Simulation of bubble motion under gravity by lattice Boltzmann method

International Nuclear Information System (INIS)

Takada, Naoki; Misawa, Masaki; Tomiyama, Akio; Hosokawa, Shigeo

2001-01-01

We describe the numerical simulation results of bubble motion under gravity by the lattice Boltzmann method (LBM), which assumes that a fluid consists of mesoscopic fluid particles repeating collision and translation and a multiphase interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. The purposes in this study are to examine the applicability of LBM to the numerical analysis of bubble motions, and to develop a three-dimensional version of the binary fluid model that introduces a free energy function. We included the buoyancy terms due to the density difference in the lattice Boltzmann equations, and simulated single-and two-bubble motions, setting flow conditions according to the Eoetvoes and Morton numbers. The two-dimensional results by LBM agree with those by the Volume of Fluid method based on the Navier-Stokes equations. The three-dimensional model possesses the surface tension satisfying the Laplace's law, and reproduces the motion of single bubble and the two-bubble interaction of their approach and coalescence in circular tube. There results prove that the buoyancy terms and the 3D model proposed here are suitable, and that LBM is useful for the numerical analysis of bubble motion under gravity. (author)

Straight velocity boundaries in the lattice Boltzmann method

Science.gov (United States)

Latt, Jonas; Chopard, Bastien; Malaspinas, Orestis; Deville, Michel; Michler, Andreas

2008-05-01

Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice boundaries which are aligned with the horizontal and vertical lattice directions. The boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes. This procedure makes it possible to compare boundary conditions on an equal footing, although they were originally derived from very different principles. It is concluded that all five boundary conditions exhibit second-order accuracy, consistent with the accuracy of the lattice Boltzmann method. The five methods are then compared numerically for accuracy and stability through benchmarks of two-dimensional and three-dimensional flows. None of the methods is found to be throughout superior to the others. Instead, the choice of a best boundary condition depends on the flow geometry, and on the desired trade-off between accuracy and stability. From the findings of the benchmarks, the boundary conditions can be classified into two major groups. The first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations. Boundary conditions in this group are found to be exceptionally accurate at low Reynolds number. Boundary conditions of the second group replace all variables on boundary nodes by new values. They exhibit generally much better numerical stability and are therefore dedicated for use in high Reynolds number flows.

Heat transport in two-dimensional materials by directly solving the phonon Boltzmann equation under Callaway's dual relaxation model

Science.gov (United States)

Guo, Yangyu; Wang, Moran

2017-10-01

The single mode relaxation time approximation has been demonstrated to greatly underestimate the lattice thermal conductivity of two-dimensional materials due to the collective effect of phonon normal scattering. Callaway's dual relaxation model represents a good approximation to the otherwise ab initio solution of the phonon Boltzmann equation. In this work we develop a discrete-ordinate-method (DOM) scheme for the numerical solution of the phonon Boltzmann equation under Callaway's model. Heat transport in a graphene ribbon with different geometries is modeled by our scheme, which produces results quite consistent with the available molecular dynamics, Monte Carlo simulations, and experimental measurements. Callaway's lattice thermal conductivity model with empirical boundary scattering rates is examined and shown to overestimate or underestimate the direct DOM solution. The length convergence of the lattice thermal conductivity of a rectangular graphene ribbon is explored and found to depend appreciably on the ribbon width, with a semiquantitative correlation provided between the convergence length and the width. Finally, we predict the existence of a phonon Knudsen minimum in a graphene ribbon only at a low system temperature and isotope concentration so that the average normal scattering rate is two orders of magnitude stronger than the intrinsic resistive one. The present work will promote not only the methodology for the solution of the phonon Boltzmann equation but also the theoretical modeling and experimental detection of hydrodynamic phonon transport in two-dimensional materials.

Regularized lattice Bhatnagar-Gross-Krook model for two- and three-dimensional cavity flow simulations.

Science.gov (United States)

Montessori, A; Falcucci, G; Prestininzi, P; La Rocca, M; Succi, S

2014-05-01

We investigate the accuracy and performance of the regularized version of the single-relaxation-time lattice Boltzmann equation for the case of two- and three-dimensional lid-driven cavities. The regularized version is shown to provide a significant gain in stability over the standard single-relaxation time, at a moderate computational overhead.

Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Delavar, Mojtaba Aghajani; Farhadi, Mousa; Sedighi, Kurosh [Faculty of Mechanical Engineering, Babol University of Technology, Babol, P.O. Box 484 (Iran)

2010-09-15

In this study Lattice Boltzmann Method (LBM) as an alternative of conventional computational fluid dynamics method is used to simulate Direct Methanol Fuel Cell (DMFC). A two dimensional lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the problem. The computational domain includes all seven parts of DMFC: anode channel, catalyst and diffusion layers, membrane and cathode channel, catalyst and diffusion layers. The model has been used to predict the flow pattern and concentration fields of different species in both clear and porous channels to investigate cell performance. The results have been compared well with results in literature for flow in porous and clear channels and cell polarization curves of the DMFC at different flow speeds and feed methanol concentrations. (author)

Lattice Boltzmann Methods to Address Fundamental Boiling and Two-Phase Problems

Energy Technology Data Exchange (ETDEWEB)

Uddin, Rizwan

2012-01-01

This report presents the progress made during the fourth (no cost extension) year of this three-year grant aimed at the development of a consistent Lattice Boltzmann formulation for boiling and two-phase flows. During the first year, a consistent LBM formulation for the simulation of a two-phase water-steam system was developed. Results of initial model validation in a range of thermo-dynamic conditions typical for Boiling Water Reactors (BWRs) were shown. Progress was made on several fronts during the second year. Most important of these included the simulation of the coalescence of two bubbles including the surface tension effects. Work during the third year focused on the development of a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model) for the 3 simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. This was reported in detail in the last progress report. Part of the efforts during the last (no-cost extension) year were focused on developing a parallel capability for the 2D as well as for the 3D codes developed in this project. This will be reported in the final report. Here we report the work carried out on testing the AILB model for conditions including the thermal effects. A simplified thermal LB model, based on the thermal energy distribution approach, was developed. The simplifications are made after neglecting the viscous heat dissipation and the work done by pressure in the original thermal energy distribution model. Details of the model are presented here, followed by a discussion of the boundary conditions, and then results for some two-phase thermal problems.

Time-independent lattice Boltzmann method calculation of hydrodynamic interactions between two particles

Science.gov (United States)

Ding, E. J.

2015-06-01

The time-independent lattice Boltzmann algorithm (TILBA) is developed to calculate the hydrodynamic interactions between two particles in a Stokes flow. The TILBA is distinguished from the traditional lattice Boltzmann method in that a background matrix (BGM) is generated prior to the calculation. The BGM, once prepared, can be reused for calculations for different scenarios, and the computational cost for each such calculation will be significantly reduced. The advantage of the TILBA is that it is easy to code and can be applied to any particle shape without complicated implementation, and the computational cost is independent of the shape of the particle. The TILBA is validated and shown to be accurate by comparing calculation results obtained from the TILBA to analytical or numerical solutions for certain problems.

Topology optimization and lattice Boltzmann methods

DEFF Research Database (Denmark)

Nørgaard, Sebastian Arlund

This thesis demonstrates the application of the lattice Boltzmann method for topology optimization problems. Specifically, the focus is on problems in which time-dependent flow dynamics have significant impact on the performance of the devices to be optimized. The thesis introduces new topology...... a discrete adjoint approach. To handle the complexity of the discrete adjoint approach more easily, a method for computing it based on automatic differentiation is introduced, which can be adapted to any lattice Boltzmann type method. For example, while it is derived in the context of an isothermal lattice...... Boltzmann model, it is shown that the method can be easily extended to a thermal model as well. Finally, the predicted behavior of an optimized design is compared to the equiva-lent prediction from a commercial finite element solver. It is found that the weakly compressible nature of the lattice Boltzmann...

The simulation of a two-dimensional (2D) transport problem in a rectangular region with Lattice Boltzmann method with two-relaxation-time

Science.gov (United States)

Sugiyanto, S.; Hardyanto, W.; Marwoto, P.

2018-03-01

Transport phenomena are found in many problems in many engineering and industrial sectors. We analyzed a Lattice Boltzmann method with Two-Relaxation Time (LTRT) collision operators for simulation of pollutant moving through the medium as a two-dimensional (2D) transport problem in a rectangular region model. This model consists of a 2D rectangular region with 54 length (x), 27 width (y), and it has isotropic homogeneous medium. Initially, the concentration is zero and is distributed evenly throughout the region of interest. A concentration of 1 is maintained at 9 < y < 18, whereas the concentration of zero is maintained at 0 < y < 9 and 18 < y < 27. A specific discharge (Darcy velocity) of 1.006 is assumed. A diffusion coefficient of 0.8333 is distributed uniformly with a uniform porosity of 0.35. A computer program is written in MATLAB to compute the concentration of pollutant at any specified place and time. The program shows that LTRT solution with quadratic equilibrium distribution functions (EDFs) and relaxation time τa=1.0 are in good agreement result with other numerical solutions methods such as 3DLEWASTE (Hybrid Three-dimensional Lagrangian-Eulerian Finite Element Model of Waste Transport Through Saturated-Unsaturated Media) obtained by Yeh and 3DFEMWATER-LHS (Three-dimensional Finite Element Model of Water Flow Through Saturated-Unsaturated Media with Latin Hypercube Sampling) obtained by Hardyanto.

Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

OpenAIRE

Song-Gui Chen; Chuan-Hu Zhang; Yun-Tian Feng; Qi-Cheng Sun; Feng Jin

2016-01-01

This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-L...

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed; Sun, Shuyu; Salama, Amgad

2013-01-01

This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed

2013-06-01

This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

The lattice Boltzmann model for the second-order Benjamin–Ono equations

International Nuclear Information System (INIS)

Lai, Huilin; Ma, Changfeng

2010-01-01

In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin–Ono equation. With the Taylor expansion and the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations

Three-dimensional coupled double-distribution-function lattice ...

Indian Academy of Sciences (India)

Ruo-Fan Qiu

2017-11-14

Nov 14, 2017 ... Abstract. Two three-dimensional (3D) lattice Boltzmann models in the framework of coupled double-distribution- function approach for compressible flows, in which specific-heat ratio and Prandtl number can be adjustable, are developed in this paper. The main differences between the two models are ...

Lattice Boltzmann simulation of flow around a confined circular cyclinder

International Nuclear Information System (INIS)

Ashrafizaadeh, M.; Zadehgol, A.

2002-01-01

A two dimensional lattice Boltzmann model (LBM) based on a single time relaxation BGK model has been developed. Several benchmark problems including the Poiseuille flow, the lid driven cavity flow and the flow around a circular cylinder have been performed employing a d2q9 lattice. The laminar flow around a circular cylinder within a channel has been extensively investigated using the present lattice Boltzmann model. Both symmetric and asymmetric placement configurations of the circular cylinder within the channel have been considered. A new treatment for the outlet velocity and pressure (density) boundary conditions has been proposed and validated. The present LBM results are in excellent agreement with those of the other existing CFD results. Careful examination of the LBM results and an appropriate calculation of the lift coefficient based on the rectangular lattice representation of the circular cylinder reveals that the periodic oscillation of the lift coefficient has a second harmonic when the cylinder is placed asymmetrically within the channel. The second harmonic could be associated with an asymmetrical shedding pattern of the vortices behind the cylinder from the upper and lower sides of the cylinder. (author)

Element Free Lattice Boltzmann Method for Fluid-Flow Problems

International Nuclear Information System (INIS)

Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung; Kwon, Young Kwon

2007-01-01

The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented

Element Free Lattice Boltzmann Method for Fluid-Flow Problems

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of); Kwon, Young Kwon [US Naval Postgraduate School, New York (United States)

2007-10-15

The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented.

Lift generation by a two-dimensional symmetric flapping wing: immersed boundary-lattice Boltzmann simulations

Energy Technology Data Exchange (ETDEWEB)

Ota, Keigo; Suzuki, Kosuke; Inamuro, Takaji, E-mail: inamuro@kuaero.kyoto-u.ac.jp [Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501 (Japan)

2012-08-01

Two-dimensional (2D) symmetric flapping flight is investigated by an immersed boundary-lattice Boltzmann method (IB-LBM). In this method, we can treat the moving boundary problem efficiently on the Cartesian grid. We consider a model consisting of 2D symmetric flapping wings without mass connected by a hinge with mass. Firstly, we investigate the effect of the Reynolds number in the range of 40-200 on flows around symmetric flapping wings under no gravity field and find that for high Reynolds numbers (Re Greater-Than-Or-Slanted-Equal-To 55), asymmetric vortices with respect to the horizontal line appear and the time-averaged lift force is induced on the wings, whereas for low Reynolds numbers (Re Less-Than-Or-Slanted-Equal-To 50), only symmetric vortices appear around the wings and no lift force is induced. Secondly, the effect of the initial position of the wings is investigated, and the range of the initial phases where the upward flight is possible is found. The effects of the mass and flapping amplitude are also studied. Finally, we carry out free flight simulations under gravity field for various Reynolds numbers in the range 60 Less-Than-Or-Slanted-Equal-To Re Less-Than-Or-Slanted-Equal-To 300 and Froude numbers in the range 3 Less-Than-Or-Slanted-Equal-To Fr Less-Than-Or-Slanted-Equal-To 60 and identify the region where upward flight is possible. (paper)

Immiscible multicomponent lattice Boltzmann model for fluids with ...

Indian Academy of Sciences (India)

College of Mechanical Engineering, Tongji University, 4800# Cao'an Road, ... was developed from a discretized fluid model known as the lattice gas automata ... of two immiscible fluids, several lattice Boltzmann (LB) models have been ...

Lattice Boltzmann model capable of mesoscopic vorticity computation

Science.gov (United States)

Peng, Cheng; Guo, Zhaoli; Wang, Lian-Ping

2017-11-01

It is well known that standard lattice Boltzmann (LB) models allow the strain-rate components to be computed mesoscopically (i.e., through the local particle distributions) and as such possess a second-order accuracy in strain rate. This is one of the appealing features of the lattice Boltzmann method (LBM) which is of only second-order accuracy in hydrodynamic velocity itself. However, no known LB model can provide the same quality for vorticity and pressure gradients. In this paper, we design a multiple-relaxation time LB model on a three-dimensional 27-discrete-velocity (D3Q27) lattice. A detailed Chapman-Enskog analysis is presented to illustrate all the necessary constraints in reproducing the isothermal Navier-Stokes equations. The remaining degrees of freedom are carefully analyzed to derive a model that accommodates mesoscopic computation of all the velocity and pressure gradients from the nonequilibrium moments. This way of vorticity calculation naturally ensures a second-order accuracy, which is also proven through an asymptotic analysis. We thus show, with enough degrees of freedom and appropriate modifications, the mesoscopic vorticity computation can be achieved in LBM. The resulting model is then validated in simulations of a three-dimensional decaying Taylor-Green flow, a lid-driven cavity flow, and a uniform flow passing a fixed sphere. Furthermore, it is shown that the mesoscopic vorticity computation can be realized even with single relaxation parameter.

A lattice Boltzmann model for the Burgers-Fisher equation.

Science.gov (United States)

Zhang, Jianying; Yan, Guangwu

2010-06-01

A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.

Convection-diffusion lattice Boltzmann scheme for irregular lattices

NARCIS (Netherlands)

Sman, van der R.G.M.; Ernst, M.H.

2000-01-01

In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the

Stabilization of the Lattice Boltzmann Method Using Information Theory

OpenAIRE

Wilson, Tyler L; Pugh, Mary; Dawson, Francis

2018-01-01

A novel Lattice Boltzmann method is derived using the Principle of Minimum Cross Entropy (MinxEnt) via the minimization of Kullback-Leibler Divergence (KLD). By carrying out the actual single step Newton-Raphson minimization (MinxEnt-LBM) a more accurate and stable Lattice Boltzmann Method can be implemented. To demonstrate this, 1D shock tube and 2D lid-driven cavity flow simulations are carried out and compared to Single Relaxation Time LBM, Two Relaxation Time LBM, Multiple Relaxation Time...

A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

Science.gov (United States)

Luo, Li-Shi

1998-01-01

A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

Two-relaxation-time lattice Boltzmann method for the anisotropic dispersive Henry problem

Science.gov (United States)

Servan-Camas, Borja; Tsai, Frank T.-C.

2010-02-01

This study develops a lattice Boltzmann method (LBM) with a two-relaxation-time collision operator (TRT) to cope with anisotropic heterogeneous hydraulic conductivity and anisotropic velocity-dependent hydrodynamic dispersion in the saltwater intrusion problem. The directional-speed-of-sound technique is further developed to address anisotropic hydraulic conductivity and dispersion tensors. Forcing terms are introduced in the LBM to correct numerical errors that arise during the recovery procedure and to describe the sink/source terms in the flow and transport equations. In order to facilitate the LBM implementation, the forcing terms are combined with the equilibrium distribution functions (EDFs) to create pseudo-EDFs. This study performs linear stability analysis and derives LBM stability domains to solve the anisotropic advection-dispersion equation. The stability domains are used to select the time step at which the lattice Boltzmann method provides stable solutions to the numerical examples. The LBM was implemented for the anisotropic dispersive Henry problem with high ratios of longitudinal to transverse dispersivities, and the results compared well to the solutions in the work of Abarca et al. (2007).

Lattice gas cellular automata and lattice Boltzmann models an introduction

CERN Document Server

Wolf-Gladrow, Dieter A

2000-01-01

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

Lattice Boltzmann simulation of droplet formation in T-junction geometries

Science.gov (United States)

Busuioc, Sergiu; Ambruş, Victor E.; Sofonea, Victor

2017-01-01

The formation of droplets in T-junction configurations is investigated using a two-dimensional Lattice Boltzmann model for liquid-vapor systems. We use an expansion of the equilibrium distribution function with respect to Hermite polynomials and an off-lattice velocity set. To evolve the distribution functions we use the second order corner transport upwind numerical scheme and a third order scheme is used to compute the gradient operators in the force term. The droplet formation successfully recovers the squeezing, dripping and jetting regimes. We find that the droplet length decreases proportionally with the flow rate of the continuous phase and increases with the flow rate of the dispersed phase in all simulation configurations and has a linear dependency on the surface tension parameter κ.

Thermal lattice Boltzmann simulation for multispecies fluid equilibration

International Nuclear Information System (INIS)

Vahala, Linda; Wah, Darren; Vahala, George; Carter, Jonathan; Pavlo, Pavol

2000-01-01

The equilibration rate for multispecies fluids is examined using thermal lattice Boltzmann simulations. Two-dimensional free-decay simulations are performed for effects of velocity shear layer turbulence on sharp temperature profiles. In particular, parameters are so chosen that the lighter species is turbulent while the heavier species is laminar--and so its vorticity layers would simply decay and diffuse in time. With species coupling, however, there is velocity equilibration followed by the final relaxation to one large co- and one large counter-rotating vortex. The temperature equilibration proceeds on a slower time scale and is in good agreement with the theoretical order of magnitude estimate of Morse [Phys. Fluids 6, 1420 (1963)]. (c) 2000 The American Physical Society

Thermal lattice Boltzmann simulation for multispecies fluid equilibration

Energy Technology Data Exchange (ETDEWEB)

Vahala, Linda [Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia 23529 (United States); Wah, Darren [Department of Physics, William and Mary College, Williamsburg, Virginia 23187 (United States); Vahala, George [Department of Physics, William and Mary College, Williamsburg, Virginia 23187 (United States); Carter, Jonathan [NERSC, Lawrence Berkeley Laboratory, Berkeley, California 97320 (United States); Pavlo, Pavol [Institute of Plasma Physics, Czech Academy of Science, Praha 8, (Czech Republic)

2000-07-01

The equilibration rate for multispecies fluids is examined using thermal lattice Boltzmann simulations. Two-dimensional free-decay simulations are performed for effects of velocity shear layer turbulence on sharp temperature profiles. In particular, parameters are so chosen that the lighter species is turbulent while the heavier species is laminar--and so its vorticity layers would simply decay and diffuse in time. With species coupling, however, there is velocity equilibration followed by the final relaxation to one large co- and one large counter-rotating vortex. The temperature equilibration proceeds on a slower time scale and is in good agreement with the theoretical order of magnitude estimate of Morse [Phys. Fluids 6, 1420 (1963)]. (c) 2000 The American Physical Society.

Lattice Boltzmann model for three-dimensional decaying homogeneous isotropic turbulence

International Nuclear Information System (INIS)

Xu Hui; Tao Wenquan; Zhang Yan

2009-01-01

We implement a lattice Boltzmann method (LBM) for decaying homogeneous isotropic turbulence based on an analogous Galerkin filter and focus on the fundamental statistical isotropic property. This regularized method is constructed based on orthogonal Hermite polynomial space. For decaying homogeneous isotropic turbulence, this regularized method can simulate the isotropic property very well. Numerical studies demonstrate that the novel regularized LBM is a promising approximation of turbulent fluid flows, which paves the way for coupling various turbulent models with LBM

Thermal equation of state for lattice Boltzmann gases

International Nuclear Information System (INIS)

Zheng, Ran

2009-01-01

The Galilean invariance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar–Gross–Krook model are proposed together with their rigorous theoretical background. From the viewpoint of group invariance, recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar–Gross–Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics

Two-dimensional numerical simulation of chimney fluidization in a granular medium using a combination of discrete element and lattice Boltzmann methods

Science.gov (United States)

Ngoma, Jeff; Philippe, Pierre; Bonelli, Stéphane; Radjaï, Farhang; Delenne, Jean-Yves

2018-05-01

We present here a numerical study dedicated to the fluidization of a submerged granular medium induced by a localized fluid injection. To this end, a two-dimensional (2D) model is used, coupling the lattice Boltzmann method (LBM) with the discrete element method (DEM) for a relevant description of fluid-grains interaction. An extensive investigation has been carried out to analyze the respective influences of the different parameters of our configuration, both geometrical (bed height, grain diameter, injection width) and physical (fluid viscosity, buoyancy). Compared to previous experimental works, the same qualitative features are recovered as regards the general phenomenology including transitory phase, stationary states, and hysteretic behavior. We also present quantitative findings about transient fluidization, for which several dimensionless quantities and scaling laws are proposed, and about the influence of the injection width, from localized to homogeneous fluidization. Finally, the impact of the present 2D geometry is discussed, by comparison to the real three-dimensional (3D) experiments, as well as the crucial role of the prevailing hydrodynamic regime within the expanding cavity, quantified through a cavity Reynolds number, that can presumably explain some substantial differences observed regarding upward expansion process of the fluidized zone when the fluid viscosity is changed.

Steady-state hydrodynamic instabilities of active liquid crystals: hybrid lattice Boltzmann simulations.

Science.gov (United States)

Marenduzzo, D; Orlandini, E; Cates, M E; Yeomans, J M

2007-09-01

We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently "extensile" rods, in the case of flow-aligning liquid crystals, and for sufficiently "contractile" ones for flow-tumbling materials. In a quasi-one-dimensional geometry, deep in the active phase of flow-aligning materials, our simulations give evidence of hysteresis and history-dependent steady states, as well as of spontaneous banded flow. Flow-tumbling materials, in contrast, rearrange themselves so that only the two boundary layers flow in steady state. Two-dimensional simulations, with periodic boundary conditions, show additional instabilities, with the spontaneous flow appearing as patterns made up of "convection rolls." These results demonstrate a remarkable richness (including dependence on anchoring conditions) in the steady-state phase behavior of active materials, even in the absence of external forcing; they have no counterpart for passive nematics. Our HLB methodology, which combines lattice Boltzmann for momentum transport with a finite difference scheme for the order parameter dynamics, offers a robust and efficient method for probing the complex hydrodynamic behavior of active nematics.

Numerical analysis of interfacial growth and deformation in horizontal stratified two-phase flow by lattice Boltzmann method

International Nuclear Information System (INIS)

Ebihara, Ken-ichi

2005-03-01

Two-phase flow is one of the important phenomena in nuclear reactors and heat exchangers at nuclear plants. It is desired for the optimum design and safe operation of such equipment to understand and predict the two-phase flow phenomenon by numerical analysis. In the present, the two-fluid model is widely used for the numerical analysis of two-phase flow. The numerical analysis method using the two-fluid model solves macroscopic hydrodynamic equations, in which fluid is regarded as continuum, with the boundary conditions at the wall, the inlet and outlet, and the interface between two phases. Since the interfacial and the wall boundary conditions utilized by this method are given as the model, such as the flow regime map and correlation, which is usually constructed on the basis of experimental results, the accuracy of the two-phase flow analysis using the two-fluid model depends on that of the utilized model or the experiment result for modeling. Tremendous progress of the computer performance and the development of new computational methods make the numerical simulation of two-phase flow with the interfacial motion possible in resent years. In such circumstances, the lattice-gas method and the lattice Boltzmann method, which represent fluid by many particles or the particle distribution function on the spatial lattice, was proposed in 1990s and these methods are applied to the numerical simulation of two-phase flow. The main feature of the two-phase fluid model of those methods is the capability of the simulation of two-phase flow without the procedure for tracking the interfacial position and shape owing to the inlet-particle potential generating the interface. Therefore it is expected that the lattice-gas method and the lattice Boltzmann method possess the predictability of the experiment by the numerical analysis of two-phase flow as well as the possibility of giving the substitute of the flow regime map and the correlation used by the two-fluid model. In this

Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

KAUST Repository

Neumann, Philipp

2012-01-01

We present simulation results of flows in the finite Knudsen range, which is in the slip and transition flow regime. Our implementations are based on the Lattice Boltzmann method and are accomplished within the Peano framework. We validate our code by solving two- and three-dimensional channel flow problems and compare our results with respective experiments from other research groups. We further apply our Lattice Boltzmann solver to the geometrical setup of a microreactor consisting of differently sized channels and a reactor chamber. Here, we apply static adaptive grids to fur-ther reduce computational costs. We further investigate the influence of using a simple BGK collision kernel in coarse grid regions which are further away from the slip boundaries. Our results are in good agreement with theory and non-adaptive simulations, demonstrating the validity and the capabilities of our adaptive simulation software for flow problems at finite Knudsen numbers.

Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions

KAUST Repository

Reis, Tim

2012-01-01

We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.

Lattice-Boltzmann Method with Dynamic Grid Refinement for Simulating Particle Deposition on a Single Fibre

Directory of Open Access Journals (Sweden)

Helmut Schomburg

2013-03-01

Full Text Available In this work a numerical approach to predict the deposition behaviour of nano-scale particles on the surface of a single fibre by resolving the resulting dendrite-like particle structures in detail is presented. The gas flow simulation is carried out by a two-dimensional Lattice-Boltzmann method, which is coupled with a Lagrangian approach for the particle motion. To decrease calculation time and system requirements the Lattice-Boltzmann model is extended to allow for local grid refinement. Because of the a priori unknown location of deposition, the simulation procedure starts on a coarse mesh which is then locally refined in a fully adaptive way in regions of accumulated particles. After each deposition the fluid flow is recalculated in order to resolve the coupling of the flow with the growing particle structures correctly. For the purpose of avoiding unphysical blocking of flow by growing particle dendrites the Lattice-Boltzmann method is extended to permeable cells in these regions using the Brinkmann equation. This extended deposition model is compared to simpler approaches, where the deposit has no retroaction on the flow or is treated as a solid structure. It is clear that the permeable model is most realistic and allows considering the particle deposition on a fibre as two-dimensional problem. Comprehensive simulations were conducted for analysing the importance of different parameters, i.e. free-stream velocity and particle diameter on the deposit structure. The results of this sensitivity analysis agree qualitatively well with former published numerical and experimental results. Finally the structure of the particle deposit was quantitatively characterised by using a modified fractal dimension.

Application of the lattice Boltzmann model to simulated stenosis growth in a two-dimensional carotid artery

International Nuclear Information System (INIS)

Boyd, J; Buick, J; Cosgrove, J A; Stansell, P

2005-01-01

The lattice Boltzmann model is used to observe changes in the velocity flow and shear stress in a carotid artery model during a simulated stenosis growth. Near wall shear stress in the unstenosed artery is found to agree with literature values. The model also shows regions of low velocity, rotational flow and low near wall shear stress along parts of the walls of the carotid artery that have been identified as being prone to atherosclerosis. These regions persist during the simulated stenosis growth, suggesting that atherosclerotic plaque build-up creates regions of flow with properties that favour atherosclerotic progression

A comparative study of lattice Boltzmann and volume of fluid method for two dimensional multiphase flows

Energy Technology Data Exchange (ETDEWEB)

Ryu, Seung Yeob [Korea Atomic Energy Research Institute (KAERI), Daejeon (Korea, Republic of); Ko, Sung Ho [Dept. of Mechanical Design Engineering, Chungnam National University, Daejeon (Korea, Republic of)

2012-08-15

The volume of fluid (VOF) model of FLUENT and the lattice Boltzmann method (LBM) are used to simulate two-phase flows. Both methods are validated for static and dynamic bubble test cases and then compared to experimental results. The VOF method does not reduce the spurious currents of the static droplet test and does not satisfy the Laplace law for small droplets at the acceptable level, as compared with the LBM. For single bubble flows, simulations are executed for various Eotvos numbers, Morton numbers and Reynolds numbers, and the results of both methods agree well with the experiments in the case of low Eotvos numbers. For high Eotvos numbers, the VOF results deviated from the experiments. For multiple bubbles, the bubble flow characteristics are related by the wake of the leading bubble. The coaxial and oblique coalescence of the bubbles are simulated successfully and the subsequent results are presented. In conclusion, the LBM performs better than the VOF method.

Axisymmetric multiphase lattice Boltzmann method for generic equations of state

NARCIS (Netherlands)

Reijers, S.A.; Gelderblom, H.; Toschi, F.

2016-01-01

We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation

On a two-relaxation-time D2Q9 lattice Boltzmann model for the Navier-Stokes equations

Science.gov (United States)

Zhao, Weifeng; Wang, Liang; Yong, Wen-An

2018-02-01

In this paper, we are concerned with the stability of some lattice kinetic schemes. First, we show that a recently proposed lattice kinetic scheme is a two-relaxation-time model different from those in the literature. Second, we analyze the stability of the model by verifying the Onsager-like relation. In addition, a necessary stability criterion for hyperbolic relaxation systems is adapted to the lattice Boltzmann method. As an application of this criterion, we find some necessary stability conditions for a previously proposed lattice kinetic scheme. Numerical experiments are conducted to validate the necessary stability conditions.

