Particle Monte Carlo and lattice-Boltzmann methods for simulations of gas-particle flows

A numerical solution concept is presented for simulating the transport and deposition to surfaces of discrete, small (nano-)particles. The motion of single particles is calculated from the Langevin equation by Lagrangian integration under consideration of different forces such as drag force, van der Waals forces, electrical Coulomb forces and not negligible for small particles, under stochastic diffusion (Brownian diffusion). This so-called particle Monte Carlo method enables the computation of macroscopic filter properties as well the detailed resolution of the structure of the deposited particles. The flow force and the external forces depend on solutions of continuum equations, as the Navier-Stokes equations for viscous, incompressible flows or a Laplace equation of the electrical potential. Solutions of the flow and potential fields are computed here using lattice-Boltzmann methods. Essential advantage of these methods are the easy and efficient treatment of three-dimensional complex geometries, given by filter geometries or particle covered surfaces. A number of numerical improvements, as grid refinement or boundary fitting, were developed for lattice-Boltzmann methods in previous studies and applied to the present problem. The interaction between the deposited particle layer and the fluid field or the external forces is included by recomputing of these fields with changed boundaries. A number of simulation results show the influence of different effects on the particle motion and deposition.     

Benchmark computations based on lattice-Boltzmann,finite element and finite volume methods for laminar flows

The goal of this article is to contribute to the discussion of the efficiency of lattice-Boltzmann (LB) methods as CFD solvers. After a short review of the basic model and extensions, we compare the accuracy and computational efficiency of two research simulation codes based on the LB and the finite-element method (FEM) for two-dimensional incompressible laminar flow problems with complex geometries. We also study the influence of the Mach number on the solution, since LB methods are weakly compressible by nature, by comparing compressible and incompressible results obtained from the LB code and the commercial code CFX. Our results indicate, that for the quantities studied (lift, drag, pressure drop) our LB prototype is competitive for incompressible transient problems, but asymptotically slower for steady-state Stokes flow because the asymptotic algorithmic complexity of the classical LB-method is not optimal compared to the multigrid solvers incorporated in the FEM and CFX code. For the weakly compressible case, the LB approach has a significant wall clock time advantage as compared to CFX. In addition, we demonstrate that the influence of the finite Mach number in LB simulations of incompressible flow is easily underestimated.     

Finite elements in fluids: Special methods and enhanced solution techniques

As a sequel to “Finite elements in fluids: stabilized formulations and moving boundaries and interfaces” [Tezduyar TE. Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids, in press, doi:10.1016/j.compfluid.2005.02.011.], in this article we provide an overview of the special methods and enhanced solution techniques we developed in conjunction with the methods described in the accompanying paper. The methods and ideas highlighted here were introduced to increase the scope and accuracy of the stabilized formulations and interface-tracking and interface-capturing techniques highlighted in the accompanying paper. They include special methods for fluid-object interactions, for flows involving objects in fast, linear or rotational relative motion, and for two-fluid flows. They also include enhanced solutions techniques, where we have enhancement in spatial discretization, enhancement in time discretization, and enhancement in iterative solution of non-linear and linear equation systems.     

Microfluidic analysis of CO<Subscript>2</Subscript> bubble dynamics using thermal lattice-Boltzmann method

By means of microfluidic analysis with a thermal lattice-Boltzmann method, we investigated the hydrophilic, thermal and geometric effects on the dynamics of CO₂ bubbles at anode microchannels (e.g., porous layers and flow channels) of a micro-direct methanol fuel cell. The simulation results show that a more hydrophilic wall provides an additional attractive force to the aqueous methanol in the flow direction and that moves the CO₂ bubble more easily. The bubble propagates quicker in the microchannel with a positive temperature gradient imposed from the inlet to the exit, mainly due to the Marangoni effect. Regarding the geometric effect of the microchannel, the bubble moves more rapidly in a divergent microchannel than in a straight or convergent channel. On the basis of the quantitative evaluation of hydrophilic, thermal and geometric effects, we are able to design the bubble-removal technique in micro fuel cells.     

Construction,mathematical description and coding of reactive lattice-gas cellular automaton

We construct a reactive lattice-gas cellular automaton (LGCA) for reaction–diffusion systems and provide extensive discussion of its software coding aspects. The software coding aspects provide rationale for some choices in the construction of LGCA which has been inspired by molecular dynamics. Portability of the C language source code, of the data structures, and of the data formats is discussed and explained. We illustrate the ideas behind the development of LGCA and its code by considering a particular reacting system, the Sel'kov model with immobile complexing species. We demonstrate usefulness of LGCA modelling of reactive systems by presenting various simulation results. We compare these results with the standard numerical simulations of reaction–diffusion equations. We conclude the paper by discussing how LGCA methodology can be applied and extended to other contexts.     

