitally based particle packing algorithm, called DigiPac, to predict bed structure in a variety of packed columns, for a range of generic pellet shapes frequently used in the chemical and process engineering industries. Resulting macroscopic properties are compared with experimental data derived from both invasive and non-destructive measurement techniques. Additionally, fluid velocity distributions, through samples of the resulting bed structures, are analysed using lattice Boltzmann method （LBM） simulations and are compared against experimental data from the literature.     

Forced Symmetry-Breaking of Square Lattice Planforms

Equivariant bifurcation theory has been used to study pattern formation in various physical systems modelled by E(2)-equivariant partial differential equations. The existence of spatially doubly periodic solutions with respect to the square lattice has been the focus of much research. Previous studies have considered the four- and eight-dimensional representation of the square lattice, where the symmetry of the model is perfect. Here we consider the forced symmetry-breaking of the group orbits of translation free axial planforms in the four- and eight-dimensional representations. This problem is abstracted to the study of the action of the symmetry group of the perturbation on the group orbit of solutions. A partial classification for the behaviour of the group orbits is obtained, showing the existence of heteroclinic cycles and networks between equilibria. Possible areas of application are discussed including Faraday waves and Rayleigh–Bénard convection. Subsequent studies will discuss other two- and three-dimensional lattices.     

Lattice approaches to packed column simulations

This work presents a review of the findings into the ability of a digitally based particle packing algorithm, called DigiPac, to predict bed structure in a variety of packed columns, for a range of generic pellet shapes frequently used in the chemical and process engineering industries.Resulting macroscopic properties are compared with experimental data derived from both invasive and non-destructive measurement techniques.Additionally, fluid velocity distributions, through samples of the resulting bed structures, are analysed using lattice Boltzmann method (LBM) simulations and are compared against experimental data from the literature.     

Lattice type of fracture model for concrete

Concrete is usually described as a three-phase material, where matrix, aggregate and interface zones are distinguished. The beam lattice model has been applied widely by many investigators to simulate fracture processes in concrete. Due to the extremely large computational effort, however, the beam lattice model faces practical difficulties. In our investigation, a new lattice called generalized beam (GB) lattice is developed to reduce computational effort. Numerical experiments conducted on a panel subjected to uniaxial tension show that the GB lattice model can reproduce the load–displacement curves and crack patterns in agreement to what are observed in tests. Moreover, the effects of the particle overlay on the fracture process are discussed in detail.     

Modulated Wave Trains in Lattice Differential Systems

The existence of weak sinks in mixed parabolic-lattice systems on the real line is established for systems that incorporate discrete coupling on an underlying lattice in addition to continuous diffusion. Sinks can be thought of as interfaces that separate two spatially periodic structures with different wave numbers: the corresponding modulated wave train is time periodic in the frame that moves with the speed of the interface. In this paper, the existence of weak sinks is proved that connect wave trains with almost identical wave number. The main difficulty is the global coupling between points on the underlying lattice, since its presence turns the equation solved by sinks into an ill-posed functional differential equation of mixed type.     

Lattice Boltzmann method for polymer kinetic theory

The purpose of this work is to extend the applicability of the lattice Boltzmann method (LBM) to the field of polymer kinetic theory or more generally suspensions that could be described in the Fokker–Planck formalism. This method has been, in a first time, used for gas kinetic theory, where the resolution space corresponds to the physical space coordinate. In a second time is has been generalized to be applied to fluid flow involving different behaviours: turbulence, porous media, multiphase flow, etc. However this powerful, parallel, and efficient algorithm has not been applied for solving Fokker–Planck equations widely used to describe suspension kinetic theory. In this scale, molecular models involve a high computational costs because of the multidimensionality of the fully coupled micro–macro complex flow. The originality of this work consists to apply the lattice Boltzmann technique for solving Fokker–Planck equation based on a discretization of the configuration space where the resolution coordinates correspond to the microscopic configuration space (and not the physical coordinates). The result of this work emphasizes the optimality of the used technique that, in addition to its parallel ability, gathers the simplicity of the stochastic simulation and the robustness of the traditional fixed mesh support (such as the finite element method). Accuracy and convergence of the LBM will be compared to the stochastic and the finite element techniques for homogeneous shear flow.     

Pullback Exponential Attractors for Non-autonomous Lattice Systems

We first present some sufficient conditions for the existence and the construction of a pullback exponential attractor for the continuous process (non-autonomous dynamical system) on Banach spaces and weighted spaces of infinite sequences. Then we apply our results to study the existence of pullback exponential attractors for first order non-autonomous differential equations and partly dissipative differential equations on infinite lattices with time-dependent coupled coefficients and time-dependent external terms in weighted spaces.     

Energy Transport in Stochastically Perturbed Lattice Dynamics

We consider lattice dynamics with a small stochastic perturbation of order ${\varepsilon}We consider lattice dynamics with a small stochastic perturbation of order e{\varepsilon} and prove that for a space–time scale of order e^-1{\varepsilon^{-1}} the local spectral density (Wigner function) evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain, the transport equation predicts a slow decay, as 1/?t{1/\sqrt t} , for the energy current correlation in equilibrium. This is in agreement with previous studies using a different method.     

1987 SEM Spring Conference

Experimental Techniques -     

模拟MKDV方程的格子BGK模型

目前,格子Boltzmann方法已被广泛应用于模拟各种非线性方程.文中用D1Q4模型给出MKDV方程的带修正项的BGK型格子Boltzmann法.数值模拟与理论结果吻合很好.