Analysis of a bubble coalescence in the multiphase lattice Boltzmann method

International Nuclear Information System (INIS)

Ryu, Seung Yeob; Park, Cheon Tae; Lee, Chung Chan; Kim, Keung Koo

2008-01-01

Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with multiphase flows, complex geometries and interfacial dynamics may be treated. To study the effect of the mobility coefficient Γ and the width of the interface layer, two stationary bubbles without a collision are considered. The gap of the two bubbles is taken as 4, while the width of the interface (w) and the mobility coefficient Γ are varied. In the present work, the lattice Boltzmann model for multiphase flows proposed by Zheng et al. is used for simulating two stationary bubbles without a collision. By adopting a finite difference gradient operator of a sufficient isotropy, the spurious currents can be made smaller. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

Three-dimensional modelling of the human carotid artery using the lattice Boltzmann method: II. Shear analysis

Energy Technology Data Exchange (ETDEWEB)

Boyd, J [Cardiovascular Research Group, Physics, University of New England, Armidale, NSW 2351 (Australia); Buick, J M [Mechanical and Design Engineering, Anglesea Building, Anglesea Road, University of Portsmouth, Portsmouth, PO1 3DJ (United Kingdom)

2008-10-21

Near-wall shear is known to be important in the pathogenesis and progression of atherosclerosis. In this paper, the shear field in a three-dimensional model of the human carotid artery is presented. The simulations are performed using the lattice Boltzmann model and are presented at six times of interest during a physiologically accurate velocity waveform. The near-wall shear rate and von Mises effective shear are also examined. Regions of low near-wall shear rates are observed near the outer wall of the bifurcation and in the lower regions of the external carotid artery. These are regions where low near-wall velocity and circulatory flows have been observed and are regions that are typically prone to atherosclerosis.

Three-dimensional modelling of the human carotid artery using the lattice Boltzmann method: II. Shear analysis

International Nuclear Information System (INIS)

Boyd, J; Buick, J M

2008-01-01

Near-wall shear is known to be important in the pathogenesis and progression of atherosclerosis. In this paper, the shear field in a three-dimensional model of the human carotid artery is presented. The simulations are performed using the lattice Boltzmann model and are presented at six times of interest during a physiologically accurate velocity waveform. The near-wall shear rate and von Mises effective shear are also examined. Regions of low near-wall shear rates are observed near the outer wall of the bifurcation and in the lower regions of the external carotid artery. These are regions where low near-wall velocity and circulatory flows have been observed and are regions that are typically prone to atherosclerosis.

Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers

KAUST Repository

Atanasov, Atanas

2016-10-17

We present an Anderson acceleration-based approach to spatially couple three-dimensional Lattice Boltzmann and Navier–Stokes (LBNS) flow simulations. This allows to locally exploit the computational features of both fluid flow solver approaches to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier–Stokes solver. We detail our coupling methodology, validate it, and study convergence and accuracy of the Anderson accelerated coupling, considering three steady-state scenarios: plane channel flow, flow around a sphere and channel flow across a porous structure. We find that the Anderson accelerated coupling yields a speed-up (in terms of iteration steps) of up to 40% in the considered scenarios, compared to strictly sequential Schwarz coupling.

Corner-transport-upwind lattice Boltzmann model for bubble cavitation

Science.gov (United States)

Sofonea, V.; Biciuşcǎ, T.; Busuioc, S.; Ambruş, Victor E.; Gonnella, G.; Lamura, A.

2018-02-01

Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann model that describes a two-dimensional (2D) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner-transport-upwind (CTU) numerical scheme on large square lattices (up to 6144 ×6144 nodes). The numerical viscosity and the regularization of the model are discussed for first- and second-order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows us to recover the solution of the 2D Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation, and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient D and the capillary number Ca is found at small Ca but with a different factor than in equilibrium liquids. A nonlinear regime is observed for Ca≳0.2 .

Two-dimensional simulation of intermediate-sized bubbles in low viscous liquids using counter diffusion lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Ryu, Seungyeob, E-mail: syryu@kaeri.re.kr [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Kim, Youngin; Kang, Hanok; Kim, Keung Koo [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Ko, Sungho, E-mail: sunghoko@cnu.ac.kr [Department of Mechanical Design Engineering, Chungnam National University, 220 Gung-dong, Yuseong-gu, Daejeon 305-764 (Korea, Republic of)

2016-08-15

Highlights: • We directly simulate intermediate-sized bubbles in low viscous liquids. • The path instability and shape oscillation can be successfully simulated. • The motion of a pair bubble and bubble swarm is presented. • Bubbles with high-Reynolds-number can be simulated with under-resolved grids. • The counter diffusion multiphase method is feasible for the direct simulation of bubbly flows. - Abstract: The counter diffusion lattice Boltzmann method (LBM) is used to simulate intermediate-sized bubbles in low viscous liquids. Bubbles at high Reynolds numbers ranging from hundreds to thousands are simulated successfully, which cannot be done for the existing LBM versions. The characteristics of the path instability of two rising bubbles are studied for a wide range of Eotvos and Morton numbers. Finally, the study presented how bubble swarms move within the flow and how the flow surrounding the bubbles is affected by the bubble motions.

Differentiated heated lid driven cavity interacting with tube: A lattice Boltzmann study

Directory of Open Access Journals (Sweden)

Bennacer Rachid

2017-01-01

Full Text Available The multiple-relaxation-time (MRT lattice-Boltzmann method is implemented to investigate combined natural and forced convection occurring in a two-dimensional square cavity. The top wall slides to the right at constant speed, while the other three remain stationary. The solution is performed for a left vertical wall at a constant temperature, which is higher than of the right wall. This yields a “cooperating” case, in which dynamic and buoyancy forces are added together. The enclosure is filled with air and contains a heat conducting circular cylinder, which is placed at various positions. The double distribution model used in lattice Boltzmann methods has been adopted to simulate the hydrodynamic and thermal fields, with the D2Q9 and D2Q5 lattices selected to perform the corresponding computations. Simulations have been conducted over a wide range of Rayleigh (Ra and Reynolds (Re numbers, and the features of dynamic and thermal fields are presented for the spectra of this mixed convection phenomenon. The flow and heat transfer characteristics of the cylinder position are described and analyzed in terms of the average Nusselt number (Nu. The computed results show the influence of the cylinder on the corresponding heat transfer in the enclosure. It has been found that the power (i.e. shear stress needed to lid the upper surface will depend on the governing parameters.

Lattice-Boltzmann simulations of droplet evaporation

KAUST Repository

Ledesma-Aguilar, Rodrigo; Vella, Dominic; Yeomans, Julia M.

2014-01-01

© the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is

Lattice-Boltzmann simulations of droplet evaporation

KAUST Repository

Ledesma-Aguilar, Rodrigo

2014-09-04

© the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is

Lattice Boltzmann method with the cell-population equilibrium

International Nuclear Information System (INIS)

Zhou Xiaoyang; Cheng Bing; Shi Baochang

2008-01-01

The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non-negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman–Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions

Lattice Boltzmann simulations of liquid crystalline fluids: active gels and blue phases

OpenAIRE

Cates, M. E.; Henrich, O.; Marenduzzo, D.; Stratford, K.

2010-01-01

Lattice Boltzmann simulations have become a method of choice to solve the hydrodynamic equations of motion of a number of complex fluids. Here we review some recent applications of lattice Boltzmann to study the hydrodynamics of liquid crystalline materials. In particular, we focus on the study of (a) the exotic blue phases of cholesteric liquid crystals, and (b) active gels - a model system for actin plus myosin solutions or bacterial suspensions. In both cases lattice Boltzmann studies have...

The Lattice Boltzmann Method applied to neutron transport

International Nuclear Information System (INIS)

Erasmus, B.; Van Heerden, F. A.

2013-01-01

In this paper the applicability of the Lattice Boltzmann Method to neutron transport is investigated. One of the main features of the Lattice Boltzmann method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. An iterative solution of the operator form of the neutron transport equation is presented here, with the first collision source as the starting point of the iteration scheme. A full description of the discretization scheme is given, along with the quadrature set used for the angular discretization. An angular refinement scheme is introduced to increase the angular coverage of the problem phase space and to mitigate lattice ray effects. The method is applied to a model problem to investigate its applicability to neutron transport and the results are compared to a reference solution calculated, using MCNP. (authors)

Modelling viscoacoustic wave propagation with the lattice Boltzmann method.

Science.gov (United States)

Xia, Muming; Wang, Shucheng; Zhou, Hui; Shan, Xiaowen; Chen, Hanming; Li, Qingqing; Zhang, Qingchen

2017-08-31

In this paper, the lattice Boltzmann method (LBM) is employed to simulate wave propagation in viscous media. LBM is a kind of microscopic method for modelling waves through tracking the evolution states of a large number of discrete particles. By choosing different relaxation times in LBM experiments and using spectrum ratio method, we can reveal the relationship between the quality factor Q and the parameter τ in LBM. A two-dimensional (2D) homogeneous model and a two-layered model are tested in the numerical experiments, and the LBM results are compared against the reference solution of the viscoacoustic equations based on the Kelvin-Voigt model calculated by finite difference method (FDM). The wavefields and amplitude spectra obtained by LBM coincide with those by FDM, which demonstrates the capability of the LBM with one relaxation time. The new scheme is relatively simple and efficient to implement compared with the traditional lattice methods. In addition, through a mass of experiments, we find that the relaxation time of LBM has a quantitative relationship with Q. Such a novel scheme offers an alternative forward modelling kernel for seismic inversion and a new model to describe the underground media.

From Pore Scale to Turbulent Flow with the Unstructured Lattice Boltzmann Method

DEFF Research Database (Denmark)

Matin, Rastin

Abstract: The lattice Boltzmann method is a class of methods in computational fluid dynamics for simulating fluid flow. Implementations on unstructured grids are particularly relevant for various engineering applications, where geometric flexibility or high resolution near a body or a wall...... is required. The main topic of this thesis is to further develop unstructured lattice Boltzmann methods for simulations of Newtonian fluid flow in three dimensions, in particular porous flow. Two methods are considered in this thesis based on the finite volume method and finite element method, respectively...

Simulating colloid hydrodynamics with lattice Boltzmann methods

International Nuclear Information System (INIS)

Cates, M E; Stratford, K; Adhikari, R; Stansell, P; Desplat, J-C; Pagonabarraga, I; Wagner, A J

2004-01-01

We present a progress report on our work on lattice Boltzmann methods for colloidal suspensions. We focus on the treatment of colloidal particles in binary solvents and on the inclusion of thermal noise. For a benchmark problem of colloids sedimenting and becoming trapped by capillary forces at a horizontal interface between two fluids, we discuss the criteria for parameter selection, and address the inevitable compromise between computational resources and simulation accuracy

Hybrid lattice Boltzmann finite difference simulation of mixed convection flows in a lid-driven square cavity

Energy Technology Data Exchange (ETDEWEB)

Bettaibi, Soufiene, E-mail: Bettaibisoufiene@gmail.com [UR: Rayonnement Thermique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis (Tunisia); Kuznik, Frédéric [INSA-Lyon, CETHIL, F-69621 Villeurbanne (France); Université de Lyon, CNRS, UMR5008, F-69622 Villeurbanne (France); Sediki, Ezeddine [UR: Rayonnement Thermique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis (Tunisia)

2014-06-27

Highlights: • Mixed convection heat transfer in 2D lid-driven cavity is studied numerically. • Hybrid scheme with multiple relaxation time lattice Boltzmann method is used to obtain the velocity field. • Finite difference method is used to compute the temperature. • Effect of both Richardson and Reynolds numbers for mixed convection is studied. - Abstract: Mixed convection heat transfer in two-dimensional lid-driven rectangular cavity filled with air (Pr=0.71) is studied numerically. A hybrid scheme with multiple relaxation time lattice Boltzmann method (MRT-LBM) is used to obtain the velocity field while the temperature field is deduced from energy balance equation by using the finite difference method (FDM). The main objective of this work is to investigate the model effectiveness for mixed convection flow simulation. Results are presented in terms of streamlines, isotherms and Nusselt numbers. Excellent agreement is obtained between our results and previous works. The different comparisons demonstrate the robustness and the accuracy of our proposed approach.

Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio.

Science.gov (United States)

Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

2016-10-01

A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.

Maxwell iteration for the lattice Boltzmann method with diffusive scaling

Science.gov (United States)

Zhao, Weifeng; Yong, Wen-An

2017-03-01

In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

Numerical simulations of a family of the coupled viscous Burgers, equation using the lattice Boltzmann method

International Nuclear Information System (INIS)

He, Y B; Tang, X H

2016-01-01

In this paper, in order to extend the lattice Boltzmann method (LBM) to deal with more nonlinear systems, a one-dimensional and five-velocity lattice Boltzmann scheme with an amending function for a family of the coupled viscous Burgers’ equation (CVBE) is proposed. With the Taylor and Chapman–Enskog expansion, a family of the CVBE is recovered correctly from the lattice Boltzmann equation through selecting the equilibrium distribution functions and amending functions properly. The method is applied to some test examples with an analytical solution. The results are compared with those obtained by the finite difference method (FDM); it is shown that the numerical solutions agree well with the analytical solutions and the errors obtained by the present method are smaller than the FDM. Furthermore, some problems without analytical solutions are numerically studied by the present method and the FDM. The results show that the numerical solutions of the LBM are in good agreement with those obtained by the FDM, which can validate the effectiveness and stability of the LBM. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

Three-dimensional modelling of the human carotid artery using the lattice Boltzmann method: I. Model and velocity analysis

Energy Technology Data Exchange (ETDEWEB)

Boyd, J [Cardiovascular Research Group Physics, University of New England, Armidale, NSW 2351 (Australia); Buick, J M [Department of Mechanical and Design Engineering, University of Portsmouth, Anglesea Building, Anglesea Road, Portsmouth PO1 3DJ (United Kingdom)

2008-10-21

Numerical modelling is a powerful tool in the investigation of human blood flow and arterial diseases such as atherosclerosis. It is known that near wall velocity and shear are important in the pathogenesis and progression of atherosclerosis. In this paper results for a simulation of blood flow in a three-dimensional carotid artery geometry using the lattice Boltzmann method are presented. The velocity fields in the body of the fluid are analysed at six times of interest during a physiologically accurate velocity waveform. It is found that the three-dimensional model agrees well with previous literature results for carotid artery flow. Regions of low near wall velocity and circulatory flow are observed near the outer wall of the bifurcation and in the lower regions of the external carotid artery, which are regions that are typically prone to atherosclerosis.

Three-dimensional modelling of the human carotid artery using the lattice Boltzmann method: I. Model and velocity analysis

International Nuclear Information System (INIS)

Boyd, J; Buick, J M

2008-01-01

Numerical modelling is a powerful tool in the investigation of human blood flow and arterial diseases such as atherosclerosis. It is known that near wall velocity and shear are important in the pathogenesis and progression of atherosclerosis. In this paper results for a simulation of blood flow in a three-dimensional carotid artery geometry using the lattice Boltzmann method are presented. The velocity fields in the body of the fluid are analysed at six times of interest during a physiologically accurate velocity waveform. It is found that the three-dimensional model agrees well with previous literature results for carotid artery flow. Regions of low near wall velocity and circulatory flow are observed near the outer wall of the bifurcation and in the lower regions of the external carotid artery, which are regions that are typically prone to atherosclerosis.

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

Science.gov (United States)

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Diffusion on unstructured triangular grids using Lattice Boltzmann

NARCIS (Netherlands)

Sman, van der R.G.M.

2004-01-01

In this paper, we present a Lattice Boltzmann scheme for diffusion on unstructured triangular grids. In this formulation there is no need for interpolation, as is required in other LB schemes on irregular grids. At the end of the propagation step, the lattice gas particles arrive exactly at

Lattice-Boltzmann scheme for natural convection in porous media

NARCIS (Netherlands)

Sman, van der R.G.M.

1997-01-01

A lattice-Boltzmann scheme for natural convection in porous media is developed and applied to the heat transfer problem of a 1000 kg potato packaging. The scheme has features new to the field of LB schemes. It is mapped on a orthorhombic lattice instead of the traditional cubic lattice. Furthermore

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

International Nuclear Information System (INIS)

Lin-Jie, Chen; Chang-Feng, Ma

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)

Lattice Boltzmann scheme for diffusion on triangular grids

NARCIS (Netherlands)

Sman, van der R.G.M.

2003-01-01

In this paper we present a Lattice Boltzmann scheme for diffusion on it unstructured triangular grids. In this formulation of a LB for irregular grids there is no need for interpolation, which is required in other LB schemes on irregular grids. At the end of the propagation step the lattice gas

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

Science.gov (United States)

Español, Malena I; Golovaty, Dmitry; Wilber, J Patrick

2018-01-01

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Zhen Chen

2017-03-01

Full Text Available An unconditionally stable thermal lattice Boltzmann method (USTLBM is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE through Chapman–Enskog (C-E expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM. Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio

International Nuclear Information System (INIS)

Shan Ming-Lei; Zhu Chang-Ping; Yao Cheng; Yin Cheng; Jiang Xiao-Yan

2016-01-01

The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multi-relaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling. (paper)

Magnetic nanoparticles in fluid environment: combining molecular dynamics and Lattice-Boltzmann

Energy Technology Data Exchange (ETDEWEB)

Melenev, Petr, E-mail: melenev@icmm.ru [Ural Federal University, 4, Turgeneva str., 620000 Ekaterinburg (Russian Federation); Institute of Continuous Media Mechanics, 1, Koroleva str., 614013 Perm (Russian Federation)

2017-06-01

Hydrodynamic interactions between magnetic nanoparticles suspended in the Newtonian liquid are accounted for using a combination of the lattice Boltzmann method and molecular dynamics simulations. Nanoparticle is modelled by the system of molecular dynamics material points (which form structure resembles raspberry) coupled to the lattice Boltzmann fluid. The hydrodynamic coupling between the colloids is studied by simulations of the thermo-induced rotational diffusion of two raspberry objects. It was found that for the considered range of model parameters the approaching of the raspberries leads to slight retard of the relaxation process. The presence of the weak magnetic dipolar interaction between the objects leads to modest decrease of the relaxation time and the extent of the acceleration of the diffusion is intensified along with magnetic forces. - Highlights: • The combination of molecular dynamics and lattice Boltzmann method is utilized for the reveal of the role of hydrodynamic interaction in rotational dynamics of colloid particles. • The verification of the model parameters is done based on the comparison with the results of Langevin dynamics. • For the task of free rotational diffusion of the pair of colloid particles the influence of the hydrodynamic interactions on the relaxation time is examined in the case of nonmagnetic particles and at the presence of weak dipolar interaction.

A mass-conserving multiphase lattice Boltzmann model for simulation of multiphase flows

Science.gov (United States)

Niu, Xiao-Dong; Li, You; Ma, Yi-Ren; Chen, Mu-Feng; Li, Xiang; Li, Qiao-Zhong

2018-01-01

In this study, a mass-conserving multiphase lattice Boltzmann (LB) model is proposed for simulating the multiphase flows. The proposed model developed in the present study is to improve the model of Shao et al. ["Free-energy-based lattice Boltzmann model for simulation of multiphase flows with density contrast," Phys. Rev. E 89, 033309 (2014)] by introducing a mass correction term in the lattice Boltzmann model for the interface. The model of Shao et al. [(the improved Zheng-Shu-Chew (Z-S-C model)] correctly considers the effect of the local density variation in momentum equation and has an obvious improvement over the Zheng-Shu-Chew (Z-S-C) model ["A lattice Boltzmann model for multiphase flows with large density ratio," J. Comput. Phys. 218(1), 353-371 (2006)] in terms of solution accuracy. However, due to the physical diffusion and numerical dissipation, the total mass of each fluid phase cannot be conserved correctly. To solve this problem, a mass correction term, which is similar to the one proposed by Wang et al. ["A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio," J. Comput. Phys. 290, 336-351 (2015)], is introduced into the lattice Boltzmann equation for the interface to compensate the mass losses or offset the mass increase. Meanwhile, to implement the wetting boundary condition and the contact angle, a geometric formulation and a local force are incorporated into the present mass-conserving LB model. The proposed model is validated by verifying the Laplace law, simulating both one and two aligned droplets splashing onto a liquid film, droplets standing on an ideal wall, droplets with different wettability splashing onto smooth wax, and bubbles rising under buoyancy. Numerical results show that the proposed model can correctly simulate multiphase flows. It was found that the mass is well-conserved in all cases considered by the model developed in the present study. The developed

Galilean-Invariant Lattice-Boltzmann Models with H Theorem

National Research Council Canada - National Science Library

Boghosian, Bruce

2003-01-01

The authors demonstrate that the requirement of Galilean invariance determines the choice of H function for a wide class of entropic lattice-Boltzmann models for the incompressible Navier-Stokes equations...

On some classes of two-dimensional local models in discrete two-dimensional monatomic FPU lattice with cubic and quartic potential

International Nuclear Information System (INIS)

Quan, Xu; Qiang, Tian

2009-01-01

This paper discusses the two-dimensional discrete monatomic Fermi–Pasta–Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather. (condensed matter: structure, thermal and mechanical properties)

Lattice Boltzmann methods for moving boundary flows

International Nuclear Information System (INIS)

Inamuro, Takaji

2012-01-01

The lattice Boltzmann methods (LBMs) for moving boundary flows are presented. The LBM for two-phase fluid flows with the same density and the LBM combined with the immersed boundary method are described. In addition, the LBM on a moving multi-block grid is explained. Three numerical examples (a droplet moving in a constricted tube, the lift generation of a flapping wing and the sedimentation of an elliptical cylinder) are shown in order to demonstrate the applicability of the LBMs to moving boundary problems. (invited review)

Lattice Boltzmann methods for moving boundary flows

Energy Technology Data Exchange (ETDEWEB)

Inamuro, Takaji, E-mail: inamuro@kuaero.kyoto-u.ac.jp [Department of Aeronautics and Astronautics, and Advanced Research Institute of Fluid Science and Engineering, Graduate School of Engineering, Kyoto University, Kyoto 606-8501 (Japan)

2012-04-01

The lattice Boltzmann methods (LBMs) for moving boundary flows are presented. The LBM for two-phase fluid flows with the same density and the LBM combined with the immersed boundary method are described. In addition, the LBM on a moving multi-block grid is explained. Three numerical examples (a droplet moving in a constricted tube, the lift generation of a flapping wing and the sedimentation of an elliptical cylinder) are shown in order to demonstrate the applicability of the LBMs to moving boundary problems. (invited review)

Thermal conduction in classical low-dimensional lattices

International Nuclear Information System (INIS)

Lepri, Stefano; Livi, Roberto; Politi, Antonio

2003-01-01

Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to simple mathematical models consisting of coupled oscillators on a lattice. The role of lattice dimensionality on the breakdown of the Fourier's law is discussed and some universal quantitative aspects are emphasized: the divergence of the finite-size thermal conductivity is characterized by universal laws in one and two dimensions. Equilibrium and non-equilibrium molecular dynamics methods are presented along with a critical survey of previous numerical results. Analytical results for the non-equilibrium dynamics can be obtained in the harmonic chain where the role of disorder and localization can be also understood. The traditional kinetic approach, based on the Boltzmann-Peierls equation is also briefly sketched with reference to one-dimensional chains. Simple toy models can be defined in which the conductivity is finite. Anomalous transport in integrable non-linear systems is briefly discussed. Finally, possible future research themes are outlined

Lattice Boltzmann methods for global linear instability analysis

Science.gov (United States)

Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis

2017-12-01

Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

Numerical Study of Single Bubble Growth on and Departure from a Horizontal Superheated Wall by Three-dimensional Lattice Boltzmann Method

Science.gov (United States)

Feng, Yuan; Li, Hui-Xiong; Guo, Kai-Kai; Zhao, Jian-Fu; Wang, Tai

2018-05-01

A three-dimensional hybrid lattice Boltzmann method was used to simulate the progress of a single bubble's growth and departure from a horizontal superheated wall. The evolutionary process of the bubble shapes and also the temperature fields during pool nucleate boiling were obtained and the influence of the gravitational acceleration on the bubble departure diameter (BDD), the bubble release frequency (BRF) and the heat flux on the superheated wall was analyzed. The simulation results obtained by the present three-dimensional numerical studies demonstrate that the BDD is proportional to g^{-0.301}, the BRF is proportional to g^{-0.58}, and the averaged wall heat flux is proportional to g^{0.201}, where g is the gravitational acceleration. These results are in good agreement with the common-used experimental correlations, indicating the rationality of the present numerical model and results.

Second order bounce back boundary condition for the lattice Boltzmann fluid simulation

International Nuclear Information System (INIS)

Kim, In Chan

2000-01-01

A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

International Nuclear Information System (INIS)

Butt, Imran A; Wattis, Jonathan A D

2006-01-01

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2 + 1)-dimensional cubic nonlinear Schroedinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalized (2 + 1)-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does not go to zero with the amplitude; we find that the energy threshold is maximized by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

Multispeed Lattice Boltzmann Model with Space-Filling Lattice for Transcritical Shallow Water Flows

Directory of Open Access Journals (Sweden)

Y. Peng

2017-01-01

Full Text Available Inspired by the recent success of applying multispeed lattice Boltzmann models with a non-space-filling lattice for simulating transcritical shallow water flows, the capabilities of their space-filling counterpart are investigated in this work. Firstly, two lattice models with five integer discrete velocities are derived by using the method of matching hydrodynamics moments and then tested with two typical 1D problems including the dam-break flow over flat bed and the steady flow over bump. In simulations, the derived space-filling multispeed models, together with the stream-collision scheme, demonstrate better capability in simulating flows with finite Froude number. However, the performance is worse than the non-space-filling model solved by finite difference scheme. The stream-collision scheme with second-order accuracy may be the reason since a numerical scheme with second-order accuracy is prone to numerical oscillations at discontinuities, which is worthwhile for further study.

A lattice based solution of the collisional Boltzmann equation with applications to microchannel flows

International Nuclear Information System (INIS)

Green, B I; Vedula, Prakash

2013-01-01

An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework. (paper)

Lattice Boltzmann methods for complex micro-flows: applicability and limitations for practical applications

Energy Technology Data Exchange (ETDEWEB)

Suga, K, E-mail: suga@me.osakafu-u.ac.jp [Department of Mechanical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 (Japan)

2013-06-15

The extensive evaluation studies of the lattice Boltzmann method for micro-scale flows ({mu}-flow LBM) by the author's group are summarized. For the two-dimensional test cases, force-driven Poiseuille flows, Couette flows, a combined nanochannel flow, and flows in a nanochannel with a square- or triangular cylinder are discussed. The three-dimensional (3D) test cases are nano-mesh flows and a flow between 3D bumpy walls. The reference data for the complex test flow geometries are from the molecular dynamics simulations of the Lennard-Jones fluid by the author's group. The focused flows are mainly in the slip and a part of the transitional flow regimes at Kn < 1. The evaluated schemes of the {mu}-flow LBMs are the lattice Bhatnagar-Gross-Krook and the multiple-relaxation time LBMs with several boundary conditions and discrete velocity models. The effects of the discrete velocity models, the wall boundary conditions, the near-wall correction models of the molecular mean free path and the regularization process are discussed to confirm the applicability and the limitations of the {mu}-flow LBMs for complex flow geometries. (invited review)

Lattice Boltzmann methods for complex micro-flows: applicability and limitations for practical applications

International Nuclear Information System (INIS)

Suga, K

2013-01-01

The extensive evaluation studies of the lattice Boltzmann method for micro-scale flows (μ-flow LBM) by the author's group are summarized. For the two-dimensional test cases, force-driven Poiseuille flows, Couette flows, a combined nanochannel flow, and flows in a nanochannel with a square- or triangular cylinder are discussed. The three-dimensional (3D) test cases are nano-mesh flows and a flow between 3D bumpy walls. The reference data for the complex test flow geometries are from the molecular dynamics simulations of the Lennard-Jones fluid by the author's group. The focused flows are mainly in the slip and a part of the transitional flow regimes at Kn < 1. The evaluated schemes of the μ-flow LBMs are the lattice Bhatnagar–Gross–Krook and the multiple-relaxation time LBMs with several boundary conditions and discrete velocity models. The effects of the discrete velocity models, the wall boundary conditions, the near-wall correction models of the molecular mean free path and the regularization process are discussed to confirm the applicability and the limitations of the μ-flow LBMs for complex flow geometries. (invited review)

Saddle-points of a two dimensional random lattice theory

International Nuclear Information System (INIS)

Pertermann, D.

1985-07-01

A two dimensional random lattice theory with a free massless scalar field is considered. We analyse the field theoretic generating functional for any given choice of positions of the lattice sites. Asking for saddle-points of this generating functional with respect to the positions we find the hexagonal lattice and a triangulated version of the hypercubic lattice as candidates. The investigation of the neighbourhood of a single lattice site yields triangulated rectangles and regular polygons extremizing the above generating functional on the local level. (author)

Lattice Boltzmann model for numerical relativity.

Science.gov (United States)

Ilseven, E; Mendoza, M

2016-02-01

In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik [Pusan National University, Busan (Korea, Republic of); Jeong, Hae Kwon [POSCO, Pohang (Korea, Republic of); Balachandar, S. [University of Florida, Florida (United States)

2013-02-15

We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

International Nuclear Information System (INIS)

Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik; Jeong, Hae Kwon; Balachandar, S.

2013-01-01

We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

Lattice Boltzmann Approach to Resistive MHD

Czech Academy of Sciences Publication Activity Database

Macnab, A.; Vahala, G.; Vahala, L.; Pavlo, Pavol; Soe, M.

2002-01-01

Roč. 47, č. 9 (2002), s. 51 ISSN 0003-0503. [Annual Meeting of the Division of Plasma Physics of the American Physical Society/44th./. Orlando , Florida, 11.11.2001-15.11.2001] R&D Projects: GA ČR GA202/00/1216 Institutional research plan: CEZ:AV0Z2043910 Keywords : Lattice Boltzmann, magnetic fields Subject RIV: BL - Plasma and Gas Discharge Physics

Many electron variational ground state of the two dimensional Anderson lattice

International Nuclear Information System (INIS)

Zhou, Y.; Bowen, S.P.; Mancini, J.D.

1991-02-01

A variational upper bound of the ground state energy of two dimensional finite Anderson lattices is determined as a function of lattice size (up to 16 x 16). Two different sets of many-electron basis vectors are used to determine the ground state for all values of the coulomb integral U. This variational scheme has been successfully tested for one dimensional models and should give good estimates in two dimensions

Adjoint Parameter Sensitivity Analysis for the Hydrodynamic Lattice Boltzmann Method with Applications to Design Optimization

DEFF Research Database (Denmark)

Pingen, Georg; Evgrafov, Anton; Maute, Kurt

2009-01-01

We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion...

Lattice Boltzmann method for weakly ionized isothermal plasmas

International Nuclear Information System (INIS)

Li Huayu; Ki, Hyungson

2007-01-01

In this paper, a lattice Boltzmann method (LBM) for weakly ionized isothermal plasmas is presented by introducing a rescaling scheme for the Boltzmann transport equation. Without using this rescaling, we found that the nondimensional relaxation time used in the LBM is too large and the LBM does not produce physically realistic results. The developed model was applied to the electrostatic wave problem and the diffusion process of singly ionized helium plasmas with a 1-3% degree of ionization under an electric field. The obtained results agree well with theoretical values

Lattice Boltzmann equation calculation of internal, pressure-driven turbulent flow

International Nuclear Information System (INIS)

Hammond, L A; Halliday, I; Care, C M; Stevens, A

2002-01-01

We describe a mixing-length extension of the lattice Boltzmann approach to the simulation of an incompressible liquid in turbulent flow. The method uses a simple, adaptable, closure algorithm to bound the lattice Boltzmann fluid incorporating a law-of-the-wall. The test application, of an internal, pressure-driven and smooth duct flow, recovers correct velocity profiles for Reynolds number to 1.25 x 10 5 . In addition, the Reynolds number dependence of the friction factor in the smooth-wall branch of the Moody chart is correctly recovered. The method promises a straightforward extension to other curves of the Moody chart and to cylindrical pipe flow

Lattice Boltzmann methods applied to large-scale three-dimensional virtual cores constructed from digital optical borehole images of the karst carbonate Biscayne aquifer in southeastern Florida

Science.gov (United States)

Sukop, Michael C.; Cunningham, Kevin J.