Numerical simulations of mixtures of fluids using upwind algorithms

This study is concerned with the development of a thermodynamic model that can be used for numerical simulations of mixtures of fluids, whereby some of the mixture components cannot be accurately modeled by a thermally perfect equation of state. Upwind-type algorithms for the discretization of the inviscid fluxes are introduced in some detail, including preconditioning for low-speed problems. Results are obtained for a challenging test case involving the combustion of a liquid oxygen/gaseous hydrogen mixture at high pressure, and they compare reasonably well with experimental data.     

Calculation of the stability ratio of suspensions using Emulsion Stability Simulations

According to Emulsion Stability Simulations (ESS), the flocculation of two non-deformable drops in the primary minimum of the interaction potential, necessarily leads to their coalescence. This property is used here for the evaluation of the stability ratio (W) of solid particles, interacting with the same inter-particle potential as the one of non-deformable droplets. Two different methodologies are used. The first one consists on the repeated evaluation of the coalescence time between two particles. The second one consists on the estimation of the time required for a decrease in the number of aggregates of the dispersion equal to n₀/2 (where n₀ is the initial number of aggregates). The results of the simulations are contrasted with the stability ratio of an anionic latex suspension subject to several ionic strengths (400-1000 mM). The first methodology is far more efficient for the evaluation of W although it misses the development of the aggregates and their growth. Absolute coagulation rates (kf) can also be obtained using one N-particle simulation for the calculation of the fast flocculation rate , and several two-particle simulations for the evaluation of W. This combined procedure is also more efficient than the N-particle evaluation of .     

Simulations of pulse propagation in optical fibers using graphics processor units

Several simple cases of pulse propagation in optical fibers have been simulated using a graphics processor unit. Comparisons with simulations in a computer processor unit are also reported. Speedups from 4 to 36 have been obtained by different numerical methods, reaching a similar accuracy both in computer processor unit and in graphics processor unit, working with double-precision floating point numbers. Best results are achieved in simulations when the number of points in t grid rises. Therefore, the results indicate that graphics processor units could be a good tool to improve numerical simulations of pulse propagation in fibers.     

基于Oldroyd-B模型的弹性流体液滴动力学研究

本文采用Oldroyd-B模型对弹性流体中线串珠结构的动力学进行数学模拟。相对于牛顿流体而言,非牛顿流体液丝破裂过程非常缓慢。这种缓慢的破裂过程为流体提供了充足的时间显现一些有趣的现象,例如液滴的排泄和移动。通过主要作用力的总合近似分析液丝拉伸过程中的受力情况。弹性力在弹性液丝动力学中起重要作用,它显著阻碍了液丝从拉伸到排泄的变化过程。     

Improving mesoscale observations from satellite altimetry using bottom pressure and tide gauge measurements in the Japan Sea

In the Japan/East Sea (Sea of Japan), the basin-scale barotropic high-frequency signals cause aliasing error in the gridded sea level anomaly (SLA) product of the satellite altimeters. The aliasing errors can produce false mesoscale eddies and alter the dynamical explanation of ocean circulation. In this article, we corrected non-tidal aliasing errors in gridded SLA product using bottom pressure (BP) data and tide gauge (TG) data. The root mean square (RMS) of the aliasing induced SLA is about 3 cm in the Sea of Japan, which accounts for about 20% of the total energy. We found that, after BP correction, the percentage of error variance (PEV) is reduced from 43% to 34% for satellite-derived velocity, and from 22% to14% for 70-day low-pass filtered gridded SLA product. However, the improvement for TG correction is not notable. The basin-scale barotropic high-frequency signals are likely to be found in other nearly enclosed marginal seas. We suggested that more BP measurements should be conducted in the marginal seas for aliasing correction. The work in this article offers a useful reference for suppressing non-tidal alias errors in other marginal seas.     

Constructing and utilizing wordnets using statistical methods

Lexical databases following the wordnet paradigm capture information about words, word senses, and their relationships. A large number of existing tools and datasets are based on the original WordNet, so extending the landscape of resources aligned with WordNet leads to great potential for interoperability and to substantial synergies. Wordnets are being compiled for a considerable number of languages, however most have yet to reach a comparable level of coverage. We propose a method for automatically producing such resources for new languages based on WordNet, and analyse the implications of this approach both from a linguistic perspective as well as by considering natural language processing tasks. Our approach takes advantage of the original WordNet in conjunction with translation dictionaries. A small set of training associations is used to learn a statistical model for predicting associations between terms and senses. The associations are represented using a variety of scores that take into account structural properties as well as semantic relatedness and corpus frequency information. Although the resulting wordnets are imperfect in terms of their quality and coverage of language-specific phenomena, we show that they constitute a cheap and suitable alternative for many applications, both for monolingual tasks as well as for cross-lingual interoperability. Apart from analysing the resources directly, we conducted tests on semantic relatedness assessment and cross-lingual text classification with very promising results.     