2014-11-01

Digital optical borehole images at approximately 2 mm vertical resolution and borehole caliper data were used to create three-dimensional renderings of the distribution of (1) matrix porosity and (2) vuggy megaporosity for the karst carbonate Biscayne aquifer in southeastern Florida. The renderings based on the borehole data were used as input into Lattice Boltzmann methods to obtain intrinsic permeability estimates for this extremely transmissive aquifer, where traditional aquifer test methods may fail due to very small drawdowns and non-Darcian flow that can reduce apparent hydraulic conductivity. Variogram analysis of the borehole data suggests a nearly isotropic rock structure at lag lengths up to the nominal borehole diameter. A strong correlation between the diameter of the borehole and the presence of vuggy megaporosity in the data set led to a bias in the variogram where the computed horizontal spatial autocorrelation is strong at lag distances greater than the nominal borehole size. Lattice Boltzmann simulation of flow across a 0.4 × 0.4 × 17 m (2.72 m3 volume) parallel-walled column of rendered matrix and vuggy megaporosity indicates a high hydraulic conductivity of 53 m s-1. This value is similar to previous Lattice Boltzmann calculations of hydraulic conductivity in smaller limestone samples of the Biscayne aquifer. The development of simulation methods that reproduce dual-porosity systems with higher resolution and fidelity and that consider flow through horizontally longer renderings could provide improved estimates of the hydraulic conductivity and help to address questions about the importance of scale.

An optimized D2Q37 Lattice Boltzmann code on GP-GPUs

NARCIS (Netherlands)

Biferale, L.; Mantovani, F.; Pivanti, M.; Pozzati, F.; Sbragaglia, M.; Scagliarini, Andrea; Schifano, S.F.; Toschi, F.

2013-01-01

We describe the implementation of a thermal compressible Lattice Boltzmann algorithm on an NVIDIA Tesla C2050 system based on the Fermi GP-GPU. We consider two different versions, including and not including reactive effects. We describe the overall organization of the algorithm and give details on

A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects

NARCIS (Netherlands)

Kamali, M.R.

2013-01-01

The aim of the present research was to explore the promises and shift the limits of the numerical framework of lattice Boltzmann (LB) for studying the physics behind multi-component two-phase heterogeneous non-isothermal reactive flows under industrial conditions. An example of such an industrially

Simple Navier’s slip boundary condition for the non-Newtonian Lattice Boltzmann fluid dynamics solver

DEFF Research Database (Denmark)

Svec, Oldrich; Skoček, Jan

2013-01-01

The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary condition...

Contact angle determination in multicomponent lattice Boltzmann simultations

NARCIS (Netherlands)

Schmieschek, S.M.P.; Harting, J.D.R.

2011-01-01

Droplets on hydrophobic surfaces are ubiquitous in microfluidic applications and there exists a number of commonly used multicomponent and multiphase lattice Boltzmann schemes to study such systems. In this paper we focus on a popular implementation of a multicomponent model as introduced by Shan

MRT Lattice Boltzmann schemes for confined suspension flows

NARCIS (Netherlands)

Sman, van der R.G.M.

2010-01-01

We introduce a novel multiple-relaxation time (modified MRT) Lattice Boltzmann scheme for simulation of confined suspension flow. Via careful tuning of the free eigenvalues of the collision operator we can substantially reduce the error in the so-called hydrodynamic radius. Its performance has been

Axisymmetric Lattice Boltzmann Model of Droplet Impact on Solid Surfaces

Science.gov (United States)

Dalgamoni, Hussein; Yong, Xin

2017-11-01

Droplet impact is a ubiquitous fluid phenomena encountered in scientific and engineering applications such as ink-jet printing, coating, electronics manufacturing, and many others. It is of great technological importance to understand the detailed dynamics of drop impact on various surfaces. The lattice Boltzmann method (LBM) emerges as an efficient method for modeling complex fluid systems involving rapidly evolving fluid-fluid and fluid-solid interfaces with complex geometries. In this work, we model droplet impact on flat solid substrates with well-defined wetting behavior using a two-phase axisymmetric LBM with high density and viscosity contrasts. We extend the two-dimensional Lee and Liu model to capture axisymmetric effect in the normal impact. First we compare the 2D axisymmetric results with the 2D and 3D results reported by Lee and Liu to probe the effect of axisymmetric terms. Then, we explore the effects of Weber number, Ohnesorge number, and droplet-surface equilibrium contact angle on the impact. The dynamic contact angle and spreading factor of the droplet during impact are investigated to qualitatively characterize the impact dynamics.

Harmonically trapped dipolar fermions in a two-dimensional square lattice

DEFF Research Database (Denmark)

Larsen, Anne-Louise G.; Bruun, Georg

2012-01-01

We consider dipolar fermions in a two-dimensional square lattice and a harmonic trapping potential. The anisotropy of the dipolar interaction combined with the lattice leads to transitions between phases with density order of different symmetries. We show that the attractive part of the dipolar...

Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

Directory of Open Access Journals (Sweden)

Song-Gui Chen

2016-01-01

Full Text Available This paper presents a three-dimensional (3D parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re and Bingham number (Bn. These results reveal the flow behavior of Bingham plastics.

Lattice Boltzmann simulations of three-dimensional incompressible flows in a four-sided lid driven cavity

Energy Technology Data Exchange (ETDEWEB)

Li, Cheng Gong [National Engineering Laboratory for MTO, Dalian National Laboratory for Clean Energy, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, 457 Zhongshan Road, Dalian 116023 (China); Maa, Jerome P-Y, E-mail: chenggongli@dicp.ac.cn [Virginia Institute of Marine Science, College of William and Mary, Gloucester Point, VA 23062 (United States)

2017-04-15

Numerical study on three-dimensional (3D), incompressible, four-sided lid (FSL) driven cavity flows has been conducted to show the effects of the transverse aspect ratio, K , on the flow field by using a multiple relaxation time lattice Boltzmann equation. The top wall is driven from left to right, the left wall is moved downward, whereas the right wall is driven upward, and the bottom wall is moved from right to left, all the four moving walls have the same speed and the others boundaries are fixed. Numerical computations are performed for several Reynolds numbers for laminar flows, up to 1000, with various transverse aspect ratios. The flow can reach a steady state and the flow pattern is symmetric with respect to the two cavity diagonals (i.e., the center of the cavity). At Reynolds number = 300, the flow structures of the 3D FSL cavity flow at steady state with various transverse aspect ratio, i.e., 3, 2, 1, 0.75, 0.5 and 0.25 only show the unstable symmetrical flow pattern. The stable asymmetrical flow pattern could be reproduced only by increasing the Reynolds number that is above a critical value which is dependent on the aspect ratio. It is found that an aspect ratio of more than 5 is needed to reproduce flow patterns, both symmetric and asymmetric flows, simulated by using 2D numerical models. (paper)

Lattice Boltzmann model for three-phase viscoelastic fluid flow

Science.gov (United States)

Xie, Chiyu; Lei, Wenhai; Wang, Moran

2018-02-01

A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

Analysis of transport of collimated radiation in a participating media using the lattice Boltzmann method

International Nuclear Information System (INIS)

Mishra, Subhash C.; Vernekar, Rohan Ranganath

2012-01-01

Application of the lattice Boltzmann method (LBM) recently proposed by Asinari et al. [Asinari P, Mishra SC, Borchiellini R. A lattice Boltzmann formulation to the analysis of radiative heat transfer problems in a participating medium. Numer Heat Transfer B 2010; 57:126–146] is extended to the analysis of transport of collimated radiation in a planar participating medium. To deal with azimuthally symmetric radiation in planar medium, a new lattice structure for the LBM is used. The transport of the collimated component in the medium is analysed by two different, viz., flux splitting and direct approaches. For different angles of incidence of the collimated radiation, the LBM formulation is tested for the effects of the extinction coefficient, the anisotropy factor, and the boundary emissivities on heat flux and emissive power distributions. Results are compared with the benchmark results obtained using the finite volume method. Both the approaches in LBM provide accurate results. -- Highlights: ► Transport of collimated radiation in participating media is studied. ► Usage of Lattice Boltzmann method (LBM) is extended in this study. ► In LBM, flux splitting and direct approaches are proposed. ► Effects of various parameters are studied on heat flux and temperature profiles. ► In all cases, LBM provides correct results.

Lattice Boltzmann simulations of sound directivity of a cylindrical pipe with mean flow

International Nuclear Information System (INIS)

Shi, Yong; Scavone, Gary P; Silva, Andrey R da

2013-01-01

This paper proposes a numerical scheme based on the lattice Boltzmann method to tackle the classical problem of sound radiation directivity of pipes issuing subsonic mean flows. The investigation is focused on normal mode radiation, which allows the use of a two-dimensional lattice with an axisymmetric condition at the pipe’s longitudinal axis. The numerical results are initially verified against an exact analytical solution for the sound radiation directivity of an unflanged pipe in the absence of a mean flow, which shows a very good agreement. Thereafter, the sound directivity results in the presence of a subsonic mean flow are compared with both analytical models and experimental data. The results are in good agreement, particularly for low values of the Helmholtz number ka. Moreover, the phenomenon known as ‘zone of relative silence’ was observed, even for mean flows associated with very low Mach numbers, though discrepancies were also observed in the comparison between the numerical results and the analytical predictions. A thorough discussion on the scheme implementation and numerical results is provided in the paper. (paper)

Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — The overall objective of the proposed project is to develop a generalized lattice Boltzmann (GLB) approach as a potential computational aeroacoustics (CAA) tool for...

A two-dimensional lattice equation as an extension of the Heideman-Hogan recurrence

Science.gov (United States)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2018-03-01

We consider a two dimensional extension of the so-called linearizable mappings. In particular, we start from the Heideman-Hogan recurrence, which is known as one of the linearizable Somos-like recurrences, and introduce one of its two dimensional extensions. The two dimensional lattice equation we present is linearizable in both directions, and has the Laurent and the coprimeness properties. Moreover, its reduction produces a generalized family of the Heideman-Hogan recurrence. Higher order examples of two dimensional linearizable lattice equations related to the Dana Scott recurrence are also discussed.

Moving charged particles in lattice Boltzmann-based electrokinetics

Science.gov (United States)

Kuron, Michael; Rempfer, Georg; Schornbaum, Florian; Bauer, Martin; Godenschwager, Christian; Holm, Christian; de Graaf, Joost

2016-12-01

The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions into the Capuani scheme has been lacking. Moving boundary conditions are needed to simulate multiple arbitrarily moving colloids. In this paper, we detail how to introduce such a particle coupling scheme, based on an analogue to the moving boundary method for the pure lattice Boltzmann solver. The key ingredients in our method are mass and charge conservation for the solute species and a partial-volume smoothing of the solute fluxes to minimize discretization artifacts. We demonstrate our algorithm's effectiveness by simulating the electrophoresis of charged spheres in an external field; for a single sphere we compare to the equivalent electro-osmotic (co-moving) problem. Our method's efficiency and ease of implementation should prove beneficial to future simulations of the dynamics in a wide range of complex nanoscopic and colloidal systems that were previously inaccessible to lattice-based continuum algorithms.

Energy Dependent Streaming in Lattice Boltzmann Simulations

Czech Academy of Sciences Publication Activity Database

Pavlo, Pavol; Vahala, G.; Vahala, L.

2001-01-01

Roč. 46, č. 8 (2001), s. 241 ISSN 0003-0503. [Annual Meeting of the Division of Plasma Physics of the American Physical Society/43rd./. Long Beach, CA, 29.10.2001-02.11.2001] R&D Projects: GA ČR GA202/00/1216 Institutional research plan: CEZ:AV0Z2043910 Keywords : Lattice Boltzmann Simulations Subject RIV: BL - Plasma and Gas Discharge Physics

Multiphase lattice Boltzmann on the Cell Broadband Engine

International Nuclear Information System (INIS)

Belletti, F.; Mantovani, F.; Tripiccione, R.; Biferale, L.; Schifano, S.F.; Toschi, F.

2009-01-01

Computational experiments are one of the most used and flexible investigation tools in fluid dynamics. The Lattice Boltzmann Equation is a well established computational method particularly promising for multi-phase flows at micro and macro scales. Here we present preliminary results on performances of the Lbe method on the Cell Broadband Engine platform.

Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

CERN Document Server

Farhat, Hassan; Kondaraju, Sasidhar

2014-01-01

Colloids are ubiquitous in the food, medical, cosmetics, polymers, water purification, and pharmaceutical industries. The thermal, mechanical, and storage properties of colloids are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a convenient and reliable tool for the study of colloids. Accelerated Lattice Boltzmann Model for Colloidal Suspensions introduce the main building-blocks for an improved lattice Boltzmann–based numerical tool designed for the study of colloidal rheology and interface morphology. This book also covers the migrating multi-block used to simulate single component, multi-component, multiphase, and single component multiphase flows and their validation by experimental, numerical, and analytical solutions.   Among other topics discussed are the hybrid lattice Boltzmann method (LBM) for surfactant-covered droplets; biological suspensions such as blood; used in conjunction with the suppression of coalescence for investigating the...

Lattice Boltzmann simulation of flow across a staggered tube bundle array

Energy Technology Data Exchange (ETDEWEB)

Tiftikçi, A.; Kocar, C., E-mail: ckocar@hacettepe.edu.tr

2016-04-15

Highlights: • Large eddy simulation of the cross-flow in a staggered tube bundle array in 3D was made. • LBM and FVM are used separately as numerical solvers and the results of each method compared with experimental data. • Effect of lattice model is studied for tube bundle flow. • Filter size effects, mesh size effects are studied for VLES turbulence model. - Abstract: The decision on the magnitude of the grid size is a crucial problem in large eddy simulations. Finer mesh requires excessive memory and causes long simulation time. Large eddy simulation model becomes inefficient when the extent of the flow geometry to be simulated with the lattice-Boltzmann method is large. Thus, in this study, it is proposed to investigate the capabilities of three turbulence models, namely, very large eddy simulation, Van Driest and Smagorinsky–Lilly. As a test case, a staggered tube bundle flow experiment is used for the validation and comparison purposes. Sensitivity analyses (including mesh and filter size) have been made. Furthermore, the effect of lattice model is investigated and it is showed that the D3Q27 and D3Q19 models do not differ significantly in lattice-Boltzmann method for this type of flow. The results of turbulence model comparisons for staggered tube bundle flow showed that very large eddy simulation is superior at low resolution. This paper might be considered as a good validation of the lattice-Boltzmann method. In turbulent flow conditions, the code successfully captures the velocity and stress profiles even if the flow is quite complicated.

Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena

International Nuclear Information System (INIS)

Lin Chuan-Dong; Li Ying-Jun; Xu Ai-Guo; Zhang Guang-Cai

2014-01-01

A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier—Stokes equations, including contribution of chemical reaction, via the Chapman—Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Simulation of Cavity Flow by the Lattice Boltzmann Method using Multiple-Relaxation-Time scheme

International Nuclear Information System (INIS)

Ryu, Seung Yeob; Kang, Ha Nok; Seo, Jae Kwang; Yun, Ju Hyeon; Zee, Sung Quun

2006-01-01

Recently, the lattice Boltzmann method(LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for pressure, and (3) ease with multiphase flows, complex geometries and interfacial dynamics may be treated. The LBM using relaxation technique was introduced by Higuerea and Jimenez to overcome some drawbacks of lattice gas automata(LGA) such as large statistical noise, limited range of physical parameters, non- Galilean invariance, and implementation difficulty in three-dimensional problem. The simplest LBM is the lattice Bhatnager-Gross-Krook(LBGK) equation, which based on a single-relaxation-time(SRT) approximation. Due to its extreme simplicity, the lattice BGK(LBGK) equation has become the most popular lattice Boltzmann model in spite of its well-known deficiencies, for example, in simulating high-Reynolds numbers flow. The Multiple-Relaxation-Time(MRT) LBM was originally developed by D'Humieres. Lallemand and Luo suggests that the use of a Multiple-Relaxation-Time(MRT) models are much more stable than LBGK, because the different relaxation times can be individually tuned to achieve 'optimal' stability. A lid-driven cavity flow is selected as the test problem because it has geometrically singular points in the flow, but geometrically simple. Results are compared with those using SRT, MRT model in the LBGK method and previous simulation data using Navier-Stokes equations for the same flow conditions. In summary, LBM using MRT model introduces much less spatial oscillations near geometrical singular points, which is important for the successful simulation of higher Reynolds number flows

Lattice Boltzmann method fundamentals and engineering applications with computer codes

CERN Document Server

Mohamad, A A

2014-01-01

Introducing the Lattice Boltzmann Method in a readable manner, this book provides detailed examples with complete computer codes. It avoids the most complicated mathematics and physics without scarifying the basic fundamentals of the method.

Lattice Boltzmann simulation for temperature-sensitive magnetic fluids in a porous square cavity

International Nuclear Information System (INIS)

Jin Licong; Zhang Xinrong; Niu Xiaodong

2012-01-01

A lattice Boltzmann method is developed to simulate temperature-sensitive magnetic fluids in a porous cavity. In the simulation, the magnetic force, efficient gravity, viscous loss term and geometric loss term in porous medium are imported to the momentum equation. To test the reliability of the method, a validation with water in porous cavity is carried out. Good agreements with the previous results verify that the present lattice Boltzmann method is promising for simulation of magnetic fluids in porous medium. In this study, we investigate the change of magnetization with external magnetic field, and we present numerical results for the streamlines, isotherms, and magnetization at vertical or horizontal mid-profiles for different values of Ram. In addition, Nusselt numbers changing with magnetic Rayleigh numbers are also investigated. - Highlights: → Developed a lattice Boltzmann method for magnetic nano-fluids in porous cavity. → Clarified flow and heat transfer for different values of (magnetic) Rayleigh numbers. → Heat transfer enhancement for magnetic fluid in porous cavity.

A free-surface lattice Boltzmann method for modelling the filling of expanding cavities by Bingham fluids.

Science.gov (United States)

Ginzburg, Irina; Steiner, Konrad

2002-03-15

The filling process of viscoplastic metal alloys and plastics in expanding cavities is modelled using the lattice Boltzmann method in two and three dimensions. These models combine the regularized Bingham model for viscoplastic fluids with a free-interface algorithm. The latter is based on a modified immiscible lattice Boltzmann model in which one species is the fluid and the other one is considered to be a vacuum. The boundary conditions at the curved liquid-vacuum interface are met without any geometrical front reconstruction from a first-order Chapman-Enskog expansion. The numerical results obtained with these models are found in good agreement with available theoretical and numerical analysis.

Lattice-Boltzmann simulation of the sedimentation of charged disks

NARCIS (Netherlands)

Capuani, F.; Pagonabarraga, I.; Frenkel, D.

2006-01-01

We report a series of lattice-Boltzmann simulations of the sedimentation velocity of charged disks. In these simulations, we explicitly account for the hydrodynamic and electrostatic forces on disks and on their electrical double layer. By comparing our results with those for spheres with equal

Convection in multiphase fluid flows using lattice Boltzmann methods

NARCIS (Netherlands)

Biferale, L.; Perlekar, P.; Sbragaglia, M.; Toschi, F.

2012-01-01

We present high-resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a lattice Boltzmann method. We first study the thermodynamical and kinematic properties of the algorithm. Then, we perform a series of 3D numerical simulations changing the

Parallelization of 2-D lattice Boltzmann codes

International Nuclear Information System (INIS)

Suzuki, Soichiro; Kaburaki, Hideo; Yokokawa, Mitsuo.

1996-03-01

Lattice Boltzmann (LB) codes to simulate two dimensional fluid flow are developed on vector parallel computer Fujitsu VPP500 and scalar parallel computer Intel Paragon XP/S. While a 2-D domain decomposition method is used for the scalar parallel LB code, a 1-D domain decomposition method is used for the vector parallel LB code to be vectorized along with the axis perpendicular to the direction of the decomposition. High parallel efficiency of 95.1% by the vector parallel calculation on 16 processors with 1152x1152 grid and 88.6% by the scalar parallel calculation on 100 processors with 800x800 grid are obtained. The performance models are developed to analyze the performance of the LB codes. It is shown by our performance models that the execution speed of the vector parallel code is about one hundred times faster than that of the scalar parallel code with the same number of processors up to 100 processors. We also analyze the scalability in keeping the available memory size of one processor element at maximum. Our performance model predicts that the execution time of the vector parallel code increases about 3% on 500 processors. Although the 1-D domain decomposition method has in general a drawback in the interprocessor communication, the vector parallel LB code is still suitable for the large scale and/or high resolution simulations. (author)

Parallelization of 2-D lattice Boltzmann codes

Energy Technology Data Exchange (ETDEWEB)

Suzuki, Soichiro; Kaburaki, Hideo; Yokokawa, Mitsuo

1996-03-01

Lattice Boltzmann (LB) codes to simulate two dimensional fluid flow are developed on vector parallel computer Fujitsu VPP500 and scalar parallel computer Intel Paragon XP/S. While a 2-D domain decomposition method is used for the scalar parallel LB code, a 1-D domain decomposition method is used for the vector parallel LB code to be vectorized along with the axis perpendicular to the direction of the decomposition. High parallel efficiency of 95.1% by the vector parallel calculation on 16 processors with 1152x1152 grid and 88.6% by the scalar parallel calculation on 100 processors with 800x800 grid are obtained. The performance models are developed to analyze the performance of the LB codes. It is shown by our performance models that the execution speed of the vector parallel code is about one hundred times faster than that of the scalar parallel code with the same number of processors up to 100 processors. We also analyze the scalability in keeping the available memory size of one processor element at maximum. Our performance model predicts that the execution time of the vector parallel code increases about 3% on 500 processors. Although the 1-D domain decomposition method has in general a drawback in the interprocessor communication, the vector parallel LB code is still suitable for the large scale and/or high resolution simulations. (author).

Lattice Boltzmann simulations of attenuation-driven acoustic streaming

International Nuclear Information System (INIS)

Haydock, David; Yeomans, J M

2003-01-01

We show that lattice Boltzmann simulations can be used to model the attenuation-driven acoustic streaming produced by a travelling wave. Comparisons are made to analytical results and to the streaming pattern produced by an imposed body force approximating the Reynolds stresses. We predict the streaming patterns around a porous material in an attenuating acoustic field

Numerical Study of Electrolyte Wetting Phenomena in the Electrode of Lithium Ion Battery Using Lattice Boltzmann Method

Energy Technology Data Exchange (ETDEWEB)

Lee, Sang Gun [Seoul Nat' l Univ., Seoul (Korea, Republic of); Jeon, Dong Hyup [Dongguk Univ., Seoul (Korea, Republic of)

2014-04-15

The electrolyte wetting phenomena in the electrode of lithium ion battery is studied numerically using a multiphase lattice Boltzmann method (LBM). When a porous electrode is compressed during roll-pressing process, the porosity and thickness of the compressed electrode are changed, which can affect its wettability. In this study, the change in electrolyte distribution and degree of saturation as a result of varying the compression ratio are investigated with two-dimensional LBM approach. We found that changes in the electrolyte transport path are caused by a reduction in through-plane pore size and result in a decrease in the wettability of the compressed electrode.

Long-range inverse two-spin correlations in one-dimensional Potts lattices

International Nuclear Information System (INIS)

Tejero, C.F.; Cuesta, J.A.; Brito, R.

1989-01-01

The inverse two-spin correlation function of a one-dimensional three-state Potts lattice with constant nearest-neighbor interactions in a uniform external field is derived exactly. It is shown that the external field induces long-range correlations. The inverse two-spin correlation function decays in a monotonic exponential fashion for a ferromagnetic lattice, while it decays in an oscillatory exponential fashion for an antiferromagnetic lattice. With no external field the inverse two-spin correlation function has a finite range equal to that of the interactions

High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

Science.gov (United States)

Li, Weidong

2017-09-01

This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

Free surface entropic lattice Boltzmann simulations of film condensation on vertical hydrophilic plates

DEFF Research Database (Denmark)

Hygum, Morten Arnfeldt; Karlin, Iliya; Popok, Vladimir

2015-01-01

A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall. It is sh......A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall...

Résumé : La méthode Lattice Boltzmann (LBM)et la celle des ...

African Journals Online (AJOL)

JOSLIN

Lattice Boltzmann Method (LBM ) , Finite Difference Explicit ( DFE ) , Hybrid combines the two previous methods and Finite ... In addition, simulations using four methods show that for Ra = 105 the system is damped oscillating, it is oscillating periodic ..... convection heat transfert in a horizontal concentric annulus".Computer ...

Advanced lattice Boltzmann scheme for high-Reynolds-number magneto-hydrodynamic flows

Science.gov (United States)

De Rosis, Alessandro; Lévêque, Emmanuel; Chahine, Robert

2018-06-01

Is the lattice Boltzmann method suitable to investigate numerically high-Reynolds-number magneto-hydrodynamic (MHD) flows? It is shown that a standard approach based on the Bhatnagar-Gross-Krook (BGK) collision operator rapidly yields unstable simulations as the Reynolds number increases. In order to circumvent this limitation, it is here suggested to address the collision procedure in the space of central moments for the fluid dynamics. Therefore, an hybrid lattice Boltzmann scheme is introduced, which couples a central-moment scheme for the velocity with a BGK scheme for the space-and-time evolution of the magnetic field. This method outperforms the standard approach in terms of stability, allowing us to simulate high-Reynolds-number MHD flows with non-unitary Prandtl number while maintaining accuracy and physical consistency.

Implementation of the Lattice Boltzmann Method on Heterogeneous Hardware and Platforms using OpenCL

Directory of Open Access Journals (Sweden)

TEKIC, P. M.

2012-02-01

Full Text Available The Lattice Boltzmann method (LBM has become an alternative method for computational fluid dynamics with a wide range of applications. Besides its numerical stability and accuracy, one of the major advantages of LBM is its relatively easy parallelization and, hence, it is especially well fitted to many-core hardware as graphics processing units (GPU. The majority of work concerning LBM implementation on GPU's has used the CUDA programming model, supported exclusively by NVIDIA. Recently, the open standard for parallel programming of heterogeneous systems (OpenCL has been introduced. OpenCL standard matures and is supported on processors from most vendors. In this paper, we make use of the OpenCL framework for the lattice Boltzmann method simulation, using hardware accelerators - AMD ATI Radeon GPU, AMD Dual-Core CPU and NVIDIA GeForce GPU's. Application has been developed using a combination of Java and OpenCL programming languages. Java bindings for OpenCL have been utilized. This approach offers the benefits of hardware and operating system independence, as well as speeding up of lattice Boltzmann algorithm. It has been showed that the developed lattice Boltzmann source code can be executed without modification on all of the used hardware accelerators. Performance results have been presented and compared for the hardware accelerators that have been utilized.

Investigating flow patterns in a channel with complex obstacles using the lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Yojina, Jiraporn; Ngamsaad, Waipot; Nuttavut, Narin; Triampo, Darapond; Lenbury, Yongwimon; Sriyab, Somchai; Triampo, Wannapong [Faculty of Science, Mahidol University, Bangkok (Thailand); Kanthang, Paisan [Rajamangala University of Technology, Bangkok (Thailand)

2010-10-15

In this work, mesoscopic modeling via a computational lattice Boltzmann method (LBM) is used to investigate the flow pattern phenomena and the physical properties of the flow field around one and two square obstacles inside a two-dimensional channel with a fixed blockage ratio,{beta} =14 , centered inside a 2D channel, for a range of Reynolds numbers (Re) from 1 to 300. The simulation results show that flow patterns can initially exhibit laminar flow at low Re and then make a transition to periodic, unsteady, and, finally, turbulent flow as the Re get higher. Streamlines and velocity profiles and a vortex shedding pattern are observed. The Strouhal numbers are calculated to characterize the shedding frequency and flow dynamics. The effect of the layouts or configurations of the obstacles are also investigated, and the possible connection between the mixing process and the appropriate design of a chemical mixing system is discussed

A review of spurious currents in the lattice Boltzmann method for multiphase flows

Energy Technology Data Exchange (ETDEWEB)

Conning Ton, Kevin; Lee, Tae Hun [The City College of the City Univ. of New York, New York (United States)

2012-12-15

A spurious current is a small amplitude artificial velocity field which arises from an imbalance between discretized forces in multiphase/multi component flows. If it occurs, the velocity field may persist indefinitely, preventing the achievement of a true equilibrium state. Spurious velocities can sometimes be as large as the characteristic velocities of the problem, causing severe instability and ambiguity between physical and spurious velocities. They are typically exacerbated by large values of numerical surface tension or when the two fluids being simulated have large density ratios. The resulting instability can restrict what parameters may be simulated. To varying degrees, spurious currents are found in all multiphase flow models of the lattice Boltzmann method (LBM). There have been many studies of the occurrence of the phenomenon, and many suggestions on how to eliminate it. This paper reviews the three main models of simulating multiphase/multi component flow in the lattice Boltzmann method, as well as the subsequent modifications made in order to reduce or eliminate spurious currents.

Numerical Simulation of Flows about a Stationary and a Free-Falling Cylinder Using Immersed Boundary-Finite Difference Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Roberto Rojas

2013-03-01

Full Text Available The applicability of the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM to high Reynolds number flows about a circular cylinder is examined. Two-dimensional simulations of flows past a stationary circular cylinder are carried out for a wide range of the Reynolds number, Re, i.e., 1 ≤ Re ≤ 1×105. An immersed boundary-lattice Boltzmann method (IB-LBM is also used for comparison. Then free-falling circular cylinders are simulated to demonstrate the feasibility of predicting moving particles at high Reynolds numbers. The main conclusions obtained are as follows: (1 steady and unsteady flows about a stationary cylinder are well predicted with IB-LBM and IB-FDLBM, provided that the spatial resolution is high enough to satisfy the conditions of numerical stability, (2 high spatial resolution is required for stable IB-LBM simulation of high Reynolds number flows, (3 IB-FDLBM can stably simulate flows at very high Reynolds numbers without increasing the spatial resolution, (4 IB-FDLBM gives reasonable predictions of the drag coefficient for 1 ≤ Re ≤ 1×105, and (5 IB-FDLBM gives accurate predictions for the motion of free-falling cylinders at intermediate Reynolds numbers.

Lattice Boltzmann methods for the simulation of heat transfer in particle suspensions

International Nuclear Information System (INIS)

McCullough, J.W.S.; Leonardi, C.R.; Jones, B.D.; Aminossadati, S.M.; Williams, J.R.

2016-01-01

Highlights: • Development of a lattice Boltzmann heat transfer model for curved boundaries. • Thermodynamic coupling aims to ensure continuity of both temperature and heat flux. • Good correlation found in transient comparison of results to analytical solutions. • Illustration of the developed model applied to a moving particle test case. - Abstract: This study examines the use of a lattice Boltzmann method framework to study heat transfer behaviours within particle suspensions. This has been done through the use of an adapted interface condition to attempt to resolve the required continuity of temperature and flux at the boundary between the solid and fluid phases. The proposed method is tested against analytical solutions for layered media in both a 1D bar and a radial layout. These tests showed that the model was able to generate results with first order convergence towards the analytical outcomes. The model was then used to examine the behaviour of two moving particles travelling along a channel to illustrate its potential for resolving complex suspension flows.

A lattice Boltzmann coupled to finite volumes method for solving phase change problems

Directory of Open Access Journals (Sweden)

El Ganaoui Mohammed

2009-01-01

Full Text Available A numerical scheme coupling lattice Boltzmann and finite volumes approaches has been developed and qualified for test cases of phase change problems. In this work, the coupled partial differential equations of momentum conservation equations are solved with a non uniform lattice Boltzmann method. The energy equation is discretized by using a finite volume method. Simulations show the ability of this developed hybrid method to model the effects of convection, and to predict transfers. Benchmarking is operated both for conductive and convective situation dominating solid/liquid transition. Comparisons are achieved with respect to available analytical solutions and experimental results.

Exact lattice supersymmetry: The two-dimensional N=2 Wess-Zumino model

International Nuclear Information System (INIS)

Catterall, Simon; Karamov, Sergey

2002-01-01

We study the two-dimensional Wess-Zumino model with extended N=2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving exactly a single supersymmetric invariance at finite lattice spacing a. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to O(ga 2 ) where g is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the mass gaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing

Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow

International Nuclear Information System (INIS)

Zheng, Lin; Zheng, Song; Zhai, Qinglan

2016-01-01

In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.

Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow

Energy Technology Data Exchange (ETDEWEB)

Zheng, Lin, E-mail: lz@njust.edu.cn [School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094 (China); Zheng, Song [School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018 (China); Zhai, Qinglan [School of Economics Management and Law, Chaohu University, Chaohu 238000 (China)

2016-02-05

In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.

Hofstadter's butterfly in a two-dimensional lattice consisting of two sublattices

International Nuclear Information System (INIS)

Vugalter, G A; Pastukhov, A S

2004-01-01

Harper's equations for simple and complex two-dimensional lattices subject to a magnetic field have been derived in the tight-binding approximation. In our derivation we do not neglect the influence of the magnetic field on the electron eigenfunctions and eigenvalues in isolated atoms. Using a variational procedure for finding eigenfunctions and eigenvalues, we have self-consistently obtained Hofstadter's butterflies. Even for a simple square lattice Hofstadter's butterfly differs from the butterfly obtained in the case in which the influence of the magnetic field on the electron eigenvalues and eigenfunctions in isolated atoms is not taken into account

Parallel-plate rheometer calibration using oil and lattice Boltzmann simulation

DEFF Research Database (Denmark)

Ferraris, Chiara F; Geiker, Mette Rica; Martys, Nicos S.

2007-01-01

compute the viscosity. This paper presents a modified parallel plate rheometer, and proposes means of calibration using standard oils and numerical simulation of the flow. A lattice Boltzmann method was used to simulate the flow in the modified rheometer, thus using an accurate numerical solution in place...

A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

KAUST Repository

Allen, Rebecca

2013-01-01

The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently

Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula

Science.gov (United States)

Dai, Jian; Song, Xing-Chang

2001-07-01

One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.

Quantum theory of two-dimensional generalized Toda lattice on bounded spatial interval

International Nuclear Information System (INIS)

Leznov, A.N.

1982-01-01

The quantization method of exactly solvable dynamical systems worked out in another paper is applied to a two-dimensional model described by the equations of generalized Toda lattice with a periodicity condition over spatial variable. The Heisenberg operators of the model are finite polynomials over the coupling constant g 2 , whose coefficients functionally depend on operators of noninteracting fields. The model has a direct relation with the string theories and reduces formally when L→infinity to two-dimensional quantum field theory described by the equations of generalized Toda lattice the formal solution of which has been found in Refs

The lattice Boltzmann method and the problem of turbulence

Energy Technology Data Exchange (ETDEWEB)

Djenidi, L. [School of Engineering The University of Newcastle, Callaghan NSW 2308 (Australia)

2015-03-10

This paper reports a brief review of numerical simulations of homogeneous isotopic turbulence (HIT) using the lattice Boltzmann method (LBM). The LBM results shows that the details of HIT are well captured and in agreement with existing data. This clearly indicates that the LBM is as good as current Navier-Stokes solvers and is very much adequate for investigating the problem of turbulence.

The lattice Boltzmann method and the problem of turbulence

International Nuclear Information System (INIS)

Djenidi, L.

2015-01-01

This paper reports a brief review of numerical simulations of homogeneous isotopic turbulence (HIT) using the lattice Boltzmann method (LBM). The LBM results shows that the details of HIT are well captured and in agreement with existing data. This clearly indicates that the LBM is as good as current Navier-Stokes solvers and is very much adequate for investigating the problem of turbulence

Effects of nanoparticles on melting process with phase-change using the lattice Boltzmann method

Directory of Open Access Journals (Sweden)

Ahmed M. Ibrahem

Full Text Available In this work, the problem of nanoparticles dispersion effects on coupled heat transfer and solid-liquid phase change has been studied. The lattice Boltzmann method (LBM enthalpy-based is employed. The collision model of lattice Bhatnagar-Gross-Krook (LBGK is used to solve the problem of 1D melting by conduction. On the other hand, we use the model of multi-distribution functions (MDF to calculate the density, the velocity and the temperature for the problem of 2D melting by free convection, associated with different boundary conditions. In these simulations, the volume fractions of copper nanoparticles (0–2% added to water-base fluid and Rayleigh numbers of 103–105. We use the Chapman-Enskog expansion to derive the governing macroscopic quantities from the mesoscopic lattice Boltzmann equation. The results obtained by these models have been compared to an analytical solution or other numerical methods. The effects of nanoparticles on conduction and natural convection during the melting process have been investigated. Moreover, the influences of nanoparticles on moving of the phase change front, the thermal conductivity and the latent heat of fusion are also studied. Keywords: Lattice Boltzmann method, Nanofluids, Conduction melting, Convection melting, BGK collision model

Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods

International Nuclear Information System (INIS)

Klassen, Alexander; Scharowsky, Thorsten; Körner, Carolin

2014-01-01

Evaporation plays an important role in many technical applications including beam-based additive manufacturing processes, such as selective electron beam or selective laser melting (SEBM/SLM). In this paper, we describe an evaporation model which we employ within the framework of a two-dimensional free surface lattice Boltzmann method. With this method, we solve the hydrodynamics as well as thermodynamics of the molten material taking into account the mass and energy losses due to evaporation and the recoil pressure acting on the melt pool. Validation of the numerical model is performed by measuring maximum melt depths and evaporative losses in samples of pure titanium and Ti–6Al–4V molten by an electron beam. Finally, the model is applied to create processing maps for an SEBM process. The results predict that the penetration depth of the electron beam, which is a function of the acceleration voltage, has a significant influence on evaporation effects. (paper)

Unconventional phases in quantum spin and pseudospin systems in two dimensional and three dimensional lattices

Science.gov (United States)

Xu, Cenke

Several examples of quantum spin systems and pseudo spin systems have been studied, and unconventional states of matters and phase transitions have been realized in all these systems under consideration. In the p +/- ip superconductor Josephson lattice and the p--band cold atomic system trapped in optical lattices, novel phases which behave similarly to 1+1 dimensional systems are realized, despite the fact that the real physical systems are in two or three dimensional spaces. For instance, by employing a spin-wave analysis together with a new duality transformation, we establish the existence and stability of a novel gapless "critical phase", which we refer to as a "bond algebraic liquid". This novel critical phase is analogous to the 1+1 dimensional algebraic boson liquid phase. The reason for the novel physics is that there is a quasilocal gauge symmetry in the effective low energy Hamiltonian. In a spin-1 system on the kagome lattice, and a hard-core boson system on the honeycomb lattice, the low energy physics is controlled by two components of compact U(1) gauge symmetries that emerge at low energy. Making use of the confinement nature of the 2+1 dimensional compact gauge theories and the powerful duality between gauge theories and height field theories, the crystalline phase diagrams are studied for both systems, and the transitions to other phases are also considered. These phase diagrams might be accessible in strongly correlated materials, or atomic systems in optical lattices. A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the

Topology optimization of unsteady flow problems using the lattice Boltzmann method

DEFF Research Database (Denmark)

Nørgaard, Sebastian Arlund; Sigmund, Ole; Lazarov, Boyan Stefanov

2016-01-01

This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems...

Lattice Boltzmann method for solving the bioheat equation

International Nuclear Information System (INIS)

Zhang Haifeng

2008-01-01

In this work, we develop the lattice Boltzmann method (LBM) as a potential solver for the bioheat problems. The accuracy of the present LBM algorithm is validated through comparison with the analytical solution and the finite element simulation. The results show that the LBM can give a precise prediction of the temperature distribution, and it is efficient to deal with the space- and time-dependent heat source, which are often encountered in the treatment planning of tumor hyperthermia. (note)

A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows

Energy Technology Data Exchange (ETDEWEB)

Fakhari, Abbas, E-mail: afakhari@nd.edu [Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556 (United States); Geier, Martin [TU Braunschweig, Institute for Computational Modeling in Civil Engineering (iRMB), TU-Braunschweig, Pockelsstr. 3, 38106 Braunschweig (Germany); Lee, Taehun [Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031 (United States)

2016-06-15

A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21]) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a

A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows

International Nuclear Information System (INIS)

Fakhari, Abbas; Geier, Martin; Lee, Taehun

2016-01-01

A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21]) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a

Simulating condensation on microstructured surfaces using Lattice Boltzmann Method

Science.gov (United States)

Alexeev, Alexander; Vasyliv, Yaroslav

2017-11-01

We simulate a single component fluid condensing on 2D structured surfaces with different wettability. To simulate the two phase fluid, we use the athermal Lattice Boltzmann Method (LBM) driven by a pseudopotential force. The pseudopotential force results in a non-ideal equation of state (EOS) which permits liquid-vapor phase change. To account for thermal effects, the athermal LBM is coupled to a finite volume discretization of the temperature evolution equation obtained using a thermal energy rate balance for the specific internal energy. We use the developed model to probe the effect of surface structure and surface wettability on the condensation rate in order to identify microstructure topographies promoting condensation. Financial support is acknowledged from Kimberly-Clark.

Lattice-Boltzmann Simulation of Tablet Disintegration

Science.gov (United States)

Jiang, Jiaolong; Sun, Ning; Gersappe, Dilip

Using the lattice-Boltzmann method, we developed a 2D model to study the tablet disintegration involving the swelling and wicking mechanisms. The surface area and disintegration profile of each component were obtained by tracking the tablet structure in the simulation. Compared to pure wicking, the total surface area is larger for swelling and wicking, which indicates that the swelling force breaks the neighboring bonds. The disintegration profiles show that the tablet disintegrates faster than pure wicking, and there are more wetted active pharmaceutical ingredient particles distributed on smaller clusters. Our results indicate how the porosity would affect the disintegration process by changing the wetting area of the tablet as well as by changing the swelling force propagation.

Two-dimensional N=(2,2) lattice gauge theories with matter in higher representations

International Nuclear Information System (INIS)

Joseph, Anosh

2014-06-01

We construct two-dimensional N=(2,2) supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU(N c ) color group. These lattice theories preserve a subset of the supercharges exact at finite lattice spacing. The method of topological twisting is used to construct such theories in the continuum and then the geometric discretization scheme is used to formulate them on the lattice. The lattice theories obtained this way are gauge-invariant, free from fermion doubling problem and exact supersymmetric at finite lattice spacing. We hope that these lattice constructions further motivate the nonperturbative explorations of models inspired by technicolor, orbifolding and orientifolding in string theories and the Corrigan-Ramond limit.

Lattice Boltzmann method to study the contraction of a viscous ligament

NARCIS (Netherlands)

Srivastava, S.; Driessen, T.W.; Jeurissen, R.J.M.; Wijshoff, H.M.A.; Toschi, F.

2013-01-01

We employ a recently formulated axisymmetric version of the multiphase Shan–Chen (SC) lattice Boltzmann method (LBM) [S. Srivastava et al., Phys. Rev. E88, 013309 (2013)] to simulate the contraction of a liquid ligament. We compare the axisymmetric LBM simulation against the slender jet (SJ)

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

Science.gov (United States)

Liang, Hong; Xu, Jiangrong; Chen, Jiangxing; Wang, Huili; Chai, Zhenhua; Shi, Baochang

2018-03-01

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

Science.gov (United States)

Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.

2018-03-01

The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.

Generalized hydrodynamic transport in lattice-gas automata

Science.gov (United States)

Luo, Li-Shi; Chen, Hudong; Chen, Shiyi; Doolen, Gary D.; Lee, Yee-Chun

1991-01-01

The generalized hydrodynamics of two-dimensional lattice-gas automata is solved analytically in the linearized Boltzmann approximation. The dependence of the transport coefficients (kinematic viscosity, bulk viscosity, and sound speed) upon wave number k is obtained analytically. Anisotropy of these coefficients due to the lattice symmetry is studied for the entire range of wave number, k. Boundary effects due to a finite mean free path (Knudsen layer) are analyzed, and accurate comparisons are made with lattice-gas simulations.

Lattice formulation of a two-dimensional topological field theory

International Nuclear Information System (INIS)

Ohta, Kazutoshi; Takimi, Tomohisa

2007-01-01

We investigate an integrable property and the observables of 2-dimensional N=(4,4) topological field theory defined on a discrete lattice by using the 'orbifolding' and 'deconstruction' methods. We show that our lattice model is integrable and, for this reason, the partition function reduces to matrix integrals of scalar fields on the lattice sites. We elucidate meaningful differences between a discrete lattice and a differentiable manifold. This is important for studying topological quantities on a lattice. We also propose a new construction of N=(2,2) supersymmetric lattice theory, which is realized through a suitable truncation of scalar fields from the N=(4,4) theory. (author)

Lattice Boltzmann method used to simulate particle motion in a conduit

Directory of Open Access Journals (Sweden)

Dolanský Jindřich

2017-06-01

Full Text Available A three-dimensional numerical simulation of particle motion in a pipe with a rough bed is presented. The simulation based on the Lattice Boltzmann Method (LBM employs the hybrid diffuse bounce-back approach to model moving boundaries. The bed of the pipe is formed by stationary spherical particles of the same size as the moving particles. Particle movements are induced by gravitational and hydrodynamic forces. To evaluate the hydrodynamic forces, the Momentum Exchange Algorithm is used. The LBM unified computational frame makes it possible to simulate both the particle motion and the fluid flow and to study mutual interactions of the carrier liquid flow and particles and the particle–bed and particle–particle collisions. The trajectories of simulated and experimental particles are compared. The Particle Tracking method is used to track particle motion. The correctness of the applied approach is assessed.

Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers

KAUST Repository

Atanasov, Atanas; Uekermann, Benjamin; Pachajoa Mejí a, Carlos; Bungartz, Hans-Joachim; Neumann, Philipp

2016-01-01

to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier

Interference patterns of Bose-condensed gases in a two-dimensional optical lattice

International Nuclear Information System (INIS)

Liu Shujuan; Xiong Hongwei; Xu Zhijun; Huang Guoxiang

2003-01-01

For a Bose-condensed gas confined in a magnetic trap and in a two-dimensional (2D) optical lattice, the non-uniform distribution of atoms in different lattice sites is considered based on the Gross-Pitaevskii equation. A propagator method is used to investigate the time evolution of 2D interference patterns after (i) only the optical lattice is switched off, and (ii) both the optical lattice and the magnetic trap are switched off. An analytical description on the motion of side peaks in the interference patterns is presented by using the density distribution in a momentum space

Two-relaxation-time lattice Boltzmann method and its application to advective-diffusive-reactive transport

Science.gov (United States)

Yan, Zhifeng; Yang, Xiaofan; Li, Siliang; Hilpert, Markus

2017-11-01

The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments. These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. The TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.

Volumetric formulation of lattice Boltzmann models with energy conservation

OpenAIRE

Sbragaglia, M.; Sugiyama, K.

2010-01-01

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum and energy. ...

Using x-ray tomography and lattice Boltzmann modeling to evaluate pore-scale processes in porous media

DEFF Research Database (Denmark)

Christensen, Britt Stenhøj Baun

-teknik (Computed Tomography) til at visualisere og kvantificere de eksperimentelle poreskala systemer. Både en medicinsk CT-scanner og et synkrotron baseret skanningssystem med høj billede opløselighed blev anvendt. Numerisk modellering af poreskala processerne blev gjort ved hjælp af en lattice Boltzmann model...... for testning af en Shan-Chen lattice Boltzmann model. Ved anvendelse af simple veldefinerede to-fase systemer blev en kalibreringsprocedure skitseret til identificering af de dimensionsløse modelparametre og deres kobling til overfladespænding og kontaktvinkel egenskaberne af det fysiske system. Det blev taget...

Lattice Boltzmann Simulation of Multiple Bubbles Motion under Gravity

Directory of Open Access Journals (Sweden)

Deming Nie

2015-01-01

Full Text Available The motion of multiple bubbles under gravity in two dimensions is numerically studied through the lattice Boltzmann method for the Eotvos number ranging from 1 to 12. Two kinds of initial arrangement are taken into account: vertical and horizontal arrangement. In both cases the effects of Eotvos number on the bubble coalescence and rising velocity are investigated. For the vertical arrangement, it has been found that the coalescence pattern is similar. The first coalescence always takes place between the two uppermost bubbles. And the last coalescence always takes place between the coalesced bubble and the bottommost bubble. For four bubbles in a horizontal arrangement, the outermost bubbles travel into the wake of the middle bubbles in all cases, which allows the bubbles to coalesce. The coalescence pattern is more complex for the case of eight bubbles, which strongly depends on the Eotvos number.

Exact compact breather-like solutions of two-dimensional Fermi-Pasta-Ulam lattice

International Nuclear Information System (INIS)

Sarkar, Ranja; Dey, Bishwajyoti

2006-01-01

We demonstrate that two-dimensional Fermi-Pasta-Ulam lattice support exact discrete compact breather-like solutions. We also find exact compact breather solutions of the same lattice in presence of long-range interaction with r -s dependence on the distance in the continuum limit. The usefulness of these solutions for energy localization and transport in various physical systems are discussed. (letter to the editor)

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies

Science.gov (United States)

Küllmer, Knut; Krämer, Andreas; Joppich, Wolfgang; Reith, Dirk; Foysi, Holger

2018-02-01

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995), 10.1007/BF02179985] and the explicit forcing model [M. L. Porter et al., Phys. Rev. E 86, 036701 (2012), 10.1103/PhysRevE.86.036701], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies.

Science.gov (United States)

Küllmer, Knut; Krämer, Andreas; Joppich, Wolfgang; Reith, Dirk; Foysi, Holger

2018-02-01

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995)JSTPBS0022-471510.1007/BF02179985] and the explicit forcing model [M. L. Porter et al., Phys. Rev. E 86, 036701 (2012)PLEEE81539-375510.1103/PhysRevE.86.036701], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

A note on the Lattice Boltzmann Method Beyond the Chapman Enskog Limits

NARCIS (Netherlands)

Sbragaglia, M.; Succi, S.

2006-01-01

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the lattice Boltzmann method, can provide semi-quantitative results also

LB3D : A parallel implementation of the Lattice-Boltzmann method for simulation of interacting amphiphilic fluids

NARCIS (Netherlands)

Schmieschek, S.; Shamardin, L.; Frijters, S.; Krüger, T.; Schiller, U.D.; Harting, J.; Coveney, P.V.

2017-01-01

We introduce the lattice-Boltzmann code LB3D, version 7.1. Building on a parallel program and supporting tools which have enabled research utilising high performance computing resources for nearly two decades, LB3D version 7 provides a subset of the research code functionality as an open source

Lattice-Boltzmann Modeling of Community Challenge MicrofluidicExperiments to Evaluate the Effects of Wettability on Two-Fluid Flowin Porous Media

Science.gov (United States)

Miller, C. T.; McClure, J. E.; Bruning, K.

2017-12-01

Variations in the wettability of a solid material are well known to affect the flow of two fluids in a porous media. However, thesemechanisms have not been modeled with high fidelity at the microscale and such mechanisms are typically not included in macroscalemodels. Recent experimental work by Zhao, MacMinn, and Juanes published in the Proceedings of the National Academy of Sciences(2016) has investigated two-fluid displacement in microfluidic cells. Displacement patterns were investigated as a function of thecontact angle and the capillary number for both drainage and imbibition. These results yielded new mechanistic understanding ofprocesses such as pore filling and post bridging, which were imaged at high resolution. In a challenge to the pore-scale modeling community,the authors of this work released their experimental data and encouraged an international set of modeling research groups tosimulate the conditions that were experimentally observed. The intent is to compare the results that materialize to shed new light on thestate-of-science in pore-scale simulation of these challenging and interesting flow systems. In this work, we summarize the experimentalfindings and report on initial efforts to simulate these community challenge experiments using a high-resolution lattice-Boltzmann method(LBM). A three-dimensional, multiple-relaxation-time color model based on a 19-site lattice is advanced in this work to matchexperimental conditions in a novel manner. A computational approach is implemented for the LBM method on hybrid CPU-GPU nodes and shown toscale near optimally. A new algorithm is described to match experimental boundary conditions. A grid-resolution study is performedto determine the resolution needed to determine grid-independent numerical approximations. Finally, the LBM simulation results arecompared to the highly resolved microfluidic experiments, displacement mechanisms are investigated, and observations and analysis of thetopological state

Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology

Science.gov (United States)

Ba, Yan; Wang, Ningning; Liu, Haihu; Li, Qiang; He, Guoqiang

2018-03-01

In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.

GPU accelerated study of heat transfer and fluid flow by lattice Boltzmann method on CUDA

Science.gov (United States)

Ren, Qinlong

Lattice Boltzmann method (LBM) has been developed as a powerful numerical approach to simulate the complex fluid flow and heat transfer phenomena during the past two decades. As a mesoscale method based on the kinetic theory, LBM has several advantages compared with traditional numerical methods such as physical representation of microscopic interactions, dealing with complex geometries and highly parallel nature. Lattice Boltzmann method has been applied to solve various fluid behaviors and heat transfer process like conjugate heat transfer, magnetic and electric field, diffusion and mixing process, chemical reactions, multiphase flow, phase change process, non-isothermal flow in porous medium, microfluidics, fluid-structure interactions in biological system and so on. In addition, as a non-body-conformal grid method, the immersed boundary method (IBM) could be applied to handle the complex or moving geometries in the domain. The immersed boundary method could be coupled with lattice Boltzmann method to study the heat transfer and fluid flow problems. Heat transfer and fluid flow are solved on Euler nodes by LBM while the complex solid geometries are captured by Lagrangian nodes using immersed boundary method. Parallel computing has been a popular topic for many decades to accelerate the computational speed in engineering and scientific fields. Today, almost all the laptop and desktop have central processing units (CPUs) with multiple cores which could be used for parallel computing. However, the cost of CPUs with hundreds of cores is still high which limits its capability of high performance computing on personal computer. Graphic processing units (GPU) is originally used for the computer video cards have been emerged as the most powerful high-performance workstation in recent years. Unlike the CPUs, the cost of GPU with thousands of cores is cheap. For example, the GPU (GeForce GTX TITAN) which is used in the current work has 2688 cores and the price is only 1

Lattice Boltzmann simulation of viscoelastic flow past a confined free rotating cylinder

Science.gov (United States)

Xia, Yi; Zhang, Peijie; Lin, Jianzhong; Ku, Xiaoke; Nie, Deming

2018-05-01

To study the dynamics of rigid body immersed in viscoelastic fluid, an Oldroyd-B fluid flow past an eccentrically situated, free rotating cylinder in a two-dimensional (2D) channel is simulated by a novel lattice Boltzmann method. Two distribution functions are employed, one of which is aimed to solve Navier-Stokes equation and the other to the constitutive equation, respectively. The unified interpolation bounce-back scheme is adopted to treat the moving curved boundary of cylinder, and the novel Galilean invariant momentum exchange method is utilized to obtain the hydrodynamic force and torque exerted on the cylinder. Results show that the center-fixed cylinder rotates inversely in the direction where a cylinder immersed in Newtonian fluid do, which generates a centerline-oriented lift force according to Magnus effect. The cylinder’s eccentricity, flow inertia, fluid elasticity and viscosity would affect the rotation of cylinder in different ways. The cylinder rotates more rapidly when located farther away from the centerline, and slows down when it is too close to the wall. The rotation frequency decreases with increasing Reynolds number, and larger rotation frequency responds to larger Weissenberg number and smaller viscosity ratio, indicating that the fluid elasticity and low solvent viscosity accelerates the flow-induced rotation of cylinder.

Grid refinement for aeroacoustics in the lattice Boltzmann method: A directional splitting approach

Science.gov (United States)

Gendre, Félix; Ricot, Denis; Fritz, Guillaume; Sagaut, Pierre

2017-08-01

This study focuses on grid refinement techniques for the direct simulation of aeroacoustics, when using weakly compressible lattice Boltzmann models, such as the D3Q19 athermal velocity set. When it comes to direct noise computation, very small errors on the density or pressure field may have great negative consequences. Even strong acoustic density fluctuations have indeed a clearly lower amplitude than the hydrodynamic ones. This work deals with such very weak spurious fluctuations that emerge when a vortical structure crosses a refinement interface, which may contaminate the resulting aeroacoustic field. We show through an extensive literature review that, within the framework described above, this issue has never been addressed before. To tackle this problem, we develop an alternative algorithm and compare its behavior to a classical one, which fits our in-house vertex-centered data structure. Our main idea relies on a directional splitting of the continuous discrete velocity Boltzmann equation, followed by an integration over specific characteristics. This method can be seen as a specific coupling between finite difference and lattice Boltzmann, locally on the interface between the two grids. The method is assessed considering two cases: an acoustic pulse and a convected vortex. We show how very small errors on the density field arise and propagate throughout the domain when a vortical flow crosses the refinement interface. We also show that an increased free stream Mach number (but still within the weakly compressible regime) strongly deteriorates the situation, although the magnitude of the errors may remain negligible for purely aerodynamic studies. A drastically reduced level of error for the near-field spurious noise is obtained with our approach, especially for under-resolved simulations, a situation that is crucial for industrial applications. Thus, the vortex case is proved useful for aeroacoustic validations of any grid refinement algorithm.

Numerical investigation of flows in Czochralski crystal growth by an axisymmetric lattice Boltzmann method

CERN Document Server

Peng, Y; Chew, Y T; Qiu, J

2003-01-01

An alternative new method called lattice Boltzmann method (LBM) is applied in this work to simulate the flows in Czochralski crystal growth, which is one of the widely used prototypical systems for melt-crystal growth. The standard LBM can only be used in Cartesian coordinate system and we extend it to be applicable to this axisymmetric thermal flow problem, avoiding the use of three-dimensional LBM on Cartesian coordinate system. The extension is based on the following idea. By inserting position and time dependent source terms into the evolution equation of standard LBM, the continuity and NS equations on the cylindrical coordinate system can be recovered. Our extension is validated by its application to the benchmark problem suggested by Wheeler .

Numerical investigation of flows in Czochralski crystal growth by an axisymmetric lattice Boltzmann method

Science.gov (United States)

Peng, Y.; Shu, C.; Chew, Y. T.; Qiu, J.

2003-03-01

An alternative new method called lattice Boltzmann method (LBM) is applied in this work to simulate the flows in Czochralski crystal growth, which is one of the widely used prototypical systems for melt-crystal growth. The standard LBM can only be used in Cartesian coordinate system and we extend it to be applicable to this axisymmetric thermal flow problem, avoiding the use of three-dimensional LBM on Cartesian coordinate system. The extension is based on the following idea. By inserting position and time dependent source terms into the evolution equation of standard LBM, the continuity and NS equations on the cylindrical coordinate system [1] can be recovered. Our extension is validated by its application to the benchmark problem suggested by Wheeler [2].

Numerical investigation of flows in Czochralski crystal growth by an axisymmetric lattice Boltzmann method

International Nuclear Information System (INIS)

Peng, Y.; Shu, C.; Chew, Y.T.; Qiu, J.

2003-01-01

An alternative new method called lattice Boltzmann method (LBM) is applied in this work to simulate the flows in Czochralski crystal growth, which is one of the widely used prototypical systems for melt-crystal growth. The standard LBM can only be used in Cartesian coordinate system and we extend it to be applicable to this axisymmetric thermal flow problem, avoiding the use of three-dimensional LBM on Cartesian coordinate system. The extension is based on the following idea. By inserting position and time dependent source terms into the evolution equation of standard LBM, the continuity and NS equations on the cylindrical coordinate system can be recovered. Our extension is validated by its application to the benchmark problem suggested by Wheeler

Lattice Boltzmann method used to simulate particle motion in a conduit

Czech Academy of Sciences Publication Activity Database

Dolanský, Jindřich; Chára, Zdeněk; Vlasák, Pavel; Kysela, Bohuš

2017-01-01

Roč. 65, č. 2 (2017), s. 105-113 ISSN 0042-790X R&D Projects: GA ČR GA15-18870S Institutional support: RVO:67985874 Keywords : Lattice Boltzmann method * particle motion * particle–fluid interaction * PIV * particle tracking Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.654, year: 2016

Application of the lattice Boltzmann method to transient conduction and radiation heat transfer in cylindrical media

International Nuclear Information System (INIS)

Chaabane, Raoudha; Askri, Faouzi; Ben Nasrallah, Sassi

2011-01-01

In this paper, the lattice Boltzmann method (LBM) is applied to solve the energy equation of a transient conduction-radiation heat transfer problem in a two-dimensional cylindrical enclosure filled with an emitting, absorbing and scattering media. The control volume finite element method (CVFEM) is used to obtain the radiative information. To demonstrate the workability of the LBM in conjunction with the CVFEM to conduction-radiation problems in cylindrical media, the energy equation of the same problem is also solved using the finite difference method (FDM). The effects of different parameters, such as the grid size, the scattering albedo, the extinction coefficient and the conduction-radiation parameter on temperature distribution within the medium are studied. Results of the present work are compared with those available in the literature. LBM-CVFEM results are also compared with those given by the FDM-CVFEM. In all cases, good agreement has been obtained.

A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

KAUST Repository

Allen, Rebecca; Reis, Tim; Sun, Shuyu

2013-01-01

-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE

Backlund transformations and three-dimensional lattice equations

NARCIS (Netherlands)

Nijhoff, F.W.; Capel, H.W.; Wiersma, G.L.; Quispel, G.R.W.

1984-01-01

A (nonlocal) linear integral equation is studied, which allows for Bäcklund transformations in the measure. The compatibility of three of these transformations leads to an integrable nonlinear three-dimensional lattice equation. In appropriate continuum limits the two-dimensional Toda-lattice

Effects of density and force discretizations on spurious velocities in lattice Boltzmann equation for two-phase flows

KAUST Repository

Xiong, Yuan

2014-04-28

Spurious current emerging in the vicinity of phase interfaces is a well-known disadvantage of the lattice Boltzmann equation (LBE) for two-phase flows. Previous analysis shows that this unphysical phenomenon comes from the force imbalance at discrete level inherited in LBE (Guo et al 2011 Phys. Rev. E 83 036707). Based on the analysis of the LBE free of checkerboard effects, in this work we further show that the force imbalance is caused by the different discretization stencils: the implicit one from the streaming process and the explicit one from the discretization of the force term. Particularly, the total contribution includes two parts, one from the difference between the intrinsically discretized density (or ideal gas pressure) gradient and the explicit ones in the force term, and the other from the explicit discretized chemical potential gradients in the intrinsically discretized force term. The former contribution is a special feature of LBE which was not realized previously.