Robust treatment of no-slip boundary condition and velocity updating for the lattice-Boltzmann simulation of particulate flows

In the past decade, the lattice-Boltzmann method (LBM) has emerged as a very useful tool in studies for the direct-numerical simulation of particulate flows. The accuracy and robustness of the LBM have been demonstrated by many researchers; however, there are several numerical problems that have not been completely resolved. One of these is the treatment of the no-slip boundary condition on the particle-fluid interface and another is the updating scheme for the particle velocity. The most common used treatment for the solid boundaries largely employs the so-called “bounce-back” method (BBM). [Ladd AJC. Numerical simulations of particulate suspensions via a discretized Boltzmann equation Part I. Theoretical foundation. J Fluid Mech (1994);271:285; Ladd AJC. Numerical simulations of particulate suspensions via a discretized Boltzmann equation Part II. Numerical results. J Fluid Mech (1994);271:311.] This often causes distortions and fluctuations of the particle shape from one time step to another. The immersed boundary method (IBM), which assigns and follows a series of points in the solid region, may be used to ensure the uniformity of particle shapes throughout the computations. To ensure that the IBM points move with the solid particles, a force density function is applied to these points. The simplest way to calculate the force density function is to use a direct-forcing scheme. In this paper, we conduct a complete study on issues related to this scheme and examine the following parameters: the generation of the forcing points; the choice of the number of forcing points and sensitivity of this choice to simulation results; and, the advantages and disadvantages associated with the IBM over the BBM. It was also observed that the commonly used velocity updating schemes cause instabilities when the densities of the fluid and the particles are close. In this paper, we present a simple and very effective velocity updating scheme that does not only facilitate the numerical solutions when the particle to fluid density ratios are close to one, but also works well for particle that are lighter than the fluid.     

Fabrication and mechanical performance of a mesoscale space-fillingtruss system

A small, lightweight, space-filling truss structure is fabricated using soft lithography in combination with electrodeposition. The truss architecture is chosen so that three-dimensionality can be achieved simply by folding a two-dimensional grid at a specific angle. The mechanical performance and structural efficiency of the truss beam are assessed under four-point bending and compared to the bending behavior of a square box beam in terms of non-dimensional indexes for stiffness, weight, and load-bearing capacity     

Simulations of gradual domain-switching in polycrystalline ferroelectrics using an optimization-based,multidomain-grain model

An optimization-based computational model is proposed to study the constrained domain switching in polycrystalline ferroelectrics composed of numerous grains, each of which consists of multiple domains. Domain switching is realized by an optimization algorithm to minimize the free energy of each grain and is thus a gradual process with applied loading. Similar to phase field modeling, no priori domain-switching criterion is imposed in the proposed model and its computational efficiency is much higher. The domain textures evolution process can also be captured. Simulation results on both tetragonal and rhombohedral PZT ceramics illustrate the efficiency of this model.     

Efficient design sensitivity analysis of incompressible fluids using SPH projection method

Using the direct differentiation method, a design sensitivity analysis method for time-dependent incompressible fluids is developed. The fluid behavior is described as the motion of particles involved by the SPH method. In the SPH projection method, instead of changing the fluid density, incompressibility is enforced by the pressure Poisson equation derived from pressure projection, which enable to use larger time steps. In spite of the additional pressure Poisson equation, the computational cost for the design sensitivity is not expensive since the factorized system matrix of pressure Poisson equation can be utilized. Aforementioned computational efficiency is very beneficial for the design sensitivity computation required for every time step in explicit time integration and updated Lagrangian schemes, for which an update scheme of design velocity field is developed using the velocity sensitivity. Through demonstrative numerical examples, the developed DSA method turns out to be efficient and shows excellent agreement with finite differencing.     

An applicability study of advanced lattice-Boltzmann techniques for moving, no-slip boundaries and local grid refinement

In this paper, two previously proposed lattice-Boltzmann techniques for no-slip boundaries and local grid refinement have been studied with the help of existing experimental and numerical data on a sedimenting sphere in a tank. These data comprise flow characteristics as well as the sedimentation trajectory and velocity of the sphere. It was found that the methods are capable of accurately describing the experimentally obtained data and show stable behaviour, even for solid-to-fluid density ratios close to one. Moreover, the proposed no-slip boundary methods produce more accurate results than the adaptive forcing technique.