An Eulerian description of the streaming process in the lattice Boltzmann equation

CERN Document Server

Lee Tae Hun

2003-01-01

This paper presents a novel strategy for solving discrete Boltzmann equation (DBE) for simulation of fluid flows. This strategy splits the solution procedure into streaming and collision steps as in the lattice Boltzmann equation (LBE) method. The streaming step can then be carried out by solving pure linear advection equations in an Eulerian framework. This offers two significant advantages over previous methods. First, the relationship between the relaxation parameter and the discretization of the collision term developed from the LBE method is directly applicable to the DBE method. The resulting DBE collision step remains local and poses no constraint on time step. Second, decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes. An implicit unstructured DBE method is constructed based on this strategy and is evaluated using several test cases of flow over a backward-facing step, lid-driven cavity flow, and flow past a circul...

Lattice Boltzmann method for multi-component, non-continuum mass diffusion

International Nuclear Information System (INIS)

Joshi, Abhijit S; Peracchio, Aldo A; Grew, Kyle N; Chiu, Wilson K S

2007-01-01

Recently, there has been a great deal of interest in extending the lattice Boltzmann method (LBM) to model transport phenomena in the non-continuum regime. Most of these studies have focused on single-component flows through simple geometries. This work examines an ad hoc extension of a recently developed LBM model for multi-component mass diffusion (Joshi et al 2007 J. Phys. D: Appl. Phys. 40 2961) to model mass diffusion in the non-continuum regime. In order to validate the method, LBM results for ternary diffusion in a two-dimensional channel are compared with predictions of the dusty gas model (DGM) over a range of Knudsen numbers. A calibration factor based on the DGM is used in the LBM to correlate Knudsen diffusivity to pore size. Results indicate that the LBM can be a useful tool for predicting non-continuum mass diffusion (Kn > 0.001), but additional research is needed to extend the range of applicability of the algorithm for a larger parameter space. Guidelines are given on using the methodology described in this work to model non-continuum mass transport in more complex geometries where the DGM is not easily applicable. In addition, the non-continuum LBM methodology can be extended to three-dimensions. An envisioned application of this technique is to model non-continuum mass transport in porous solid oxide fuel cell electrodes

Non-perturbative effects in two-dimensional lattice O(N) models

International Nuclear Information System (INIS)

Ogilvie, M.C.; Maryland Univ., College Park

1981-01-01

Non-abelian analogues of Kosterlitz-Thouless vortices may have important effects in two-dimensional lattice spin systems with O(N) symmetries. Renormalization group equations which include these effects are developed in two ways. The first set of equations extends the renormalization group equations of Kosterlitz to 0(N) spin systems, in a form suggested by Cardy and Hamber. The second is derived from a Villain-type 0(N) model using Migdal's recursion relations. Using these equations, the part played by topological excitations int he crossover from weak to strong coupling behavior is studied. Another effect which influences crossover behavior is also discussed; irrelevant operators which occur naturally in lattice theories can make important contributions to the renormalization group flow in the crossover region. When combined with conventional perturbative results, these two effects may explain the observed crossover behavior of these models. (orig.)

Hofstadter's butterfly in a two-dimensional lattice consisting of two sublattices

Energy Technology Data Exchange (ETDEWEB)

Vugalter, G A; Pastukhov, A S [Department of Physics, Nizhny Novgorod State University, 23 Gagarin Avenue, Nizhny Novgorod 603950 (Russian Federation)

2004-06-04

Harper's equations for simple and complex two-dimensional lattices subject to a magnetic field have been derived in the tight-binding approximation. In our derivation we do not neglect the influence of the magnetic field on the electron eigenfunctions and eigenvalues in isolated atoms. Using a variational procedure for finding eigenfunctions and eigenvalues, we have self-consistently obtained Hofstadter's butterflies. Even for a simple square lattice Hofstadter's butterfly differs from the butterfly obtained in the case in which the influence of the magnetic field on the electron eigenvalues and eigenfunctions in isolated atoms is not taken into account.

Numerical simulation of the droplet formation in a cross-junction microchannel using the Lattice Boltzmann Method

International Nuclear Information System (INIS)

Li, Zilu; Kang, Jinfen; Park, Jae Hyun; Suh, Yong Kweon

2007-01-01

This study describes the numerical simulation of two-dimensional droplet formation and the following motion by using the Lattice Boltzmann Method (LBM) with the phase field equation. The free energy model is used to treat the interfacial force and the deformation of a binary fluid system, drawn into a cross-junction microchannel. While one fluid is introduced through the central inlet channel, the other fluid is drawn into the main channel through the two vertical inlet channels. Due to the effect of surface tension on the interface between the two fluids, the droplets of the first fluid are formed near the cross-junction. The aim in this investigation is to examine the applicability of LBM to the numerical analysis of the droplet formation and its motion in the microchannel. It was found from comparison with the experimentally visualized patterns that LBM with the free energy model can reproduce the droplet formation successfully. However because of the stability problem which is intrinsic for high surface-tension cases, it requires a very long computational time. This issue is to be resolved in the future.

Numerical simulation of the droplet formation in a cross-junction microchannel using the Lattice Boltzmann Method

International Nuclear Information System (INIS)

Li, Zi Lu; Kang, Jin Fen; Park, Jae Hyun; Suh, Yong Kweon

2007-01-01

This study describes the numerical simulation of two-dimensional droplet formation and the following motion by using the Lattice Boltzmann Method (LBM) with the phase field equation. The free energy model is used to treat the interfacial force and the deformation of a binary fluid system, drawn into a cross-junction microchannel. While one fluid is introduced through the central inlet channel, the other fluid is drawn into the main channel through the two vertical inlet channels. Due to the effect of surface tension on the interface between the two fluids, the droplets of the first fluid are formed near the cross-junction. The aim in this investigation is to examine the applicability of LBM to the numerical analysis of the droplet formation and its motion in the microchannel. It was found from comparison with the experimentally visualized patterns that LBM with the free energy model can reproduce the droplet formation successfully. However because of the stability problem which is intrinsic for high surface-tension cases, it requires a very long computational time. This issue is to be resolved in the future

Flux Limiter Lattice Boltzmann Scheme Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

International Nuclear Information System (INIS)

Gan Yanbiao; Li Yingjun; Xu Aiguo; Zhang Guangcai

2011-01-01

We further develop the lattice Boltzmann (LB) model [Physica A 382 (2007) 502] for compressible flows from two aspects. Firstly, we modify the Bhatnagar-Gross-Krook (BGK) collision term in the LB equation, which makes the model suitable for simulating flows with different Prandtl numbers. Secondly, the flux limiter finite difference (FLFD) scheme is employed to calculate the convection term of the LB equation, which makes the unphysical oscillations at discontinuities be effectively suppressed and the numerical dissipations be significantly diminished. The proposed model is validated by recovering results of some well-known benchmarks, including (i) The thermal Couette flow; (ii) One- and two-dimensional Riemann problems. Good agreements are obtained between LB results and the exact ones or previously reported solutions. The flexibility, together with the high accuracy of the new model, endows the proposed model considerable potential for tracking some long-standing problems and for investigating nonlinear nonequilibrium complex systems. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Application of a Steady Meandering River with Piers Using a Lattice Boltzmann Sub-Grid Model in Curvilinear Coordinate Grid

Directory of Open Access Journals (Sweden)

Liping Chen

2018-05-01

Full Text Available A sub-grid multiple relaxation time (MRT lattice Boltzmann model with curvilinear coordinates is applied to simulate an artificial meandering river. The method is based on the D2Q9 model and standard Smagorinsky sub-grid scale (SGS model is introduced to simulate meandering flows. The interpolation supplemented lattice Boltzmann method (ISLBM and the non-equilibrium extrapolation method are used for second-order accuracy and boundary conditions. The proposed model was validated by a meandering channel with a 180° bend and applied to a steady curved river with piers. Excellent agreement between the simulated results and previous computational and experimental data was found, showing that MRT-LBM (MRT lattice Boltzmann method coupled with a Smagorinsky sub-grid scale (SGS model in a curvilinear coordinates grid is capable of simulating practical meandering flows.

Simulation of turbulent flow over staggered tube bundles using multi-relaxation time lattice Boltzmann method

International Nuclear Information System (INIS)

Park, Jong Woon; Choi, Hyun Gyung

2014-01-01

A turbulent fluid flow over staggered tube bundles is of great interest in many engineering fields including nuclear fuel rods, heat exchangers and especially a gas cooled reactor lower plenum. Computational methods have evolved for the simulation of such flow for decades and lattice Boltzmann method (LBM) is one of the attractive methods due to its sound physical basis and ease of computerization including parallelization. In this study to find computational performance of the LBM in turbulent flows over staggered tubes, a fluid flow analysis code employing multi-relaxation time lattice Boltzmann method (MRT-LBM) is developed based on a 2-dimensional D2Q9 lattice model and classical sub-grid eddy viscosity model of Smagorinsky. As a first step, fundamental performance MRT-LBM is investigated against a standard problem of a flow past a cylinder at low Reynolds number in terms of drag forces. As a major step, benchmarking of the MRT-LBM is performed over a turbulent flow through staggered tube bundles at Reynolds number of 18,000. For a flow past a single cylinder, the accuracy is validated against existing experimental data and previous computations in terms of drag forces on the cylinder. Mainly, the MRT-LBM computation for a flow through staggered tube bundles is performed and compared with experimental data and general purpose computational fluid dynamic (CFD) analyses with standard k-ω turbulence and large eddy simulation (LES) equipped with turbulence closures of Smagrinsky-Lilly and wall-adapting local eddy-viscosity (WALE) model. The agreement between the experimental and the computational results from the present MRT-LBM is found to be reasonably acceptable and even comparable to the LES whereas the computational efficiency is superior. (orig.)

Simulation of turbulent flow over staggered tube bundles using multi-relaxation time lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Park, Jong Woon; Choi, Hyun Gyung [Dongguk Univ., Gyeongju (Korea, Republic of). Nuclear and Energy Engineering Dept.

2014-02-15

A turbulent fluid flow over staggered tube bundles is of great interest in many engineering fields including nuclear fuel rods, heat exchangers and especially a gas cooled reactor lower plenum. Computational methods have evolved for the simulation of such flow for decades and lattice Boltzmann method (LBM) is one of the attractive methods due to its sound physical basis and ease of computerization including parallelization. In this study to find computational performance of the LBM in turbulent flows over staggered tubes, a fluid flow analysis code employing multi-relaxation time lattice Boltzmann method (MRT-LBM) is developed based on a 2-dimensional D2Q9 lattice model and classical sub-grid eddy viscosity model of Smagorinsky. As a first step, fundamental performance MRT-LBM is investigated against a standard problem of a flow past a cylinder at low Reynolds number in terms of drag forces. As a major step, benchmarking of the MRT-LBM is performed over a turbulent flow through staggered tube bundles at Reynolds number of 18,000. For a flow past a single cylinder, the accuracy is validated against existing experimental data and previous computations in terms of drag forces on the cylinder. Mainly, the MRT-LBM computation for a flow through staggered tube bundles is performed and compared with experimental data and general purpose computational fluid dynamic (CFD) analyses with standard k-ω turbulence and large eddy simulation (LES) equipped with turbulence closures of Smagrinsky-Lilly and wall-adapting local eddy-viscosity (WALE) model. The agreement between the experimental and the computational results from the present MRT-LBM is found to be reasonably acceptable and even comparable to the LES whereas the computational efficiency is superior. (orig.)

Lattice Boltzmann simulations of the permeability and capillary adsorption of cement model microstructures

Energy Technology Data Exchange (ETDEWEB)

Zalzale, M. [Laboratory of Construction Materials, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne (Switzerland); McDonald, P.J., E-mail: p.mcdonald@surrey.ac.uk [Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH (United Kingdom)

2012-12-15

The lattice Boltzmann method is used to investigate the permeability of microstructures of cement pastes generated using the numerical models CEMHYD3D (Bentz, 1997) and {mu}IC (Bishnoi and Scrivener, 2009). Results are reported as a function of paste water-to-cement ratio and degree of hydration. The permeability decreases with increasing hydration and decreasing water-to-cement ratio in agreement with experiment. However the permeability is larger than the experimental data recorded using beam bending methods (Vichit-Vadakan and Scherer, 2002). Notwithstanding, the lattice Boltzmann results compare favourably with alternate numerical methods of permeability calculation for cement model microstructures. In addition, we show early results for the liquid/vapour capillary adsorption and desorption isotherms in the same model {mu}IC structures. The broad features of the experimental capillary porosity isotherm are reproduced, although further work is required to adequately parameterise the model.

Surface Reconstruction-Induced Coincidence Lattice Formation Between Two-Dimensionally Bonded Materials and a Three-Dimensionally Bonded Substrate

NARCIS (Netherlands)

Boschker, Jos E.; Momand, Jamo; Bragaglia, Valeria; Wang, Ruining; Perumal, Karthick; Giussani, Alessandro; Kooi, Bart J.; Riechert, Henning; Calarco, Raffaella

Sb2Te3 films are used for studying the epitaxial registry between two-dimensionally bonded (2D) materials and three-dimensional bonded (3D) substrates. In contrast to the growth of 3D materials, it is found that the formation of coincidence lattices between Sb2Te3 and Si(111) depends on the geometry

Controlling spatiotemporal chaos in one- and two-dimensional coupled logistic map lattices

International Nuclear Information System (INIS)

Astakhov, V.V.; Anishchenko, V.S.; Strelkova, G.I.; Shabunin, A.V.

1996-01-01

A method of control of spatiotemporal chaos in lattices of coupled maps is proposed in this work. Forms of spatiotemporal perturbations of a system parameter are analytically determined for one- and two-dimensional logistic map lattices with different kinds of coupling to stabilize chosen spatiotemporal states previously unstable. The results are illustrated by numerical simulation. Controlled transition from the regime of spatiotemporal chaos to the previously chosen regular spatiotemporal patterns is demonstrated. copyright 1996 American Institute of Physics

Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi—Pasta—Ulam lattice

International Nuclear Information System (INIS)

Xu Quan; Tian Qiang

2013-01-01

Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi—Pasta—Ulam (FPU) lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too. (condensed matter: structural, mechanical, and thermal properties)

N = 2 two dimensional Wess-Zumino model on the lattice

International Nuclear Information System (INIS)

Elitzur, S.; Schwimmer, A.

1983-04-01

A lattice version of the N = 2 SUSY two dimensional Wess-Zumino model was constructed and studied. The correct continuum limit is checked in perturbation theory. The strong coupling limit is defined and investigated. We find that the ground state of the model has zero energy and infinite degeneracy. The connection between this degeneracy and the properties of the Nicolai-Parisi-Sourlas transformation is discussed. (author)

Entropic multiple-relaxation-time multirange pseudopotential lattice Boltzmann model for two-phase flow

Science.gov (United States)

Qin, Feifei; Mazloomi Moqaddam, Ali; Kang, Qinjun; Derome, Dominique; Carmeliet, Jan

2018-03-01

An entropic multiple-relaxation-time lattice Boltzmann approach is coupled to a multirange Shan-Chen pseudopotential model to study the two-phase flow. Compared with previous multiple-relaxation-time multiphase models, this model is stable and accurate for the simulation of a two-phase flow in a much wider range of viscosity and surface tension at a high liquid-vapor density ratio. A stationary droplet surrounded by equilibrium vapor is first simulated to validate this model using the coexistence curve and Laplace's law. Then, two series of droplet impact behavior, on a liquid film and a flat surface, are simulated in comparison with theoretical or experimental results. Droplet impact on a liquid film is simulated for different Reynolds numbers at high Weber numbers. With the increase of the Sommerfeld parameter, onset of splashing is observed and multiple secondary droplets occur. The droplet spreading ratio agrees well with the square root of time law and is found to be independent of Reynolds number. Moreover, shapes of simulated droplets impacting hydrophilic and superhydrophobic flat surfaces show good agreement with experimental observations through the entire dynamic process. The maximum spreading ratio of a droplet impacting the superhydrophobic flat surface is studied for a large range of Weber numbers. Results show that the rescaled maximum spreading ratios are in good agreement with a universal scaling law. This series of simulations demonstrates that the proposed model accurately captures the complex fluid-fluid and fluid-solid interfacial physical processes for a wide range of Reynolds and Weber numbers at high density ratios.

Lattice Boltzmann simulation of endothermal catalytic reaction in catalyst porous media

International Nuclear Information System (INIS)

Li Xunfeng; Cai Jun; Xin Fang; Huai Xiulan; Guo Jiangfeng

2013-01-01

Gas catalytic reaction in a fixed bed reactor is a general process in chemical industry. The chemical reaction process involves the complex multi-component flow, heat and mass transfer coupling chemical reaction in the catalyst porous structure. The lattice Boltzmann method is developed to simulate the complex process of the surface catalytic reaction in the catalyst porous media. The non-equilibrium extrapolation method is used to treat the boundaries. The porous media is structured by Sierpinski carpet fractal structure. The velocity correction is adopted on the reaction surface. The flow, temperature and concentration fields calculated by the lattice Boltzmann method are compared with those computed by the CFD software. The effects of the inlet velocity, porosity and inlet components ratio on the conversion are also studied. Highlights: ► LBM is developed to simulate the surface catalytic reaction. ► The Sierpinski carpet structure is used to construct the porous media. ► The LBM results are in agreement with the CFD predictions. ► Velocity, temperature and concentration fields are obtained. ► Effects of the velocity, porosity and concentration on conversion are analyzed.

Mixed convection in inclined lid driven cavity by Lattice Boltzmann Method and heat flux boundary condition

International Nuclear Information System (INIS)

D'Orazio, A; Karimipour, A; Nezhad, A H; Shirani, E

2014-01-01

Laminar mixed convective heat transfer in two-dimensional rectangular inclined driven cavity is studied numerically by means of a double population thermal Lattice Boltzmann method. Through the top moving lid the heat flux enters the cavity whereas it leaves the system through the bottom wall; side walls are adiabatic. The counter-slip internal energy density boundary condition, able to simulate an imposed non zero heat flux at the wall, is applied, in order to demonstrate that it can be effectively used to simulate heat transfer phenomena also in case of moving walls. Results are analyzed over a range of the Richardson numbers and tilting angles of the enclosure, encompassing the dominating forced convection, mixed convection, and dominating natural convection flow regimes. As expected, heat transfer rate increases as increases the inclination angle, but this effect is significant for higher Richardson numbers, when buoyancy forces dominate the problem; for horizontal cavity, average Nusselt number decreases with the increase of Richardson number because of the stratified field configuration

An Implicit Scheme of Lattice Boltzmann Method for Sine-Gordon Equation

International Nuclear Information System (INIS)

Hui-Lin, Lai; Chang-Feng, Ma

2008-01-01

We establish an implicit scheme of lattice Boltzmann method for simulating the sine-Gordon equation, which can be transformed into the explicit one, so the computation of the scheme is simple. Moreover, the parameter θ of the implicit scheme is independent of the relaxation time, which makes the model more flexible. The numerical results show that this method is very effective. (fundamental areas of phenomenology (including applications))

Invasion percolation of single component, multiphase fluids with lattice Boltzmann models

International Nuclear Information System (INIS)

Sukop, M.C.; Or, Dani

2003-01-01

Application of the lattice Boltzmann method (LBM) to invasion percolation of single component multiphase fluids in porous media offers an opportunity for more realistic modeling of the configurations and dynamics of liquid/vapor and liquid/solid interfaces. The complex geometry of connected paths in standard invasion percolation models arises solely from the spatial arrangement of simple elements on a lattice. In reality, fluid interfaces and connectivity in porous media are naturally controlled by the details of the pore geometry, its dynamic interaction with the fluid, and the ambient fluid potential. The multiphase LBM approach admits realistic pore geometry derived from imaging techniques and incorporation of realistic hydrodynamics into invasion percolation models

Multiscale Lattice Boltzmann method for flow simulations in highly heterogenous porous media

KAUST Repository

Li, Jun

2013-01-01

A lattice Boltzmann method (LBM) for flow simulations in highly heterogeneous porous media at both pore and Darcy scales is proposed in the paper. In the pore scale simulations, flow of two phases (e.g., oil and gas) or two immiscible fluids (e.g., water and oil) are modeled using cohesive or repulsive forces, respectively. The relative permeability can be computed using pore-scale simulations and seamlessly applied for intermediate and Darcy-scale simulations. A multiscale LBM that can reduce the computational complexity of existing LBM and transfer the information between different scales is implemented. The results of coarse-grid, reduced-order, simulations agree very well with the averaged results obtained using fine grid.

Flux Limiter Lattice Boltzmann for Compressible Flows

International Nuclear Information System (INIS)

Chen Feng; Li Yingjun; Xu Aiguo; Zhang Guangcai

2011-01-01

In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann (LB) model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Improvement of the instability of compressible lattice Boltzmann model by shockdetecting sensor

International Nuclear Information System (INIS)

Esfahanian, Vahid; Ghadyani, Mohsen

2015-01-01

Recently, lattice Boltzmann method (LBM) has drawn attention as an alternative and promising numerical technique for simulating fluid flows. The stability of LBM is a challenging problem in the simulation of compressible flows with different types of embedded discontinuities. This study, proposes a complementary scheme for simulating inviscid flows by a compressible lattice Boltzmann model in order to improve the instability using a shock-detecting procedure. The advantages and disadvantages of using a numerical hybrid filter on the primitive or conservative variables, in addition to, macroscopic or mesoscopic variables are investigated. The study demonstrates that the robustness of the utilized LB model is improved for inviscid compressible flows by implementation of the complementary scheme on mesoscopic variables. The validity of the procedure to capture shocks and resolve contact discontinuity and rarefaction waves in well-known benchmark problems is investigated. The numerical results show that the scheme is capable of generating more robust solutions in the simulation of compressible flows and prevents the formation of oscillations. Good agreements are obtained for all test cases.

Improvement of the instability of compressible lattice Boltzmann model by shockdetecting sensor

Energy Technology Data Exchange (ETDEWEB)

Esfahanian, Vahid [University of Tehran, Tehran (Iran, Islamic Republic of); Ghadyani, Mohsen [Islamic Azad University, Tehran (Iran, Islamic Republic of)

2015-05-15

Recently, lattice Boltzmann method (LBM) has drawn attention as an alternative and promising numerical technique for simulating fluid flows. The stability of LBM is a challenging problem in the simulation of compressible flows with different types of embedded discontinuities. This study, proposes a complementary scheme for simulating inviscid flows by a compressible lattice Boltzmann model in order to improve the instability using a shock-detecting procedure. The advantages and disadvantages of using a numerical hybrid filter on the primitive or conservative variables, in addition to, macroscopic or mesoscopic variables are investigated. The study demonstrates that the robustness of the utilized LB model is improved for inviscid compressible flows by implementation of the complementary scheme on mesoscopic variables. The validity of the procedure to capture shocks and resolve contact discontinuity and rarefaction waves in well-known benchmark problems is investigated. The numerical results show that the scheme is capable of generating more robust solutions in the simulation of compressible flows and prevents the formation of oscillations. Good agreements are obtained for all test cases.

A multi-GPU implementation of a D2Q37 lattice Boltzmann code

NARCIS (Netherlands)

Biferale, L.; Mantovani, F.; Pivanti, M.; Pozzati, F.; Sbragaglia, M.; Scagliarini, Andrea; Schifano, S.F.; Toschi, F.; Tripiccione, R.; Wyrzykowski, R.; Dongarra, J.; Karczewski, K.; Wasniewski, J.

2012-01-01

We describe a parallel implementation of a compressible Lattice Boltzmann code on a multi-GPU cluster based on Nvidia Fermi processors. We analyze how to optimize the algorithm for GP-GPU architectures, describe the implementation choices that we have adopted and compare our performance results with

Calibration of modified parallel-plate rheometer through calibrated oil and lattice Boltzmann simulation

DEFF Research Database (Denmark)

Ferraris, Chiara F; Geiker, Mette Rica; Martys, Nicos S

2007-01-01

inapplicable here. This paper presents the analysis of a modified parallel plate rheometer for measuring cement mortar and propose a methodology for calibration using standard oils and numerical simulation of the flow. A lattice Boltzmann method was used to simulate the flow in the modified rheometer, thus...

Calibrating the Shan-Chen lattice Boltzmann model for immiscible displacement in porous media

DEFF Research Database (Denmark)

Christensen, Britt Stenhøj Baun; Schaap, M.G.; Wildenschild, D.

2006-01-01

The lattice Boltzmann (LB) modeling technique is increasingly being applied in a variety of fields where computational fluid dynamics are investigated. In our field of interest, environmentally related flow processes in porous media, the use of the LB method is still not common. For the LB...

Essentially Entropic Lattice Boltzmann Model

Science.gov (United States)

Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh

2017-12-01

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

Modeling heat transfer in supercritical fluid using the lattice Boltzmann method.

Science.gov (United States)

Házi, Gábor; Márkus, Attila

2008-02-01

A lattice Boltzmann model has been developed to simulate heat transfer in supercritical fluids. A supercritical viscous fluid layer between two plates heated from the bottom has been studied. It is demonstrated that the model can be used to study heat transfer near the critical point where the so-called piston effect speeds up the transfer of heat and results in homogeneous heating in the bulk of the layer. We have also studied the onset of convection in a Rayleigh-Bénard configuration. It is shown that our model can well predict qualitatively the onset of convection near the critical point, where there is a crossover between the Rayleigh and Schwarzschild criteria.

Non-Newtonian particulate flow simulation: A direct-forcing immersed boundary-lattice Boltzmann approach

Science.gov (United States)

Amiri Delouei, A.; Nazari, M.; Kayhani, M. H.; Kang, S. K.; Succi, S.

2016-04-01

In the current study, a direct-forcing immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB-NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonian fluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.

Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

KAUST Repository

Neumann, Philipp; Rohrmann, Till

2012-01-01

We present simulation results of flows in the finite Knudsen range, which is in the slip and transition flow regime. Our implementations are based on the Lattice Boltzmann method and are accomplished within the Peano framework. We validate our code

Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions

KAUST Repository

Reis, Tim; Dellar, Paul J.

2012-01-01

lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier

Boundary Slip and Surface Interaction: A Lattice Boltzmann Simulation

International Nuclear Information System (INIS)

Yan-Yan, Chen; Hua-Bing, Li; Hou-Hui, Yi

2008-01-01

The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions. The main factors influencing the boundary slip are the strength of interactions between fluid-fluid and fluid-wall particles. Other factors, such as fluid viscosity, bulk pressure may also change the slip length. We find that boundary slip only occurs under a certain density (bulk pressure). If the density is large enough, the slip length will tend to zero. In our simulations, a low density layer near the wall does not need to be postulated a priori but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is the low density layer that induces the boundary slip. The results may be helpful to understand recent experimental observations on the slippage of micro flows

Modeling and simulation of ocean wave propagation using lattice Boltzmann method

Science.gov (United States)

Nuraiman, Dian

2017-10-01

In this paper, we present on modeling and simulation of ocean wave propagation from the deep sea to the shoreline. This requires high computational cost for simulation with large domain. We propose to couple a 1D shallow water equations (SWE) model with a 2D incompressible Navier-Stokes equations (NSE) model in order to reduce the computational cost. The coupled model is solved using the lattice Boltzmann method (LBM) with the lattice Bhatnagar-Gross-Krook (BGK) scheme. Additionally, a special method is implemented to treat the complex behavior of free surface close to the shoreline. The result shows the coupled model can reduce computational cost significantly compared to the full NSE model.

Lattice Boltzmann flow simulations with applications of reduced order modeling techniques

KAUST Repository

Brown, Donald

2014-01-01

With the recent interest in shale gas, an understanding of the flow mechanisms at the pore scale and beyond is necessary, which has attracted a lot of interest from both industry and academia. One of the suggested algorithms to help understand flow in such reservoirs is the Lattice Boltzmann Method (LBM). The primary advantage of LBM is its ability to approximate complicated geometries with simple algorithmic modificatoins. In this work, we use LBM to simulate the flow in a porous medium. More specifically, we use LBM to simulate a Brinkman type flow. The Brinkman law allows us to integrate fast free-flow and slow-flow porous regions. However, due to the many scales involved and complex heterogeneities of the rock microstructure, the simulation times can be long, even with the speed advantage of using an explicit time stepping method. The problem is two-fold, the computational grid must be able to resolve all scales and the calculation requires a steady state solution implying a large number of timesteps. To help reduce the computational complexity and total simulation times, we use model reduction techniques to reduce the dimension of the system. In this approach, we are able to describe the dynamics of the flow by using a lower dimensional subspace. In this work, we utilize the Proper Orthogonal Decomposition (POD) technique, to compute the dominant modes of the flow and project the solution onto them (a lower dimensional subspace) to arrive at an approximation of the full system at a lowered computational cost. We present a few proof-of-concept examples of the flow field and the corresponding reduced model flow field.

Effects of Nanoparticles on Melting Process with Phase-Change Using the Lattice Boltzmann Method

KAUST Repository

Ibrahem, Ahmed M.

2017-05-04

In this work, the problem of nanoparticles dispersion effects on coupled heat transfer and solid-liquid phase change has been studied. The lattice Boltzmann method (LBM) enthalpy-based is employed. The collision model of lattice Bhatangar-Gross-Krook (LBGK) is used to solve the problem of 1D melting by conduction. On the other hand, we use the model of multi-distribution functions (MDF) to calculate the density, the velocity and the temperature for the problem of 2D melting by free convection, associated with different boundary conditions. In these simulations, the volume fractions of copper nanoparticles (0-2%) added to water-base fluid and Rayleigh numbers of 103to105. We use the Chapman-Enskog expansion to derive the governing macroscopic quantities from the mesoscopic lattice Boltzmann equation. The results obtained by these models have been compared to an analytical solution or other numerical methods. The effects of nanoparticles on conduction and natural convection during the melting process have been investigated. Moreover, the influences of nanoparticles on moving of the phase change front, the thermal conductivity and the latent heat of fusion are also studied.

Lattice Boltzmann model for melting with natural convection

International Nuclear Information System (INIS)

Huber, Christian; Parmigiani, Andrea; Chopard, Bastien; Manga, Michael; Bachmann, Olivier

2008-01-01

We develop a lattice Boltzmann method to couple thermal convection and pure-substance melting. The transition from conduction-dominated heat transfer to fully-developed convection is analyzed and scaling laws and previous numerical results are reproduced by our numerical method. We also investigate the limit in which thermal inertia (high Stefan number) cannot be neglected. We use our results to extend the scaling relations obtained at low Stefan number and establish the correlation between the melting front propagation and the Stefan number for fully-developed convection. We conclude by showing that the model presented here is particularly well-suited to study convection melting in geometrically complex media with many applications in geosciences

Coupled numerical approach combining finite volume and lattice Boltzmann methods for multi-scale multi-physicochemical processes

Energy Technology Data Exchange (ETDEWEB)

Chen, Li; He, Ya-Ling [Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Kang, Qinjun [Computational Earth Science Group (EES-16), Los Alamos National Laboratory, Los Alamos, NM (United States); Tao, Wen-Quan, E-mail: wqtao@mail.xjtu.edu.cn [Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)

2013-12-15

A coupled (hybrid) simulation strategy spatially combining the finite volume method (FVM) and the lattice Boltzmann method (LBM), called CFVLBM, is developed to simulate coupled multi-scale multi-physicochemical processes. In the CFVLBM, computational domain of multi-scale problems is divided into two sub-domains, i.e., an open, free fluid region and a region filled with porous materials. The FVM and LBM are used for these two regions, respectively, with information exchanged at the interface between the two sub-domains. A general reconstruction operator (RO) is proposed to derive the distribution functions in the LBM from the corresponding macro scalar, the governing equation of which obeys the convection–diffusion equation. The CFVLBM and the RO are validated in several typical physicochemical problems and then are applied to simulate complex multi-scale coupled fluid flow, heat transfer, mass transport, and chemical reaction in a wall-coated micro reactor. The maximum ratio of the grid size between the FVM and LBM regions is explored and discussed. -- Highlights: •A coupled simulation strategy for simulating multi-scale phenomena is developed. •Finite volume method and lattice Boltzmann method are coupled. •A reconstruction operator is derived to transfer information at the sub-domains interface. •Coupled multi-scale multiple physicochemical processes in micro reactor are simulated. •Techniques to save computational resources and improve the efficiency are discussed.

Theory and application of the RAZOR two-dimensional continuous energy lattice physics code

International Nuclear Information System (INIS)

Zerkle, M.L.; Abu-Shumays, I.K.; Ott, M.W.; Winwood, J.P.

1997-01-01

The theory and application of the RAZOR two-dimensional, continuous energy lattice physics code are discussed. RAZOR solves the continuous energy neutron transport equation in one- and two-dimensional geometries, and calculates equivalent few-group diffusion theory constants that rigorously account for spatial and spectral self-shielding effects. A dual energy resolution slowing down algorithm is used to reduce computer memory and disk storage requirements for the slowing down calculation. Results are presented for a 2D BWR pin cell depletion benchmark problem

Involving the Navier-Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method.

Science.gov (United States)

Verschaeve, Joris C G

2011-06-13

By means of the continuity equation of the incompressible Navier-Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

Finite-size scaling of clique percolation on two-dimensional Moore lattices

Science.gov (United States)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

Quantum phases of dipolar rotors on two-dimensional lattices.

Science.gov (United States)

Abolins, B P; Zillich, R E; Whaley, K B

2018-03-14

The quantum phase transitions of dipoles confined to the vertices of two-dimensional lattices of square and triangular geometry is studied using path integral ground state quantum Monte Carlo. We analyze the phase diagram as a function of the strength of both the dipolar interaction and a transverse electric field. The study reveals the existence of a class of orientational phases of quantum dipolar rotors whose properties are determined by the ratios between the strength of the anisotropic dipole-dipole interaction, the strength of the applied transverse field, and the rotational constant. For the triangular lattice, the generic orientationally disordered phase found at zero and weak values of both dipolar interaction strength and applied field is found to show a transition to a phase characterized by net polarization in the lattice plane as the strength of the dipole-dipole interaction is increased, independent of the strength of the applied transverse field, in addition to the expected transition to a transverse polarized phase as the electric field strength increases. The square lattice is also found to exhibit a transition from a disordered phase to an ordered phase as the dipole-dipole interaction strength is increased, as well as the expected transition to a transverse polarized phase as the electric field strength increases. In contrast to the situation with a triangular lattice, on square lattices, the ordered phase at high dipole-dipole interaction strength possesses a striped ordering. The properties of these quantum dipolar rotor phases are dominated by the anisotropy of the interaction and provide useful models for developing quantum phases beyond the well-known paradigms of spin Hamiltonian models, implementing in particular a novel physical realization of a quantum rotor-like Hamiltonian that possesses an anisotropic long range interaction.

Quantum phases of dipolar rotors on two-dimensional lattices

Science.gov (United States)

Abolins, B. P.; Zillich, R. E.; Whaley, K. B.

2018-03-01

The quantum phase transitions of dipoles confined to the vertices of two-dimensional lattices of square and triangular geometry is studied using path integral ground state quantum Monte Carlo. We analyze the phase diagram as a function of the strength of both the dipolar interaction and a transverse electric field. The study reveals the existence of a class of orientational phases of quantum dipolar rotors whose properties are determined by the ratios between the strength of the anisotropic dipole-dipole interaction, the strength of the applied transverse field, and the rotational constant. For the triangular lattice, the generic orientationally disordered phase found at zero and weak values of both dipolar interaction strength and applied field is found to show a transition to a phase characterized by net polarization in the lattice plane as the strength of the dipole-dipole interaction is increased, independent of the strength of the applied transverse field, in addition to the expected transition to a transverse polarized phase as the electric field strength increases. The square lattice is also found to exhibit a transition from a disordered phase to an ordered phase as the dipole-dipole interaction strength is increased, as well as the expected transition to a transverse polarized phase as the electric field strength increases. In contrast to the situation with a triangular lattice, on square lattices, the ordered phase at high dipole-dipole interaction strength possesses a striped ordering. The properties of these quantum dipolar rotor phases are dominated by the anisotropy of the interaction and provide useful models for developing quantum phases beyond the well-known paradigms of spin Hamiltonian models, implementing in particular a novel physical realization of a quantum rotor-like Hamiltonian that possesses an anisotropic long range interaction.

Enhanced 29Si spin-lattice relaxation and observation of three-dimensional lattice connectivity in zeolites by two-dimensional 29Si MASS NMR

International Nuclear Information System (INIS)

Sivadinarayana, C.; Choudhary, V.R.; Ganapathy, S.

1994-01-01

It is shown that considerable sensitivity enhancement is achieved in the 29 Si magic angle sample spinning (MASS) NMR spectra of highly siliceous zeolites by pre treating the material with oxygen. The presence of adsorbed molecular oxygen in zeolite channels promotes an efficient 29 Si spin-lattice relaxation via a paramagnetic interaction between the lattice 29 Si T-site and the adsorbed oxygen on zeolite channels. This affords an efficient 2-D data collection and leads to increased sensitivity. The utility of this method is demonstrated in a two-dimensional COSY-45 NMR experiment of a high silica zeolite ZSM-5. (author). 20 refs., 3 figs., 1 tab

Recursive regularization step for high-order lattice Boltzmann methods

Science.gov (United States)

Coreixas, Christophe; Wissocq, Gauthier; Puigt, Guillaume; Boussuge, Jean-François; Sagaut, Pierre

2017-09-01

A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 106, and where a thorough analysis of the case at Re=3 ×104 is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.

Optimization of multi-phase compressible lattice Boltzmann codes on massively parallel multi-core systems

NARCIS (Netherlands)

Biferale, L.; Mantovani, F.; Pivanti, M.; Pozzati, F.; Sbragaglia, M.; Schifano, S.F.; Toschi, F.; Tripiccione, R.

2011-01-01

We develop a Lattice Boltzmann code for computational fluid-dynamics and optimize it for massively parallel systems based on multi-core processors. Our code describes 2D multi-phase compressible flows. We analyze the performance bottlenecks that we find as we gradually expose a larger fraction of

Lattice Boltzmann based multicomponent reactive transport model coupled with geochemical solver for scale simulations

NARCIS (Netherlands)

Patel, R.A.; Perko, J.; Jaques, D.; De Schutter, G.; Ye, G.; Van Breugel, K.

2013-01-01

A Lattice Boltzmann (LB) based reactive transport model intended to capture reactions and solid phase changes occurring at the pore scale is presented. The proposed approach uses LB method to compute multi component mass transport. The LB multi-component transport model is then coupled with the

Simulation of plume dynamics by the Lattice Boltzmann Method

Science.gov (United States)

Mora, Peter; Yuen, David A.

2017-09-01

The Lattice Boltzmann Method (LBM) is a semi-microscopic method to simulate fluid mechanics by modelling distributions of particles moving and colliding on a lattice. We present 2-D simulations using the LBM of a fluid in a rectangular box being heated from below, and cooled from above, with a Rayleigh of Ra = 108, similar to current estimates of the Earth's mantle, and a Prandtl number of 5000. At this Prandtl number, the flow is found to be in the non-inertial regime where the inertial terms denoted I ≪ 1. Hence, the simulations presented lie within the regime of relevance for geodynamical problems. We obtain narrow upwelling plumes with mushroom heads and chutes of downwelling fluid as expected of a flow in the non-inertial regime. The method developed demonstrates that the LBM has great potential for simulating thermal convection and plume dynamics relevant to geodynamics, albeit with some limitations.

Study of flow over object problems by a nodal discontinuous Galerkin-lattice Boltzmann method

Science.gov (United States)

Wu, Jie; Shen, Meng; Liu, Chen

2018-04-01

The flow over object problems are studied by a nodal discontinuous Galerkin-lattice Boltzmann method (NDG-LBM) in this work. Different from the standard lattice Boltzmann method, the current method applies the nodal discontinuous Galerkin method into the streaming process in LBM to solve the resultant pure convection equation, in which the spatial discretization is completed on unstructured grids and the low-storage explicit Runge-Kutta scheme is used for time marching. The present method then overcomes the disadvantage of standard LBM for depending on the uniform meshes. Moreover, the collision process in the LBM is completed by using the multiple-relaxation-time scheme. After the validation of the NDG-LBM by simulating the lid-driven cavity flow, the simulations of flows over a fixed circular cylinder, a stationary airfoil and rotating-stationary cylinders are performed. Good agreement of present results with previous results is achieved, which indicates that the current NDG-LBM is accurate and effective for flow over object problems.

Cooper pair induced frustration and nematicity of two-dimensional magnetic adatom lattices

Science.gov (United States)

Schecter, Michael; Syljuâsen, Olav F.; Paaske, Jens

2018-05-01

We propose utilizing the Cooper pair to induce magnetic frustration in systems of two-dimensional (2D) magnetic adatom lattices on s -wave superconducting surfaces. The competition between singlet electron correlations and the RKKY coupling is shown to lead to a variety of hidden-order states that break the point-group symmetry of the 2D adatom lattice at finite temperature. The phase diagram is constructed using a newly developed effective bond theory [M. Schecter et al., Phys. Rev. Lett. 119, 157202 (2017), 10.1103/PhysRevLett.119.157202], and exhibits broad regions of long-range vestigial nematic order.

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy.

Science.gov (United States)

Ansumali, S; Karlin, I V; Arcidiacono, S; Abbas, A; Prasianakis, N I

2007-03-23

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.

Modeling of flow of particles in a non-Newtonian fluid using lattice Boltzmann method

DEFF Research Database (Denmark)

Skocek, Jan; Svec, Oldrich; Spangenberg, Jon

2011-01-01

is necessary. In this contribution, the model at the scale of aggregates is introduced. The conventional lattice Boltzmann method for fluid flow is enriched with the immersed boundary method with direct forcing to simulate the flow of rigid particles in a non- Newtonian liquid. Basic ingredients of the model...

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

International Nuclear Information System (INIS)

Luz, H. L. F. da; Gammal, A.; Abdullaev, F. Kh.; Salerno, M.; Tomio, Lauro

2010-01-01

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

Science.gov (United States)

da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro

2010-10-01

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities

KAUST Repository

Allen, Rebecca

2016-06-29

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.

Lattice Boltzmann simulations of heat transfer in fully developed periodic incompressible flows

Science.gov (United States)

Wang, Zimeng; Shang, Helen; Zhang, Junfeng

2017-06-01

Flow and heat transfer in periodic structures are of great interest for many applications. In this paper, we carefully examine the periodic features of fully developed periodic incompressible thermal flows, and incorporate them in the lattice Boltzmann method (LBM) for flow and heat transfer simulations. Two numerical approaches, the distribution modification (DM) approach and the source term (ST) approach, are proposed; and they can both be used for periodic thermal flows with constant wall temperature (CWT) and surface heat flux boundary conditions. However, the DM approach might be more efficient, especially for CWT systems since the ST approach requires calculations of the streamwise temperature gradient at all lattice nodes. Several example simulations are conducted, including flows through flat and wavy channels and flows through a square array with circular cylinders. Results are compared to analytical solutions, previous studies, and our own LBM calculations using different simulation techniques (i.e., the one-module simulation vs. the two-module simulation, and the DM approach vs. the ST approach) with good agreement. These simple, however, representative simulations demonstrate the accuracy and usefulness of our proposed LBM methods for future thermal periodic flow simulations.

Fully coupled Lattice Boltzmann simulation of fiber reinforced self compacting concrete flow

DEFF Research Database (Denmark)

Svec, Oldrich; Skocek, Jan; Stang, Henrik

accurately the most important phenomena is introduced. A conventional Lattice Boltzmann method has been chosen as a fluid dynamics solver of the non-Newtonian fluid. A Mass Tracking Algorithm has been implemented to correctly represent a free surface and a modified Immersed Boundary Method (IBM) with direct...

A comparative study of the lattice Boltzmann and volume of fluid method for the rising bubble flows

Energy Technology Data Exchange (ETDEWEB)

Ryu, Seung Yeob; Park, Cheon Tae; Choi, Suhn [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2010-10-15

Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with the way multiphase flows, complex geometries and interfacial dynamics may be treated. Nevertheless, the LBM is considered as a mere alternative CFD tools, not a promising approach. The motion of the bubbles in a liquid has been the focus of both academic and practical interest. The central problem is the relationship between the rise velocity, bubble shape due to the interface deformation and flow field. The buoyancy effect due to density difference in the two phase flows is characterized with Eotvos and Morton numbers. In this study, a single bubble rising under a buoyancy is simulated with LBM and VOF based on conventional CFD method. The two simulation results are compared with the previous experiments. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

A comparative study of the lattice Boltzmann and volume of fluid method for the rising bubble flows

International Nuclear Information System (INIS)

Ryu, Seung Yeob; Park, Cheon Tae; Choi, Suhn

2010-01-01

Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with the way multiphase flows, complex geometries and interfacial dynamics may be treated. Nevertheless, the LBM is considered as a mere alternative CFD tools, not a promising approach. The motion of the bubbles in a liquid has been the focus of both academic and practical interest. The central problem is the relationship between the rise velocity, bubble shape due to the interface deformation and flow field. The buoyancy effect due to density difference in the two phase flows is characterized with Eotvos and Morton numbers. In this study, a single bubble rising under a buoyancy is simulated with LBM and VOF based on conventional CFD method. The two simulation results are compared with the previous experiments. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

Five-dimensional Lattice Gauge Theory as Multi-Layer World

OpenAIRE

Murata, Michika; So, Hiroto

2003-01-01

A five-dimensional lattice space can be decomposed into a number of four-dimens ional lattices called as layers. The five-dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. In the theory, there exist two independent coupling constants; $\\beta_4$ controls the dynamics inside a layer and $\\beta_5$ does the strength of the inter-layer interaction.We propose the new possibility to realize t...

Gauge theories and integrable lattice models

International Nuclear Information System (INIS)

Witten, E.

1989-01-01

Investigations of new knot polynomials discovered in the last few years have shown them to be intimately connected with soluble models of two dimensional lattice statistical mechanics. In this paper, these results, which in time may illuminate the whole question of why integrable lattice models exist, are reconsidered from the point of view of three dimensional gauge theory. Expectation values of Wilson lines in three dimensional Chern-Simons gauge theories can be computed by evaluating the partition functions of certain lattice models on finite graphs obtained by projecting the Wilson lines to the plane. The models in question - previously considered in both the knot theory and statistical mechanics literature - are IRF models in which the local Boltzmann weights are the matrix elements of braiding matrices in rational conformal field theories. These matrix elements, in turn, can be represented in three dimensional gauge theory in terms of the expectation value of a certain tetrahedral configuration of Wilson lines. This representation makes manifest a surprising symmetry of the braiding matrix elements in conformal field theory. (orig.)

Lattice Boltzmann simulation for the energy and entropy of excitable systems

Institute of Scientific and Technical Information of China (English)

Deng Min-Yi; Tang Guo-Ning; Kong Ling-Jiang; Liu Mu-Ren

2011-01-01

The internal energy and the spatiotemporal entropy of excitable systems are investigated with the lattice Boltzmann method. The numerical results show that the breakup of spiral wave is attributed to the inadequate supply of energy, i.e., the internal energy of system is smaller than the energy of self-sustained spiral wave. It is observed that the average internal energy of a regular wave state reduces with its spatiotemporal entropy decreasing. Interestingly, although the energy difference between two regular wave states is very small, the different states can be distinguished obviously due to the large difference between their spatiotemporal entropies. In addition, when the unstable spiral wave converts into the spatiotemporal chaos, the internal energy of system decreases, while the spatiotemporal entropy increases, which behaves as the thermodynamic entropy in an isolated system.

Evolution of a neutral-ion 2 fluid system using thermal lattice Boltzmann model

International Nuclear Information System (INIS)

Vahala, L.; Vahala, G.; Carter, J.; Pavlo, P.

2000-01-01

The 2D evolution of a 2-species system is examined using the thermal lattice Boltzmann model (TLBM). The effects of velocity shear layers on sharp heat fronts are considered for a neutral-ion system in the case where both species are turbulent. The rate at which the species velocities and temperatures equilibrate no longer follow the Morse estimate. (author)

Discrete breathers in a two-dimensional hexagonal Fermi Pasta Ulam lattice

Science.gov (United States)

Butt, Imran A.; Wattis, Jonathan A. D.

2007-02-01

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a reduction to a cubic nonlinear Schrödinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher order analysis yielding a generalized NLS, which includes known stabilizing terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, asymptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximized for stationary breathers and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt and Wattis 2006 J. Phys. A: Math. Gen. 39 4955), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalized NLS equation.

Lattice Boltzmann simulations of the contact angle in a liquid-gas system

International Nuclear Information System (INIS)

Ryu, Seung Yeob; Park, Cheon Tae; Kim, Keung Koo

2008-01-01

Recently, the lattice Boltzmann method (LBM) has gained much attention for its ability to simulate fluid flows, and for its potential advantages over a conventional CFD method. The key advantages of LBM are, (1) suitability for parallel computations, (2) absence of the need to solve the time-consuming Poisson equation for a pressure, and (3) an ease with multiphase flows, complex geometries and interfacial dynamics may be treated. The shape of a moving droplet is difficult to investigate analytically because the classical continuum hydrodynamic equations of motion with the usual no-slip condition at the surface predict a singularity in the stress at the contact line. Briant et al. have proposed a wetting boundary condition by using the wetting potential. In this study, we introduce the wetting boundary condition into the LBM proposed by Zheng et al. The static contact angle of a droplet onto a wall in order to validate the method is calculated. By adopting a finite difference gradient operator of a sufficient isotropy, the spurious currents can be made small in the wall surface. The main objective of the present work is to establish the lattice Boltzmann method as a viable tool for the simulation of multiphase or multi-component flows

A partial entropic lattice Boltzmann MHD simulation of the Orszag-Tang vortex

Science.gov (United States)

Flint, Christopher; Vahala, George

2018-02-01

Karlin has introduced an analytically determined entropic lattice Boltzmann (LB) algorithm for Navier-Stokes turbulence. Here, this is partially extended to an LB model of magnetohydrodynamics, on using the vector distribution function approach of Dellar for the magnetic field (which is permitted to have field reversal). The partial entropic algorithm is benchmarked successfully against standard simulations of the Orszag-Tang vortex [Orszag, S.A.; Tang, C.M. J. Fluid Mech. 1979, 90 (1), 129-143].

Two-Dimensional Tellurene as Excellent Thermoelectric Material

KAUST Repository

Sharma, Sitansh

2018-04-20

We study the thermoelectric properties of two-dimensional tellurene by first-principles calculations and semiclassical Boltzmann transport theory. The HSE06 hybrid functional results in a moderate direct band gap of 1.48 eV at the Γ point. A high room temperature Seebeck coefficient (Sxx = 0.38 mV/K, Syy = 0.36 mV/K) is combined with anisotropic lattice thermal conductivity (κxxl = 0.43 W/m K, κyyl = 1.29 W/m K). Phonon band structures demonstrate a key role of optical phonons in the record low thermal conductivity that leads to excellent thermoelectric performance of tellurene. At room temperature and moderate hole doping of 1.2 × 10–11 cm–2, for example, a figure of merit of ZTxx = 0.8 is achieved.

Structures and Dynamics of Two-Dimensional Dust Lattices with and without Coulomb Molecules in Plasmas

International Nuclear Information System (INIS)

Huang Feng; Wang Xue-Jin; Liu Yan-Hong; Ye Mao-Fu; Wang Long

2010-01-01

Structures and dynamics of two-dimensional dust lattices with and without Coulomb molecules in plasmas are investigated. The experimental results show that the lattices have the crystal-like hexagonal structures, i.e. most particles have six nearest-neighboring particles. However, the lattice points can be occupied by the individual particles or by a pair of particles called Coulomb molecules. The pair correlation function is used to compare the structures between the lattices with or without the Coulomb molecules. In the experiments, the Coulomb molecules can also decompose and recombine with another individual particle to form a new molecule. (physics of gases, plasmas, and electric discharges)

Commutativity of the source generation procedure and integrable semi-discretizations: the two-dimensional Leznov lattice

International Nuclear Information System (INIS)

Hu Juan; Yu Guofu; Tam, Hon-Wah

2012-01-01

The source generation procedure (SGP) is applied to a y-directional discrete version and an x-directional discrete version of the Leznov lattice. Consequently, a y-discrete Leznov lattice equation with self-consistent sources (y-discrete Leznov ESCS) and an x-discrete Leznov ESCS are presented. Also utilizing the SGP, a new type of Leznov lattice equation with self-consistent sources (new Leznov ESCS) is derived. It is interesting that the two semi-discrete Leznov ESCS produced constitute a y-discretization for the Leznov ESCS given by Wang et al (2007 J. Phys. A: Math. Theor. 40 12691) and an x-discretization for the new Leznov ESCS, respectively. This means that the commutativity of SGP and integrable semi-discretizations is valid for the two-dimensional Leznov lattice equation. (paper)

Effective thermal conductivity estimate of heterogenous media by a lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Arab, M.R.; Pateyron, B.; El Ganaoui, M.; Labbe, J.C. [Limoges Univ., Limoges (France). Science des Procedes Ceramiques et de Traitements de Surface

2009-07-01

Statistical lattice Boltzmann methods (LBM) are often used to simulate isothermal fluid flow for problems with complex geometry or porous structures. This study used an LBM algorithm to evaluate the effective thermal conductivity (ETC) of simple 2-D configurations. The LBM algorithm was also used to estimate the ECT of a porous structure. The Bhatnagar-Gross-Krook approximation was used to determine the discrete form of the Boltzmann equation for a single phase flow. A comparison with the finite element method (FEM) was also conducted. Results of the study demonstrated that the LBM algorithm accurately simulates the phenomena of heat and mass transfer for both the simple 2-D configurations as well as the porous media. The tool will be used to determine the influence of thermal contact resistance on heat transfer. 6 refs., 1 tab., 7 figs.

Pythagoras's theorem on a two-dimensional lattice from a 'natural' Dirac operator and Connes's distance formula

Energy Technology Data Exchange (ETDEWEB)

Dai Jian [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: jdai@mail.phy.pku.edu.cn; Song Xingchang [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: songxc@ibm320h.phy.pku.edu.cn

2001-07-13

One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as 'natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices. (author)

A Dirac-Kaehler approach to the two dimensional Wess-Zumino N=2 model on the lattice

International Nuclear Information System (INIS)

Zimerman, A.H.; Aratyn, H.

1983-08-01

We introduce a Dirac-Kaehler model for the two dimensional Wess-Zumino N=2 Lagrangean. We can show that in the model, when we go to the euclidean space-time lattive, we have no energy doubling, the action has no lattice surface terms (contrary to other authors), while the Hamiltonians (when time is continuous) present lattice surface terms. (orig.)

Consistent forcing scheme in the cascaded lattice Boltzmann method.

Science.gov (United States)

Fei, Linlin; Luo, Kai Hong

2017-11-01

In this paper, we give an alternative derivation for the cascaded lattice Boltzmann method (CLBM) within a general multiple-relaxation-time (MRT) framework by introducing a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The consistency of the nonslip rule, the second-order convergence rate in space, and the property of isotropy for the consistent forcing scheme is demonstrated through numerical simulations of several canonical problems. Several existing forcing schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework.

Consistent forcing scheme in the cascaded lattice Boltzmann method

Science.gov (United States)

Fei, Linlin; Luo, Kai Hong

2017-11-01

In this paper, we give an alternative derivation for the cascaded lattice Boltzmann method (CLBM) within a general multiple-relaxation-time (MRT) framework by introducing a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The consistency of the nonslip rule, the second-order convergence rate in space, and the property of isotropy for the consistent forcing scheme is demonstrated through numerical simulations of several canonical problems. Several existing forcing schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework.

Calculation of the permeability in porous media using the lattice Boltzmann method

International Nuclear Information System (INIS)

Eshghinejadfard, Amir; Daróczy, László; Janiga, Gábor; Thévenin, Dominique

2016-01-01

Highlights: • Lattice Boltzmann simulation of fluid flow in porous media delivers a high accuracy. • Domain size, relaxation time and force scheme affect the calculated permeability. • Multiple relaxation time model shows very low viscosity dependence as compared to single relaxation time. • The choice of relaxation time and force scheme is a trade-off between the required accuracy and computational cost. - Abstract: In this paper, the lattice Boltzmann method (LBM) is used to simulate three-dimensional laminar flows in porous media and to calculate the associated permeability. An in-house, parallelized code using the message passing interface technique is employed for the study. Three different flow configurations are studied: first, by manually specifying solid cells in a face-centered cube (FCC); then, doing the same in a body-centered cube (BCC); and finally by reading the solid cells for a real 3D geometry from a set of experimental 2D computed tomography images. In all simulations, the Reynolds number is kept well below 1. It was found that the current LBM simulations yield good estimates for the permeability value. The impact of the employed force scheme and single- or multiple-relaxation time (SRT, MRT) was also studied. Although each force scheme (Guo-SRT, Guo-MRT and Shan-Chen-SRT) may show better results in some regions, the strong dependency of SRT models on relaxation time suggests that the proper choice of the force scheme, relaxation time and domain resolution is a compromise between the required accuracy and computational cost. First, higher resolutions lead as expected to increasingly accurate results but requires more computational cost and time. Second, the MRT model shows a lower viscosity dependence in comparison with SRT models but is somewhat slower. Also, the results are more sensitive to the relaxation time value for coarser domains. Furthermore, lower relaxation times necessitate a higher number of iterations to reach the steady

Memory transfer optimization for a lattice Boltzmann solver on Kepler architecture nVidia GPUs

Science.gov (United States)

Mawson, Mark J.; Revell, Alistair J.

2014-10-01

The Lattice Boltzmann method (LBM) for solving fluid flow is naturally well suited to an efficient implementation for massively parallel computing, due to the prevalence of local operations in the algorithm. This paper presents and analyses the performance of a 3D lattice Boltzmann solver, optimized for third generation nVidia GPU hardware, also known as 'Kepler'. We provide a review of previous optimization strategies and analyse data read/write times for different memory types. In LBM, the time propagation step (known as streaming), involves shifting data to adjacent locations and is central to parallel performance; here we examine three approaches which make use of different hardware options. Two of which make use of 'performance enhancing' features of the GPU; shared memory and the new shuffle instruction found in Kepler based GPUs. These are compared to a standard transfer of data which relies instead on optimized storage to increase coalesced access. It is shown that the more simple approach is most efficient; since the need for large numbers of registers per thread in LBM limits the block size and thus the efficiency of these special features is reduced. Detailed results are obtained for a D3Q19 LBM solver, which is benchmarked on nVidia K5000M and K20C GPUs. In the latter case the use of a read-only data cache is explored, and peak performance of over 1036 Million Lattice Updates Per Second (MLUPS) is achieved. The appearance of a periodic bottleneck in the solver performance is also reported, believed to be hardware related; spikes in iteration-time occur with a frequency of around 11 Hz for both GPUs, independent of the size of the problem.

Extended lattice Boltzmann scheme for droplet combustion.

Science.gov (United States)

Ashna, Mostafa; Rahimian, Mohammad Hassan; Fakhari, Abbas

2017-05-01

The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n-butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.

Tunable spin-orbit coupling for ultracold atoms in two-dimensional optical lattices

Science.gov (United States)

Grusdt, Fabian; Li, Tracy; Bloch, Immanuel; Demler, Eugene

2017-06-01

Spin-orbit coupling (SOC) is at the heart of many exotic band structures and can give rise to many-body states with topological order. Here we present a general scheme based on a combination of microwave driving and lattice shaking for the realization of two-dimensional SOC with ultracold atoms in systems with inversion symmetry. We show that the strengths of Rashba and Dresselhaus SOC can be independently tuned in a spin-dependent square lattice. More generally, our method can be used to open gaps between different spin states without breaking time-reversal symmetry. We demonstrate that this allows for the realization of topological insulators with nontrivial spin textures closely related to the Kane-Mele model.

The Lattice Boltzmann method principles and practice

CERN Document Server

Krüger, Timm; Kuzmin, Alexandr; Shardt, Orest; Silva, Goncalo; Viggen, Erlend Magnus

2017-01-01

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a va...

Bose-Einstein condensate in an optical lattice with Raman-assisted two-dimensional spin-orbit coupling

Science.gov (United States)

Pan, Jian-Song; Zhang, Wei; Yi, Wei; Guo, Guang-Can

2016-10-01

In a recent experiment (Z. Wu, L. Zhang, W. Sun, X.-T. Xu, B.-Z. Wang, S.-C. Ji, Y. Deng, S. Chen, X.-J. Liu, and J.-W. Pan, arXiv:1511.08170 [cond-mat.quant-gas]), a Raman-assisted two-dimensional spin-orbit coupling has been realized for a Bose-Einstein condensate in an optical lattice potential. In light of this exciting progress, we study in detail key properties of the system. As the Raman lasers inevitably couple atoms to high-lying bands, the behaviors of the system in both the single- and many-particle sectors are significantly affected. In particular, the high-band effects enhance the plane-wave phase and lead to the emergence of "roton" gaps at low Zeeman fields. Furthermore, we identify high-band-induced topological phase boundaries in both the single-particle and the quasiparticle spectra. We then derive an effective two-band model, which captures the high-band physics in the experimentally relevant regime. Our results not only offer valuable insights into the two-dimensional lattice spin-orbit coupling, but also provide a systematic formalism to model high-band effects in lattice systems with Raman-assisted spin-orbit couplings.

A three-dimensional numerical study on dynamics behavior of a rising vapor bubble in uniformly superheated liquid by lattice Boltzmann method

International Nuclear Information System (INIS)

Sun, Tao; Sun, Jiangang; Ang, Xueye; Li, Shanshan; Su, Xin

2016-01-01

Highlights: • Dynamics of vapor bubble in uniformly superheated liquid is studied by a 3D LBM. • The growth rate reaches a maximum value and then decrease until a certain value. • The vapor bubble will take place a larger deformation at high ratio of Re/Eo. • The bubble wake has a great influence on motion and deformation of vapor bubble. • Ratio of Re/Eo has an important influence on evolution of temperature field. - Abstract: In this paper, dynamics behaviors of a rising vapor bubble in uniformly superheated liquid are firstly studied by a hybrid three-dimensional lattice Boltzmann model. In order to validate this model, two test cases regarding bubble rising in an isothermal system and vapor bubble growth in a superheated liquid are performed, respectively. The test results are consistent with existing results and indicate the feasibility of the hybrid model. The hybrid model is further applied to simulate growth and deformation of a rising vapor bubble in different physical conditions. Some physical parameters of vapor bubble such as equivalent diameter and growth rate are evaluated accurately by three-dimensional simulations. It is found that the growth rate of vapor bubble changes with time and temperature gradient. It reaches a maximum value at the initial stage and then decrease until a certain value. The growth and deformation of vapor bubble at different ratios of Re/Eo are discussed. The numerical results show the vapor bubble will take place a larger deformation at high ratio of Re/Eo at the middle and final stages. In addition, the hybrid model is also applied to predict the evolution of flow and temperature fields. The bubble wake has a great influence on the motion and deformation of vapor bubble during rising process. As far as the temperature field is concerned, a ratio of Re/Eo has an important influence on heat transfer and evolution of temperature field.

Numerical evidence for two types of localized states in a two-dimensional disordered lattice

International Nuclear Information System (INIS)

Tit, N.; Kumar, N.

1992-06-01

We report results of our numerical calculations, based on the equation of motion method, of dc-electrical conductivity and of density of states up to 40x40 two-dimensional square lattices modelling a right-binding Hamiltonian for a binary (AB) compound, disordered by randomly distributed B vacancies up to 10%. Our results indicate strongly localized states away from band centers separated from the relatively weakly localized states toward midband. This is in qualitative agreement with the idea of a ''mobility edge'' separating exponentially localized states from the power-law localized states as suggested by the two-parameter scaling theory of Kaevh in two dimensions. (author). 7 refs, 4 figs

Finite Boltzmann schemes

NARCIS (Netherlands)

Sman, van der R.G.M.

2006-01-01

In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the

Coupling effect of topological states and Chern insulators in two-dimensional triangular lattices

Science.gov (United States)

Zhang, Jiayong; Zhao, Bao; Xue, Yang; Zhou, Tong; Yang, Zhongqin

2018-03-01

We investigate topological states of two-dimensional (2D) triangular lattices with multiorbitals. Tight-binding model calculations of a 2D triangular lattice based on px and py orbitals exhibit very interesting doubly degenerate energy points at different positions (Γ and K /K' ) in momentum space, with quadratic non-Dirac and linear Dirac band dispersions, respectively. Counterintuitively, the system shows a global topologically trivial rather than nontrivial state with consideration of spin-orbit coupling due to the "destructive interference effect" between the topological states at the Γ and K /K' points. The topologically nontrivial state can emerge by introducing another set of triangular lattices to the system (bitriangular lattices) due to the breakdown of the interference effect. With first-principles calculations, we predict an intrinsic Chern insulating behavior (quantum anomalous Hall effect) in a family of the 2D triangular lattice metal-organic framework of Co(C21N3H15) (TPyB-Co) from this scheme. Our results provide a different path and theoretical guidance for the search for and design of new 2D topological quantum materials.

Relative permeabilities of supercritical CO2 and brine in carbon sequestration by a two-phase lattice Boltzmann method

Science.gov (United States)

Xie, Jian.-Fei.; He, S.; Zu, Y. Q.; Lamy-Chappuis, B.; Yardley, B. W. D.

2017-08-01

In this paper, the migration of supercritical carbon dioxide (CO2) in realistic sandstone rocks under conditions of saline aquifers, with applications to the carbon geological storage, has been investigated by a two-phase lattice Boltzmann method (LBM). Firstly the digital images of sandstone rocks were reproduced utilizing the X-ray computed microtomography (micro-CT), and high resolutions (up to 2.5 μm) were applied to the pore-scale LBM simulations. For the sake of numerical stability, the digital images were "cleaned" by closing the dead holes and removing the suspended particles in sandstone rocks. In addition, the effect of chemical reactions occurred in the carbonation process on the permeability was taken into account. For the wetting brine and non-wetting supercritical CO2 flows, they were treated as the immiscible fluids and were driven by pressure gradients in sandstone rocks. Relative permeabilities of brine and supercritical CO2 in sandstone rocks were estimated. Particularly the dynamic saturation was applied to improve the reliability of the calculations of the relative permeabilities. Moreover, the effects of the viscosity ratio of the two immiscible fluids and the resolution of digital images on the relative permeability were systematically investigated.

Progress in lattice Boltzmann methods for magnetohydrodynamic flows relevant to fusion applications

International Nuclear Information System (INIS)

Pattison, M.J.; Premnath, K.N.; Morley, N.B.; Abdou, M.A.

2008-01-01

In this paper, an approach to simulating magnetohydrodynamic (MHD) flows based on the lattice Boltzmann method (LBM) is presented. The dynamics of the flow are simulated using a so-called multiple relaxation time (MRT) lattice Boltzmann equation (LBE), in which a source term is included for the Lorentz force. The evolution of the magnetic induction is represented by introducing a vector distribution function and then solving an appropriate lattice kinetic equation for this function. The solution of both distribution functions are obtained through a simple, explicit, and computationally efficient stream-and-collide procedure. The use of the MRT collision term enhances the numerical stability over that of a single relaxation time approach. To apply the methodology to solving practical problems, a new extrapolation-based method for imposing magnetic boundary conditions is introduced and a technique for simulating steady-state flows with low magnetic Prandtl number is developed. In order to resolve thin layers near the walls arising in the presence of high magnetic fields, a non-uniform gridding strategy is introduced through an interpolated-streaming step applied to both distribution functions. These advances are particularly important for applications in fusion engineering where liquid metal flows with low magnetic Prandtl numbers and high Hartmann numbers are introduced. A number of MHD benchmark problems, under various physical and geometrical conditions are presented, including 3-D MHD lid driven cavity flow, high Hartmann number flows and turbulent MHD flows, with good agreement with prior data. Due to the local nature of the method, the LBM also demonstrated excellent performance on parallel machines, with almost linear scaling up to 128 processors for a MHD flow problem

Evaluation of permeability and non-Darcy flow in vuggy macroporous limestone aquifer samples with lattice Boltzmann methods

Science.gov (United States)

Sukop, Michael C.; Huang, Haibo; Alvarez, Pedro F.; Variano, Evan A.; Cunningham, Kevin J.

2013-01-01

Lattice Boltzmann flow simulations provide a physics-based means of estimating intrinsic permeability from pore structure and accounting for inertial flow that leads to departures from Darcy's law. Simulations were used to compute intrinsic permeability where standard measurement methods may fail and to provide better understanding of departures from Darcy's law under field conditions. Simulations also investigated resolution issues. Computed tomography (CT) images were acquired at 0.8 mm interscan spacing for seven samples characterized by centimeter-scale biogenic vuggy macroporosity from the extremely transmissive sole-source carbonate karst Biscayne aquifer in southeastern Florida. Samples were as large as 0.3 m in length; 7–9 cm-scale-length subsamples were used for lattice Boltzmann computations. Macroporosity of the subsamples was as high as 81%. Matrix porosity was ignored in the simulations. Non-Darcy behavior led to a twofold reduction in apparent hydraulic conductivity as an applied hydraulic gradient increased to levels observed at regional scale within the Biscayne aquifer; larger reductions are expected under higher gradients near wells and canals. Thus, inertial flows and departures from Darcy's law may occur under field conditions. Changes in apparent hydraulic conductivity with changes in head gradient computed with the lattice Boltzmann model closely fit the Darcy-Forchheimer equation allowing estimation of the Forchheimer parameter. CT-scan resolution appeared adequate to capture intrinsic permeability; however, departures from Darcy behavior were less detectable as resolution coarsened.

Stable biexcitons in two-dimensional metal-halide perovskites with strong dynamic lattice disorder

Science.gov (United States)

Thouin, Félix; Neutzner, Stefanie; Cortecchia, Daniele; Dragomir, Vlad Alexandru; Soci, Cesare; Salim, Teddy; Lam, Yeng Ming; Leonelli, Richard; Petrozza, Annamaria; Kandada, Ajay Ram Srimath; Silva, Carlos

2018-03-01

With strongly bound and stable excitons at room temperature, single-layer, two-dimensional organic-inorganic hybrid perovskites are viable semiconductors for light-emitting quantum optoelectronics applications. In such a technological context, it is imperative to comprehensively explore all the factors—chemical, electronic, and structural—that govern strong multiexciton correlations. Here, by means of two-dimensional coherent spectroscopy, we examine excitonic many-body effects in pure, single-layer (PEA) 2PbI4 (PEA = phenylethylammonium). We determine the binding energy of biexcitons—correlated two-electron, two-hole quasiparticles—to be 44 ±5 meV at room temperature. The extraordinarily high values are similar to those reported in other strongly excitonic two-dimensional materials such as transition-metal dichalcogenides. Importantly, we show that this binding energy increases by ˜25 % upon cooling to 5 K. Our work highlights the importance of multiexciton correlations in this class of technologically promising, solution-processable materials, in spite of the strong effects of lattice fluctuations and dynamic disorder.

A Momentum-Exchange/Fictitious Domain-Lattice Boltzmann Method for Solving Particle Suspensions

Energy Technology Data Exchange (ETDEWEB)

Jeon, Seok Yun; Yoon, Joon Yong [Hanyang Univ., Seoul (Korea, Republic of); Kim, Chul Kyu [Korea Institute of Civil Engineering and Building Technology, Goyang (Korea, Republic of); Shin, Myung Seob [Korea Intellectual Property Office(KIPO), Daejeon (Korea, Republic of)

2016-06-15

This study presents a Lattice Boltzmann Method (LBM) coupled with a momentum-exchange approach/fictitious domain (MEA/FD) method for the simulation of particle suspensions. The method combines the advantages of the LB and the FD methods by using two unrelated meshes, namely, a Eulerian mesh for the flow domain and a Lagrangian mesh for the solid domain. The rigid body conditions are enforced by the momentum-exchange scheme in which the desired value of velocity is imposed directly in the particle inner domain by introducing a pseudo body force to satisfy the constraint of rigid body motion, which is the key idea of a fictitious domain (FD) method. The LB-MEA/FD method has been validated by simulating two different cases, and the results have been compared with those through other methods. The numerical evidence illustrated the capability and robustness of the present method for simulating particle suspensions.

Lattice Boltzmann modeling an introduction for geoscientists and engineers

CERN Document Server

Sukop, Michael C

2005-01-01

Lattice Boltzmann models have a remarkable ability to simulate single- and multi-phase fluids and transport processes within them. A rich variety of behaviors, including higher Reynolds numbers flows, phase separation, evaporation, condensation, cavitation, buoyancy, and interactions with surfaces can readily be simulated. This book provides a basic introduction that emphasizes intuition and simplistic conceptualization of processes. It avoids the more difficult mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those with more interest in model application than detailed mathematical foundations will find this a powerful "quick start" guide. Example simulations, exercises, and computer codes are included. Working code is provided on the Internet.

Micropatterning of bacteria on two-dimensional lattice protein surface observed by atomic force microscopy

International Nuclear Information System (INIS)

Oh, Y.J.; Jo, W.; Lim, J.; Park, S.; Kim, Y.S.; Kim, Y.

2008-01-01

In this study, we characterized the two-dimensional lattice of bovine serum albumin (BSA) as a chemical and physical barrier against bacterial adhesion, using fluorescence microscopy and atomic force microscopy (AFM). The lattice of BSA on glass surface was fabricated by micro-contact printing (μCP), which is a useful way to pattern a wide range of molecules into microscale features on different types of substrates. The contact-mode AFM measurements showed that the average height of the printed BSA monolayer was 5-6 nm. Escherichia coli adhered rapidly on bare glass slide, while the bacterial adhesion was minimized on the lattices in the range of 1-3 μm 2 . Especially, the bacterial adhesion was completely inhibited on a 1 μm 2 lattice. The results suggest that the anti-adhesion effects are due by the steric repulsion forces exerted by BSA

On integrability of a noncommutative q-difference two-dimensional Toda lattice equation

Energy Technology Data Exchange (ETDEWEB)

Li, C.X., E-mail: trisha_li2001@163.com [School of Mathematical Sciences, Capital Normal University, Beijing 100048 (China); Department of Mathematics, College of Charleston, Charleston, SC 29401 (United States); Nimmo, J.J.C., E-mail: jonathan.nimmo@glasgow.ac.uk [School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Shen, Shoufeng, E-mail: mathssf@zjut.edu.cn [Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023 (China)

2015-12-18

In our previous work (C.X. Li and J.J.C. Nimmo, 2009 [18]), we presented a generalized type of Darboux transformations in terms of a twisted derivation in a unified form. The twisted derivation includes ordinary derivatives, forward difference operators, super derivatives and q-difference operators as its special cases. This result not only enables one to recover the known Darboux transformations and quasideterminant solutions to the noncommutative KP equation, the non-Abelian two-dimensional Toda lattice equation, the non-Abelian Hirota–Miwa equation and the super KdV equation, but also inspires us to investigate quasideterminant solutions to q-difference soliton equations. In this paper, we first construct the bilinear Bäcklund transformations for the known bilinear q-difference two-dimensional Toda lattice equation (q-2DTL) and then derive a Lax pair whose compatibility gives a formally different nonlinear q-2DTL equation and finally obtain its quasideterminant solutions by iterating its Darboux transformations. - Highlights: • Examples are given to illustrate the extensive applications of twisted derivations. • Bilinear Bäcklund transformation is constructed for the known q-2DTL equation. • Lax pair is obtained for an equivalent q-2DTL equation. • Quasideterminant solutions are found for the nc q-2DTL equation.

Resource-Efficient, Hierarchical Auto-Tuning of a Hybrid Lattice Boltzmann Computation on the Cray XT4

International Nuclear Information System (INIS)

Williams, Samuel; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine

2009-01-01

We apply auto-tuning to a hybrid MPI-pthreads lattice Boltzmann computation running on the Cray XT4 at National Energy Research Scientific Computing Center (NERSC). Previous work showed that multicore-specific auto-tuning can improve the performance of lattice Boltzmann magnetohydrodynamics (LBMHD) by a factor of 4x when running on dual- and quad-core Opteron dual-socket SMPs. We extend these studies to the distributed memory arena via a hybrid MPI/pthreads implementation. In addition to conventional auto-tuning at the local SMP node, we tune at the message-passing level to determine the optimal aspect ratio as well as the correct balance between MPI tasks and threads per MPI task. Our study presents a detailed performance analysis when moving along an isocurve of constant hardware usage: fixed total memory, total cores, and total nodes. Overall, our work points to approaches for improving intra- and inter-node efficiency on large-scale multicore systems for demanding scientific applications

Numerical simulation of heat transfer in particulate flows using a thermal immersed boundary lattice Boltzmann method

International Nuclear Information System (INIS)

Eshghinejadfard, A.; Thévenin, D.

2016-01-01

In the current work the lattice Boltzmann method (LBM) is applied to investigate heat transfer phenomena in particulate flows. Different cases involving both two- and three-dimensional configurations are studied. For the fluid–particle interactions the direct-forcing and direct-heating immersed boundary (IB) method are applied to calculate the hydrodynamic force and energy exchange between the particle and the fluid, respectively. This Eulerian–Lagrangian approach captures the fluid flow around the particles with high accuracy. The Boussinesq approximation is applied to the coupling between flow and temperature fields. The energy equation is solved using a double-population model in the LBM framework. Numerical simulations reveal that this thermal IB-LBM can accurately predict the particle motion. A particularly interesting case involves particles with a variable temperature, where the competition between gravity and buoyancy induced by the temperature gradient can make particles sink or rise. It is observed that cold particles settle down faster than hot particles. Also, the thermal IB-LBM has been implemented for a collection of spherical particles. In this manner, the behavior of catalyst particles can be accurately predicted, as demonstrated in the last application, involving 60 particles interacting in an enclosure.

Large-scale grid-enabled lattice-Boltzmann simulations of complex fluid flow in porous media and under shear

NARCIS (Netherlands)

Harting, J.D.R.; Venturoli, M.; Coveney, P.V.

2004-01-01

Well–designed lattice Boltzmann codes exploit the essentially embarrassingly parallel features of the algorithm and so can be run with considerable efficiency on modern supercomputers. Such scalable codes permit us to simulate the behaviour of increasingly large quantities of complex condensed

Lattice Boltzmann simulations of the time-averaged forces on a cylinder in a sound field

International Nuclear Information System (INIS)

Haydock, David

2005-01-01

We show that lattice Boltzmann simulations can be used to model the radiation force on an object in a standing wave acoustic field and comparisons are made to theoretical predictions. We show how viscous effects change the radiation force and predict the motion of a particle placed near a boundary where viscous effects are important

Lattice Boltzmann simulations of the time-averaged forces on a cylinder in a sound field

Energy Technology Data Exchange (ETDEWEB)

Haydock, David [Unilever R and D Colworth, Sharnbrook, Bedford MK44 1LQ (United Kingdom); Department of Physics, Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP (United Kingdom)

2005-04-15

We show that lattice Boltzmann simulations can be used to model the radiation force on an object in a standing wave acoustic field and comparisons are made to theoretical predictions. We show how viscous effects change the radiation force and predict the motion of a particle placed near a boundary where viscous effects are important.

Application of the lattice Boltzmann method for simulation of the mold filling process in the casting industry

Science.gov (United States)

Szucki, Michal; Suchy, J. S.; Lelito, J.; Malinowski, P.; Sobczyk, J.

2017-12-01

The aim of this work is the development of the lattice Boltzmann model for simulation of the mold filling process. The authors present a simplified approach to the modeling of liquid metal-gas flows with particular emphasis on the interactions between these phases. The boundary condition for momentum transfer of the moving free surface to the gaseous phase is shown. Simultaneously, the method for modeling influence of gas back pressure on a position and shape of the interfacial boundary is explained in details. The problem of the lattice Boltzmann method (LBM) stability is also analyzed. Since large differences in viscosity of both fluids are a source of the model instability, the so-called fractional step (FS) method allowing to improve the computation stability is applied. The presented solution is verified on the bases of the available reference data and the results of experiments. It is shown that the model describes properly such effects as: gas bubbles formation and air back pressure, accompanying liquid-gas flows in the casting mold. At the same time the proposed approach is easy to be implemented and characterized by a lower demand of operating memory as compared to typical LBM models of two-phase flows.

Numerical simulation of the flow field in pump intakes by means of Lattice Boltzmann methods

International Nuclear Information System (INIS)

Schneider, A; Conrad, D; Böhle, M

2013-01-01

Lattice Boltzmann Methods are nowadays popular schemes for solving fluid flow problems of engineering interest. This popularity is due to the advantages of these schemes: For example, the meshing of the fluid domain can be performed fully automatically which results in great simplicity in handling complex geometries. In this paper a numerical scheme for the flow simulation in pump intakes based on a Lattice Boltzmann large eddy approach is presented. The ability of this scheme to capture the flow phenomena of the intake flow at different operating conditions is analysed. For the operational reliability and efficiency of pumps and pump systems, the incoming flow conditions are crucial. Since the efficiency and reliability requirements of pumps are rising and must be guaranteed, the flow conditions in pump intakes have to be evaluated during plant planning. Recent trends show that pump intakes are built more and more compact, which makes the flow in the intake even more complex. Numerical methods are a promising technique for conduction flow analysis in pump intakes, because they can be realised rapidly and cheaply

Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.

Science.gov (United States)

Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko

2014-04-01

The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials.

Inverse analysis of a rectangular fin using the lattice Boltzmann method

International Nuclear Information System (INIS)

Bamdad, Keivan; Ashorynejad, Hamid Reza

2015-01-01

Highlights: • Lattice Boltzmann method is used to study a transient conductive-convective fin. • LBM and Conjugate Gradient Method (CGM) are used to solve an inverse problem in fins. • LBM–ACGM estimates the unknown boundary conditions of fins accurately. • The accuracy and CPU time of LBM–ACGM are compared to IFDM–ACGM. • LBM–ACGM could be a good alternative for the conventional inverse methods. - Abstract: Inverse methods have many applications in determining unknown variables in heat transfer problems when direct measurements are impossible. As most common inverse methods are iterative and time consuming especially for complex geometries, developing more efficient methods seems necessary. In this paper, a direct transient conduction–convection heat transfer problem (fin) under several boundary conditions was solved by using lattice Boltzmann method (LBM), and then the results were successfully validated against both the finite difference method and analytical solution. Then, in the inverse problem both unknown base temperatures and heat fluxes in the rectangular fin were estimated by combining the adjoint conjugate gradient method (ACGM) and LBM. A close agreement between the exact values and estimated results confirmed the validity and accuracy of the ACGM–LBM. To compare the calculation time of ACGM–LBM, the inverse problem was solved by implicit finite difference methods as well. This comparison proved that the ACGM–LBM was an accurate and fast method to determine unknown thermal boundary conditions in transient conduction–convection heat transfer problems. The findings can efficiently determine the unknown variables in fins when a desired temperature distribution is available

Few quantum particles on one dimensional lattices

Energy Technology Data Exchange (ETDEWEB)

Valiente Cifuentes, Manuel

2010-06-18

There is currently a great interest in the physics of degenerate quantum gases and low-energy few-body scattering due to the recent experimental advances in manipulation of ultracold atoms by light. In particular, almost perfect periodic potentials, called optical lattices, can be generated. The lattice spacing is fixed by the wavelength of the laser field employed and the angle betwen the pair of laser beams; the lattice depth, defining the magnitude of the different band gaps, is tunable within a large interval of values. This flexibility permits the exploration of different regimes, ranging from the ''free-electron'' picture, modified by the effective mass for shallow optical lattices, to the tight-binding regime of a very deep periodic potential. In the latter case, effective single-band theories, widely used in condensed matter physics, can be implemented with unprecedent accuracy. The tunability of the lattice depth is nowadays complemented by the use of magnetic Feshbach resonances which, at very low temperatures, can vary the relevant atom-atom scattering properties at will. Moreover, optical lattices loaded with gases of effectively reduced dimensionality are experimentally accessible. This is especially important for one spatial dimension, since most of the exactly solvable models in many-body quantum mechanics deal with particles on a line; therefore, experiments with one-dimensional gases serve as a testing ground for many old and new theories which were regarded as purely academic not so long ago. The physics of few quantum particles on a one-dimensional lattice is the topic of this thesis. Most of the results are obtained in the tight-binding approximation, which is amenable to exact numerical or analytical treatment. For the two-body problem, theoretical methods for calculating the stationary scattering and bound states are developed. These are used to obtain, in closed form, the two-particle solutions of both the Hubbard and

Few quantum particles on one dimensional lattices

International Nuclear Information System (INIS)

Valiente Cifuentes, Manuel

2010-01-01

There is currently a great interest in the physics of degenerate quantum gases and low-energy few-body scattering due to the recent experimental advances in manipulation of ultracold atoms by light. In particular, almost perfect periodic potentials, called optical lattices, can be generated. The lattice spacing is fixed by the wavelength of the laser field employed and the angle betwen the pair of laser beams; the lattice depth, defining the magnitude of the different band gaps, is tunable within a large interval of values. This flexibility permits the exploration of different regimes, ranging from the ''free-electron'' picture, modified by the effective mass for shallow optical lattices, to the tight-binding regime of a very deep periodic potential. In the latter case, effective single-band theories, widely used in condensed matter physics, can be implemented with unprecedent accuracy. The tunability of the lattice depth is nowadays complemented by the use of magnetic Feshbach resonances which, at very low temperatures, can vary the relevant atom-atom scattering properties at will. Moreover, optical lattices loaded with gases of effectively reduced dimensionality are experimentally accessible. This is especially important for one spatial dimension, since most of the exactly solvable models in many-body quantum mechanics deal with particles on a line; therefore, experiments with one-dimensional gases serve as a testing ground for many old and new theories which were regarded as purely academic not so long ago. The physics of few quantum particles on a one-dimensional lattice is the topic of this thesis. Most of the results are obtained in the tight-binding approximation, which is amenable to exact numerical or analytical treatment. For the two-body problem, theoretical methods for calculating the stationary scattering and bound states are developed. These are used to obtain, in closed form, the two-particle solutions of both the Hubbard and extended Hubbard models

Tracer dispersion in two-dimensional rough fractures.

Science.gov (United States)

Drazer, G; Koplik, J

2001-05-01

Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness are studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a boundary condition for tracer particles that improves the accuracy of the method. The reduction in the diffusive transport, due to the fractal geometry of the fracture surfaces, is analyzed for different fracture apertures. In the limit of small aperture fluctuations we derive the correction to the diffusive coefficient in terms of the tortuosity, which accounts for the irregular geometry of the fractures. Dispersion is studied when the two fracture surfaces are simply displaced normally to the mean fracture plane and when there is a lateral shift as well. Numerical results are analyzed using the Lambda parameter, related to convective transport within the fracture, and simple arguments based on lubrication approximation. At very low Péclet number, in the case where fracture surfaces are laterally shifted, we show using several different methods that convective transport reduces dispersion.

Second order phase transition in two dimensional sine-Gordon field theory - lattice model

International Nuclear Information System (INIS)

Babu Joseph, K.; Kuriakose, V.C.

1978-01-01

Two dimensional sine-Gordon (SG) field theory on a lattice is studied using the single-site basis variational method of Drell and others. The nature of the phase transition associated with the spontaneous symmetry breakdown in a SG field system is clarified to be of second order. A generalisation is offered for a SG-type field theory in two dimensions with a potential of the form [cossup(n)((square root of lambda)/m)phi-1].(author)

Lattice Boltzmann simulation of flow and heat transfer in random porous media constructed by simulated annealing algorithm

International Nuclear Information System (INIS)

Liu, Minghua; Shi, Yong; Yan, Jiashu; Yan, Yuying

2017-01-01

Highlights: • A numerical capability combining the lattice Boltzmann method with simulated annealing algorithm is developed. • Digitized representations of random porous media are constructed using limited but meaningful statistical descriptors. • Pore-scale flow and heat transfer information in random porous media is obtained by the lattice Boltzmann simulation. • The effective properties at the representative elementary volume scale are well specified using appropriate upscale averaging. - Abstract: In this article, the lattice Boltzmann (LB) method for transport phenomena is combined with the simulated annealing (SA) algorithm for digitized porous-medium construction to study flow and heat transfer in random porous media. Importantly, in contrast to previous studies which simplify porous media as arrays of regularly shaped objects or effective pore networks, the LB + SA method in this article can model statistically meaningful random porous structures in irregular morphology, and simulate pore-scale transport processes inside them. Pore-scale isothermal flow and heat conduction in a set of constructed random porous media characterized by statistical descriptors were then simulated through use of the LB + SA method. The corresponding averages over the computational volumes and the related effective transport properties were also computed based on these pore scale numerical results. Good agreement between the numerical results and theoretical predictions or experimental data on the representative elementary volume scale was found. The numerical simulations in this article demonstrate combination of the LB method with the SA algorithm is a viable and powerful numerical strategy for simulating transport phenomena in random porous media in complex geometries.

A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

KAUST Repository

Reis, T.

2011-07-01

Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the widths of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee (1990) [3] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin (2000) [1] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving, gives correct average propagation speeds over many timesteps, and is shown to significantly delay the onset of pinning as the interface width is reduced. © 2010 Elsevier Ltd.

A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

KAUST Repository

Reis, T.; Dellar, P.J.

2011-01-01

Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the widths of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee (1990) [3] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin (2000) [1] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving, gives correct average propagation speeds over many timesteps, and is shown to significantly delay the onset of pinning as the interface width is reduced. © 2010 Elsevier Ltd.

An improved lattice Boltzmann scheme for multiphase fluid with multi-range interactions

Energy Technology Data Exchange (ETDEWEB)

Maquignon, Nicolas; Duchateau, Julien; Roussel, Gilles; Rousselle, François; Renaud, Christophe [Laboratoire Informatique Signal et Image de la Côte d' Opale, 50 rue Ferdinand Buisson, 62100 Calais (France); Université du Littoral Côte d' Opale, 1 place de l' Yser, 59140, Dunkerque (France); Association INNOCOLD, MREI 1, 145 (France)

2014-10-06

Modeling of fluids with liquid to gas phase transition has become important for understanding many environmental or industrial processes. Such simulations need new techniques, because traditional solvers are often limited. The Lattice Boltzmann Model (LBM) allows simulate complex fluids, because its mesoscopic nature gives possibility to incorporate additional physics in comparison to usual methods. In this work, an improved lattice Boltzmann model for phase transition flow will be introduced. First, the state of art for Shan and Chen (SC) type of LBM will be reminded. Then, link to real thermodynamics will be established with Maxwell equal areas construction. Convergence to isothermal liquid vapor equilibrium will be shown and discussed. Inclusion of an equation of state for real fluid and better incorporation of force term is presented. Multi-range interactions have been used for SC model, but it hasn't been yet applied to real fluid with non-ideal equation of state. In this work, we evaluate this model when it is applied to real liquid-vapor equilibrium. We show that important differences are found for evaluation of gas density. In order to recover thermodynamic consistency, we use a new scheme for calculation of force term, which is a combination of multi range model and numerical weighting used by Gong and Cheng. We show the superiority of our new model by studying convergence to equilibrium values over a large temperature range. We prove that spurious velocities remaining at equilibrium are decreased.

Entropic lattice Boltzmann model for charged leaky dielectric multiphase fluids in electrified jets.

Science.gov (United States)

Lauricella, Marco; Melchionna, Simone; Montessori, Andrea; Pisignano, Dario; Pontrelli, Giuseppe; Succi, Sauro

2018-03-01

We present a lattice Boltzmann model for charged leaky dielectric multiphase fluids in the context of electrified jet simulations, which are of interest for a number of production technologies including electrospinning. The role of nonlinear rheology on the dynamics of electrified jets is considered by exploiting the Carreau model for pseudoplastic fluids. We report exploratory simulations of charged droplets at rest and under a constant electric field, and we provide results for charged jet formation under electrospinning conditions.

Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries

Science.gov (United States)

Xu, Ao; Shyy, Wei; Zhao, Tianshou

2017-06-01

Fuel cells and flow batteries are promising technologies to address climate change and air pollution problems. An understanding of the complex multiscale and multiphysics transport phenomena occurring in these electrochemical systems requires powerful numerical tools. Over the past decades, the lattice Boltzmann (LB) method has attracted broad interest in the computational fluid dynamics and the numerical heat transfer communities, primarily due to its kinetic nature making it appropriate for modeling complex multiphase transport phenomena. More importantly, the LB method fits well with parallel computing due to its locality feature, which is required for large-scale engineering applications. In this article, we review the LB method for gas-liquid two-phase flows, coupled fluid flow and mass transport in porous media, and particulate flows. Examples of applications are provided in fuel cells and flow batteries. Further developments of the LB method are also outlined.

Flow simulation of fiber reinforced self compacting concrete using Lattice Boltzmann method

DEFF Research Database (Denmark)

Svec, Oldrich; Skocek, Jan; Stang, Henrik

2011-01-01

Self compacting concrete (SCC) is a promising material in the civil engineering industry. One of the benefits of the SCC is a fast and simplified casting followed by decreased labor costs. The SCC as any other type of concrete has a significantly lower tensile and shear strength in comparison to ....... A relatively new group of models - Lattice Boltzmann Modeling (LBM) - is presented in this paper. The conventional LBM is modified to include fiber and particle suspensions and non-Newtonian rheology and is used to model the fiber reinforced self compacting concrete flow....

New continual analogs of two-dimensional Toda lattices related with nonlinear integro-differential equations

International Nuclear Information System (INIS)

Savel'ev, M.V.

1988-01-01

Continual ''extensions'' of two-dimensional Toda lattices are proposed. They are described by integro-differential equations, generally speaking, with singular kernels, depending on new (third) variable. The problem of their integrability on the corresponding class of the initial discrete system solutions is discussed. The latter takes place, in particular, for the kernel coinciding with the causal function

Lattice Boltzmann computation of creeping fluid flow in roll-coating applications

Science.gov (United States)

Rajan, Isac; Kesana, Balashanker; Perumal, D. Arumuga

2018-04-01

Lattice Boltzmann Method (LBM) has advanced as a class of Computational Fluid Dynamics (CFD) methods used to solve complex fluid systems and heat transfer problems. It has ever-increasingly attracted the interest of researchers in computational physics to solve challenging problems of industrial and academic importance. In this current study, LBM is applied to simulate the creeping fluid flow phenomena commonly encountered in manufacturing technologies. In particular, we apply this novel method to simulate the fluid flow phenomena associated with the "meniscus roll coating" application. This prevalent industrial problem encountered in polymer processing and thin film coating applications is modelled as standard lid-driven cavity problem to which creeping flow analysis is applied. This incompressible viscous flow problem is studied in various speed ratios, the ratio of upper to lower lid speed in two different configurations of lid movement - parallel and anti-parallel wall motion. The flow exhibits interesting patterns which will help in design of roll coaters.

Analysis of conduction–radiation heat transfer during phase change process of semitransparent materials using lattice Boltzmann method

International Nuclear Information System (INIS)

Maroufi, Arman; Aghanajafi, Cyrus

2013-01-01

This article deals with the analysis of solidification of a 2-D semitransparent material using the lattice Boltzmann method (LBM). Both conduction and radiation terms in governing energy equation were computed using the LBM. First, the LBM formulation regarding conduction component was validated and the results analyzed. Next, the results involving phase change or radiation term in the LBM were compared with the finite volume method (FVM). The results show good accuracy and less time consumption during LBM implementation. Finally, temperature distribution, the location of solid-liquid front, mushy zone thickness and the effects of heat transfer parameters were studied. -- Highlights: ► Solidification of 2-D semitransparent material is studied. ► Both conduction and radiation were computed using lattice Boltzmann method (LBM). ► LBM results validated by solving three benchmark problems. ► Effects of various parameters were studied on temperature distributions. ► Results show good accuracy and less time consumption during LBM implementation.

Mean-field description of ultracold bosons on disordered two-dimensional optical lattices

International Nuclear Information System (INIS)

Buonsante, Pierfrancesco; Massel, Francesco; Penna, Vittorio; Vezzani, Alessandro

2007-01-01

In the present communication, we describe the properties induced by disorder on an ultracold gas of bosonic atoms loaded into a two-dimensional optical lattice with global confinement ensured by a parabolic potential. Our analysis is centred on the spatial distribution of the various phases, focusing particularly on the superfluid properties of the system as a function of external parameters and disorder amplitude. In particular, it is shown how disorder can suppress superfluidity, while partially preserving the system coherence. (fast track communication)

Lattice Boltzmann method for short-pulsed laser transport in a multi-layered medium

International Nuclear Information System (INIS)

Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping

2015-01-01

We construct a lattice Boltzmann method (LBM) for transient radiative transfer in one-dimensional multi-layered medium with distinct refractive index in each layer. The left boundary is irradiated normally by a short-pulsed laser. The Fresnel interfaces conditions, which incorporate reflection and refraction, are used at the boundaries and the interfaces. Based on the Fresnel's law and Snell's law, the interfacial intensity formulas are introduced. The collimated and diffuse intensities are treated individually. At a transient time step, the collimated component is first solved by LBM and then embedded into the transient radiative transfer equation as a source term. To keep the consistency of the directions in all the layers, angular interpolation of the intensities at the interfaces is adopted. The transient radiative transfer in a two-layer medium is first investigated, and the time-resolved results are validated by comparing with those by the Monte Carlo method (MCM). Of particular interest, the angular intensities along the slab at different times are presented to illustrate a variety of interesting phenomena, and the discontinuous nature of the intensity at the interfaces is discussed. The effects of various parameters on the time-resolved signals are examined. - Highlights: • Transient radiative transfer in a multi-layered medium is solved by LBM. • The boundary and interfaces are all considered as Fresnel surfaces. • The LBM solution for the collimated pulse is derived. • Discontinuous nature of the intensity at the interface is illustrated and discussed

Entropic Lattice Boltzmann: an implicit Large-Eddy Simulation?

Science.gov (United States)

Tauzin, Guillaume; Biferale, Luca; Sbragaglia, Mauro; Gupta, Abhineet; Toschi, Federico; Ehrhardt, Matthias; Bartel, Andreas

2017-11-01

We study the modeling of turbulence implied by the unconditionally stable Entropic Lattice Boltzmann Method (ELBM). We first focus on 2D homogeneous turbulence, for which we conduct numerical simulations for a wide range of relaxation times τ. For these simulations, we analyze the effective viscosity obtained by numerically differentiating the kinetic energy and enstrophy balance equations averaged over sub-domains of the computational grid. We aim at understanding the behavior of the implied sub-grid scale model and verify a formulation previously derived using Chapman-Enskog expansion. These ELBM benchmark simulations are thus useful to understand the range of validity of ELBM as a turbulence model. Finally, we will discuss an extension of the previously obtained results to the 3D case. Supported by the European Unions Framework Programme for Research and Innovation Horizon 2020 (2014-2020) under the Marie Sklodowska-Curie Grant Agreement No. 642069 and by the European Research Council under the ERC Grant Agreement No. 339032.

A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

Directory of Open Access Journals (Sweden)

Stuart Bartlett

2017-08-01

Full Text Available The lattice Boltzmann method is an efficient computational fluid dynamics technique that can accurately model a broad range of complex systems. As well as single-phase fluids, it can simulate thermohydrodynamic systems and passive scalar advection. In recent years, it also gained attention as a means of simulating chemical phenomena, as interest in self-organization processes increased. This paper will present a widely-used and versatile lattice Boltzmann model that can simultaneously incorporate fluid dynamics, heat transfer, buoyancy-driven convection, passive scalar advection, chemical reactions and enthalpy changes. All of these effects interact in a physically accurate framework that is simple to code and readily parallelizable. As well as a complete description of the model equations, several example systems will be presented in order to demonstrate the accuracy and versatility of the method. New simulations, which analyzed the effect of a reversible reaction on the transport properties of a convecting fluid, will also be described in detail. This extra chemical degree of freedom was utilized by the system to augment its net heat flux. The numerical method outlined in this paper can be readily deployed for a vast range of complex flow problems, spanning a variety of scientific disciplines.

Dynamically adaptive Lattice Boltzmann simulation of shallow water flows with the Peano framework

KAUST Repository

Neumann, Philipp

2015-09-01

© 2014 Elsevier Inc. All rights reserved. We present a dynamically adaptive Lattice Boltzmann (LB) implementation for solving the shallow water equations (SWEs). Our implementation extends an existing LB component of the Peano framework. We revise the modular design with respect to the incorporation of new simulation aspects and LB models. The basic SWE-LB implementation is validated in different breaking dam scenarios. We further provide a numerical study on stability of the MRT collision operator used in our simulations.

Macroscopic lattice Boltzmann model for heat and moisture transfer process with phase transformation in unsaturated porous media during freezing process

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Song Wenyu

2017-06-01

Full Text Available In the current study, a macroscopic lattice Boltzmann model for simulating the heat and moisture transport phenomenon in unsaturated porous media during the freezing process was proposed. The proposed model adopted percolation threshold to reproduce the extra resistance in frozen fringe during the freezing process. The freezing process in Kanagawa sandy loam soil was demonstrated by the proposed model. The numerical result showed good agreement with the experimental result. The proposed model also offered higher computational efficiency and better agreement with the experimental result than the existing numerical models. Lattice Boltzmann method is suitable for simulating complex heat and mass transfer process in porous media at macroscopic scale under proper dimensionless criterion, which makes it a potentially powerful tool for engineering application.

Lattice Boltzmann Method of Different BGA Orientations on I-Type Dispensing Method.

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Aizat Abas

Full Text Available This paper studies the three dimensional (3D simulation of fluid flows through the ball grid array (BGA to replicate the real underfill encapsulation process. The effect of different solder bump arrangements of BGA on the flow front, pressure and velocity of the fluid is investigated. The flow front, pressure and velocity for different time intervals are determined and analyzed for potential problems relating to solder bump damage. The simulation results from Lattice Boltzmann Method (LBM code will be validated with experimental findings as well as the conventional Finite Volume Method (FVM code to ensure highly accurate simulation setup. Based on the findings, good agreement can be seen between LBM and FVM simulations as well as the experimental observations. It was shown that only LBM is capable of capturing the micro-voids formation. This study also shows an increasing trend in fluid filling time for BGA with perimeter, middle empty and full orientations. The perimeter orientation has a higher pressure fluid at the middle region of BGA surface compared to middle empty and full orientation. This research would shed new light for a highly accurate simulation of encapsulation process using LBM and help to further increase the reliability of the package produced.

Multi-component Lattice Boltzmann simulation of the hydrodynamics in drip emitters

Directory of Open Access Journals (Sweden)

Giacomo Falcucci

2017-09-01

Full Text Available In this paper, we propose a fast and efficient numerical technique based on the Lattice Boltzmann method (LBM to model the flow through a reference drip emitter geometry. The aim of the study is to demonstrate the applicability of the LBM as a reliable simulation tool for the hydraulic optimisation of irrigation systems. Results for the water flow through a rectangular drip emitter are in good agreement with literature numerical and experimental data. Furthermore, we demonstrate the feasibility of the proposed model to simulate a multi-component flow that could be used to simulate the presence of additives, contaminants, and suspended particles.

Quantum transport in d -dimensional lattices

International Nuclear Information System (INIS)

Manzano, Daniel; Chuang, Chern; Cao, Jianshu

2016-01-01

We show that both fermionic and bosonic uniform d -dimensional lattices can be reduced to a set of independent one-dimensional chains. This reduction leads to the expression for ballistic energy fluxes in uniform fermionic and bosonic lattices. By the use of the Jordan–Wigner transformation we can extend our analysis to spin lattices, proving the coexistence of both ballistic and non-ballistic subspaces in any dimension and for any system size. We then relate the nature of transport to the number of excitations in the homogeneous spin lattice, indicating that a single excitation always propagates ballistically and that the non-ballistic behaviour of uniform spin lattices is a consequence of the interaction between different excitations. (paper)

Application of mesh free lattice Boltzmann method to the analysis of very high temperature reactor lower plenum

Energy Technology Data Exchange (ETDEWEB)

Park, Jong Woon [Dongguk Univ., Gyeongju (Korea, Republic of). Dept. of Energy and Environment

2011-11-15

Inside a helium-cooled very high temperature reactor (VHTR) lower plenum, hot gas jets from upper fuel channels with very high velocities and temperatures and is mixed before flowing out. One of the major concerns is local hot spots in the plenum due to inefficient mixing of the helium exiting from differentially heated fuel channels and it involves complex fluid flow physics. For this situation, mesh-free technique, especially Lattice Boltzmann Method (LBM), is thus of particular interest owing to its merit of no mesh generation. As an attempt to find efficiency of the method in such a problem, 3 dimensional flow field inside a scaled test model of the VHTR lower plenum is computed with commercial XFLOW code. Large eddy simulation (LES) and classical Smagorinsky eddy viscosity (EV) turbulence models are employed to investigate the capability of the LBM in capturing large scale vortex shedding. (orig.)

Numerical modeling of carrier gas flow in atomic layer deposition vacuum reactor: A comparative study of lattice Boltzmann models

International Nuclear Information System (INIS)

Pan, Dongqing; Chien Jen, Tien; Li, Tao; Yuan, Chris

2014-01-01

This paper characterizes the carrier gas flow in the atomic layer deposition (ALD) vacuum reactor by introducing Lattice Boltzmann Method (LBM) to the ALD simulation through a comparative study of two LBM models. Numerical models of gas flow are constructed and implemented in two-dimensional geometry based on lattice Bhatnagar–Gross–Krook (LBGK)-D2Q9 model and two-relaxation-time (TRT) model. Both incompressible and compressible scenarios are simulated and the two models are compared in the aspects of flow features, stability, and efficiency. Our simulation outcome reveals that, for our specific ALD vacuum reactor, TRT model generates better steady laminar flow features all over the domain with better stability and reliability than LBGK-D2Q9 model especially when considering the compressible effects of the gas flow. The LBM-TRT is verified indirectly by comparing the numerical result with conventional continuum-based computational fluid dynamics solvers, and it shows very good agreement with these conventional methods. The velocity field of carrier gas flow through ALD vacuum reactor was characterized by LBM-TRT model finally. The flow in ALD is in a laminar steady state with velocity concentrated at the corners and around the wafer. The effects of flow fields on precursor distributions, surface absorptions, and surface reactions are discussed in detail. Steady and evenly distributed velocity field contribute to higher precursor concentration near the wafer and relatively lower particle velocities help to achieve better surface adsorption and deposition. The ALD reactor geometry needs to be considered carefully if a steady and laminar flow field around the wafer and better surface deposition are desired

Numerical modeling of carrier gas flow in atomic layer deposition vacuum reactor: A comparative study of lattice Boltzmann models

Energy Technology Data Exchange (ETDEWEB)

Pan, Dongqing; Chien Jen, Tien [Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201 (United States); Li, Tao [School of Mechanical Engineering, Dalian University of Technology, Dalian 116024 (China); Yuan, Chris, E-mail: cyuan@uwm.edu [Department of Mechanical Engineering, University of Wisconsin-Milwaukee, 3200 North Cramer Street, Milwaukee, Wisconsin 53211 (United States)

2014-01-15

This paper characterizes the carrier gas flow in the atomic layer deposition (ALD) vacuum reactor by introducing Lattice Boltzmann Method (LBM) to the ALD simulation through a comparative study of two LBM models. Numerical models of gas flow are constructed and implemented in two-dimensional geometry based on lattice Bhatnagar–Gross–Krook (LBGK)-D2Q9 model and two-relaxation-time (TRT) model. Both incompressible and compressible scenarios are simulated and the two models are compared in the aspects of flow features, stability, and efficiency. Our simulation outcome reveals that, for our specific ALD vacuum reactor, TRT model generates better steady laminar flow features all over the domain with better stability and reliability than LBGK-D2Q9 model especially when considering the compressible effects of the gas flow. The LBM-TRT is verified indirectly by comparing the numerical result with conventional continuum-based computational fluid dynamics solvers, and it shows very good agreement with these conventional methods. The velocity field of carrier gas flow through ALD vacuum reactor was characterized by LBM-TRT model finally. The flow in ALD is in a laminar steady state with velocity concentrated at the corners and around the wafer. The effects of flow fields on precursor distributions, surface absorptions, and surface reactions are discussed in detail. Steady and evenly distributed velocity field contribute to higher precursor concentration near the wafer and relatively lower particle velocities help to achieve better surface adsorption and deposition. The ALD reactor geometry needs to be considered carefully if a steady and laminar flow field around the wafer and better surface deposition are desired.

Vibrational spectra and thermal rectification in three-dimensional anharmonic lattices

International Nuclear Information System (INIS)

Lan Jinghua; Li Baowen

2007-01-01

We study thermal rectification in a three-dimensional model consisting of two segments of anharmonic lattices. One segment consists of layers of harmonic oscillator arrays coupled to a substrate potential, which is a three-dimensional Frenkel-Kontorova model, and the other segment is a three-dimensional Fermi-Pasta-Ulam model. We study the vibrational bands of the two lattices analytically and numerically, and find that, by choosing the system parameters properly, the rectification can be as high as a few thousands, which is high enough to be observed in experiment. Possible experiments in nanostructures are discussed

Topics in two dimensional conformal field theory and three dimensional topological lattice field theory

International Nuclear Information System (INIS)

Chung, Stephen-wei.

1993-01-01

The authors first construct new parafermions in two-dimensional conformal field theory, generalizing the Z L parafermion theories from integer L to rational L. These non-unitary parafermions have some novel features: an infinite number of currents with negative conformal dimensions for most (if not all) of them. String functions of these new parafermion theories are calculated. They also construct new representations of N = 2 superconformal field theories, whose characters are obtained in terms of these new string functions. They then generalize Felder's BRST cohomology method to construct the characters and branching functions of the SU(2) L x SU(2) K /SU(2) K+L coset theories, where one of the (K,L) is an integer. This method of obtaining the branching functions also serves as a check of their new Z L parafermion theories. The next topic is the Lagrangian formulation of conformal field theory. They construct a chiral gauged WZW theory where the gauge fields are chiral and belong to the subgroups H L and H R , which can be different groups. This new construction is beyond the ordinary vector gauged WZW theory, whose gauge group H is a subgroup of both G L and G R . In the special case where H L = H R , the quantum theory of chiral gauged WZW theory is equivalent to that of the vector gauged WZW theory. It can be further shown that the chiral gauged WZW theory is equivalent to [G L /H L ](z) direct-product [G R /H R ](bar z) coset models in conformal field theory. In the second half of this thesis, they construct topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, they impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two local lattice moves. Invariant solutions are in one-to-one correspondence with Hopf algebras satisfying a certain constraint

Sailfish: A flexible multi-GPU implementation of the lattice Boltzmann method

Science.gov (United States)

Januszewski, M.; Kostur, M.

2014-09-01

We present Sailfish, an open source fluid simulation package implementing the lattice Boltzmann method (LBM) on modern Graphics Processing Units (GPUs) using CUDA/OpenCL. We take a novel approach to GPU code implementation and use run-time code generation techniques and a high level programming language (Python) to achieve state of the art performance, while allowing easy experimentation with different LBM models and tuning for various types of hardware. We discuss the general design principles of the code, scaling to multiple GPUs in a distributed environment, as well as the GPU implementation and optimization of many different LBM models, both single component (BGK, MRT, ELBM) and multicomponent (Shan-Chen, free energy). The paper also presents results of performance benchmarks spanning the last three NVIDIA GPU generations (Tesla, Fermi, Kepler), which we hope will be useful for researchers working with this type of hardware and similar codes. Catalogue identifier: AETA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License, version 3 No. of lines in distributed program, including test data, etc.: 225864 No. of bytes in distributed program, including test data, etc.: 46861049 Distribution format: tar.gz Programming language: Python, CUDA C, OpenCL. Computer: Any with an OpenCL or CUDA-compliant GPU. Operating system: No limits (tested on Linux and Mac OS X). RAM: Hundreds of megabytes to tens of gigabytes for typical cases. Classification: 12, 6.5. External routines: PyCUDA/PyOpenCL, Numpy, Mako, ZeroMQ (for multi-GPU simulations), scipy, sympy Nature of problem: GPU-accelerated simulation of single- and multi-component fluid flows. Solution method: A wide range of relaxation models (LBGK, MRT, regularized LB, ELBM, Shan-Chen, free energy, free surface) and boundary conditions within the lattice

Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method

Science.gov (United States)

Peng, Cheng; Geneva, Nicholas; Guo, Zhaoli; Wang, Lian-Ping

2018-03-01

In this paper, we present a first direct numerical simulation (DNS) of a turbulent pipe flow using the mesoscopic lattice Boltzmann method (LBM) on both a D3Q19 lattice grid and a D3Q27 lattice grid. DNS of turbulent pipe flows using LBM has never been reported previously, perhaps due to inaccuracy and numerical stability associated with the previous implementations of LBM in the presence of a curved solid surface. In fact, it was even speculated that the D3Q19 lattice might be inappropriate as a DNS tool for turbulent pipe flows. In this paper, we show, through careful implementation, accurate turbulent statistics can be obtained using both D3Q19 and D3Q27 lattice grids. In the simulation with D3Q19 lattice, a few problems related to the numerical stability of the simulation are exposed. Discussions and solutions for those problems are provided. The simulation with D3Q27 lattice, on the other hand, is found to be more stable than its D3Q19 counterpart. The resulting turbulent flow statistics at a friction Reynolds number of Reτ = 180 are compared systematically with both published experimental and other DNS results based on solving the Navier-Stokes equations. The comparisons cover the mean-flow profile, the r.m.s. velocity and vorticity profiles, the mean and r.m.s. pressure profiles, the velocity skewness and flatness, and spatial correlations and energy spectra of velocity and vorticity. Overall, we conclude that both D3Q19 and D3Q27 simulations yield accurate turbulent flow statistics. The use of the D3Q27 lattice is shown to suppress the weak secondary flow pattern in the mean flow due to numerical artifacts.

An adaptive mesh refinement-multiphase lattice Boltzmann flux solver for simulation of complex binary fluid flows

Science.gov (United States)

Yuan, H. Z.; Wang, Y.; Shu, C.

2017-12-01

This paper presents an adaptive mesh refinement-multiphase lattice Boltzmann flux solver (AMR-MLBFS) for effective simulation of complex binary fluid flows at large density ratios. In this method, an AMR algorithm is proposed by introducing a simple indicator on the root block for grid refinement and two possible statuses for each block. Unlike available block-structured AMR methods, which refine their mesh by spawning or removing four child blocks simultaneously, the present method is able to refine its mesh locally by spawning or removing one to four child blocks independently when the refinement indicator is triggered. As a result, the AMR mesh used in this work can be more focused on the flow region near the phase interface and its size is further reduced. In each block of mesh, the recently proposed MLBFS is applied for the solution of the flow field and the level-set method is used for capturing the fluid interface. As compared with existing AMR-lattice Boltzmann models, the present method avoids both spatial and temporal interpolations of density distribution functions so that converged solutions on different AMR meshes and uniform grids can be obtained. The proposed method has been successfully validated by simulating a static bubble immersed in another fluid, a falling droplet, instabilities of two-layered fluids, a bubble rising in a box, and a droplet splashing on a thin film with large density ratios and high Reynolds numbers. Good agreement with the theoretical solution, the uniform-grid result, and/or the published data has been achieved. Numerical results also show its effectiveness in saving computational time and virtual memory as compared with computations on uniform meshes.

A pore-scale model for the cathode electrode of a proton exchange membrane fuel cell by lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Molaeimanesh, Gholam Reza; Akbari, Mohammad Hadi [Shiraz University, Shiraz (Iran, Islamic Republic of)

2015-03-15

A pore-scale model based on the lattice Boltzmann method (LBM) is proposed for the cathode electrode of a PEM fuel cell with heterogeneous and anisotropic porous gas diffusion layer (GDL) and interdigitated flow field. An active approach is implemented to model multi-component transport in GDL, which leads to enhanced accuracy, especially at higher activation over-potentials. The core of the paper is the implementation of an electrochemical reaction with an active approach in a multi-component lattice Boltzmann model for the first time. After model validation, the capability of the presented model is demonstrated through a parametric study. Effects of activation over-potential, pressure differential between inlet and outlet gas channels, land width to channel width ratio, and channel width are investigated. The results show the significant influence of GDL microstructure on the oxygen distribution and current density profile.

Lattice Boltzmann method and gas-kinetic BGK scheme in the low-Mach number viscous flow simulations

International Nuclear Information System (INIS)

Xu Kun; He Xiaoyi

2003-01-01

Both lattice Boltzmann method (LBM) and the gas-kinetic BGK scheme are based on the numerical discretization of the Boltzmann equation with collisional models, such as, the Bhatnagar-Gross-Krook (BGK) model. LBM tracks limited number of particles and the viscous flow behavior emerges automatically from the intrinsic particle stream and collisions process. On the other hand, the gas-kinetic BGK scheme is a finite volume scheme, where the time-dependent gas distribution function with continuous particle velocity space is constructed and used in the evaluation of the numerical fluxes across cell interfaces. Currently, LBM is mainly used for low Mach number, nearly incompressible flow simulation. For the gas-kinetic scheme, the application is focusing on the high speed compressible flows. In this paper, we are going to compare both schemes in the isothermal low-Mach number flow simulations. The methodology for developing both schemes will be clarified through the introduction of operator splitting Boltzmann model and operator averaging Boltzmann model. From the operator splitting Boltzmann model, the error rooted in many kinetic schemes, which are based on the decoupling of particle transport and collision, can be easily understood. As to the test case, we choose to use the 2D cavity flow since it is one of the most extensively studied cases. Detailed simulation results with different Reynolds numbers, as well as the benchmark solutions, are presented

Electrostatic modulation of periodic potentials in a two-dimensional electron gas: From antidot lattice to quantum dot lattice

Energy Technology Data Exchange (ETDEWEB)

Goswami, Srijit; Aamir, Mohammed Ali; Shamim, Saquib; Ghosh, Arindam [Department of Physics, Indian Institute of Science, Bangalore 560 012 (India); Siegert, Christoph; Farrer, Ian; Ritchie, David A. [Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Pepper, Michael [Department of Electrical and Electronic Engineering, University College, London WC1E 7JE (United Kingdom)

2013-12-04

We use a dual gated device structure to introduce a gate-tuneable periodic potential in a GaAs/AlGaAs two dimensional electron gas (2DEG). Using only a suitable choice of gate voltages we can controllably alter the potential landscape of the bare 2DEG, inducing either a periodic array of antidots or quantum dots. Antidots are artificial scattering centers, and therefore allow for a study of electron dynamics. In particular, we show that the thermovoltage of an antidot lattice is particularly sensitive to the relative positions of the Fermi level and the antidot potential. A quantum dot lattice, on the other hand, provides the opportunity to study correlated electron physics. We find that its current-voltage characteristics display a voltage threshold, as well as a power law scaling, indicative of collective Coulomb blockade in a disordered background.

Electrostatic modulation of periodic potentials in a two-dimensional electron gas: From antidot lattice to quantum dot lattice

International Nuclear Information System (INIS)

Goswami, Srijit; Aamir, Mohammed Ali; Shamim, Saquib; Ghosh, Arindam; Siegert, Christoph; Farrer, Ian; Ritchie, David A.; Pepper, Michael

2013-01-01

We use a dual gated device structure to introduce a gate-tuneable periodic potential in a GaAs/AlGaAs two dimensional electron gas (2DEG). Using only a suitable choice of gate voltages we can controllably alter the potential landscape of the bare 2DEG, inducing either a periodic array of antidots or quantum dots. Antidots are artificial scattering centers, and therefore allow for a study of electron dynamics. In particular, we show that the thermovoltage of an antidot lattice is particularly sensitive to the relative positions of the Fermi level and the antidot potential. A quantum dot lattice, on the other hand, provides the opportunity to study correlated electron physics. We find that its current-voltage characteristics display a voltage threshold, as well as a power law scaling, indicative of collective Coulomb blockade in a disordered background

Turing instability for a two-dimensional Logistic coupled map lattice

International Nuclear Information System (INIS)

Xu, L.; Zhang, G.; Han, B.; Zhang, L.; Li, M.F.; Han, Y.T.

2010-01-01

In this Letter, stability analysis is applied to a two-dimensional Logistic coupled map lattice with the periodic boundary conditions. The conditions of Turing instability are obtained, and various patterns can be exhibited by numerical simulations in the Turing instability region. For example, space-time periodic structures, periodic or quasiperiodic traveling wave solutions, stationary wave solutions, spiral waves, and spatiotemporal chaos, etc. have been observed. In particular, the different pattern structures have also been observed for same parameters and different initial values. That is, pattern structures also depend on the initial values. The similar patterns have also been seen in relevant references. However, the present Letter owes to pattern formation via diffusion-driven instabilities because the system is stable in the absence of diffusion.

Three Dimensional Simulations of Multiphase Flows Using a Lattice Boltzmann Method Suitable for High Density Ratios - 12126

Energy Technology Data Exchange (ETDEWEB)

Gokaltun, Seckin; McDaniel, Dwayne; Roelant, David [Applied Research Center, Florida International University, 10555 West Flagler Street, Suite 2100, Miami, FL 33174 (United States)

2012-07-01

Multiphase flows involving gas and liquid phases can be observed in engineering operations at various Department of Energy sites, such as mixing of slurries using pulsed-air mixers and hydrogen gas generation in liquid waste tanks etc. The dynamics of the gas phase in the liquid domain play an important role in the mixing effectiveness of the pulsed-air mixers or in the level of gas pressure build-up in waste tanks. To understand such effects, computational fluid dynamics methods (CFD) can be utilized by developing a three-dimensional computerized multiphase flow model that can predict accurately the behavior of gas motion inside liquid-filled tanks by solving the governing mathematical equations that represent the physics of the phenomena. In this paper, such a CFD method, lattice Boltzmann method (LBM), is presented that can model multiphase flows accurately and efficiently. LBM is favored over traditional Navier-Stokes based computational models since interfacial forces are handled more effectively in LBM. The LBM is easier to program, more efficient to solve on parallel computers, and has the ability to capture the interface between different fluid phases intrinsically. The LBM used in this paper can solve for the incompressible and viscous flow field in three dimensions, while at the same time, solve the Cahn-Hillard equation to track the position of the gas-liquid interface specifically when the density and viscosity ratios between the two fluids are high. This feature is of primary importance since the previous LBM models proposed for multiphase flows become unstable when the density ratio is larger than 10. The ability to provide stable and accurate simulations at large density ratios becomes important when the simulation case involves fluids such as air and water with a density ratio around 1000 that are common to many engineering problems. In order to demonstrate the capability of the 3D LBM method at high density ratios, a static bubble simulation is

Simulation of sound waves using the Lattice Boltzmann Method for fluid flow: Benchmark cases for outdoor sound propagation

NARCIS (Netherlands)

Salomons, E.M.; Lohman, W.J.A.; Zhou, H.

2016-01-01

Propagation of sound waves in air can be considered as a special case of fluid dynamics. Consequently, the lattice Boltzmann method (LBM) for fluid flow can be used for simulating sound propagation. In this article application of the LBM to sound propagation is illustrated for various cases:

Hofstadter's butterfly energy spectrum of ultracold fermions on the two-dimensional triangular optical lattice

International Nuclear Information System (INIS)

Hou Jingmin; Lu Qingqing

2009-01-01

We study the energy spectrum of ultracold fermionic atoms on the two-dimensional triangular optical lattice subjected to a perpendicular effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations and numerically solve them, then we obtain the Hofstadter's butterfly-like energy spectrum, which has a novel fractal structure. The observability of the Hofstadter's butterfly spectrum is also discussed

Lattice Boltzmann Simulation of Permeability and Tortuosity for Flow through Dense Porous Media

Directory of Open Access Journals (Sweden)

Ping Wang

2014-01-01

Full Text Available Discrete element method (DEM is used to produce dense and fixed porous media with rigid mono spheres. Lattice Boltzmann method (LBM is adopted to simulate the fluid flow in interval of dense spheres. To simulating the same physical problem, the permeability is obtained with different lattice number. We verify that the permeability is irrelevant to the body force and the media length along flow direction. The relationships between permeability, tortuosity and porosity, and sphere radius are researched, and the results are compared with those reported by other authors. The obtained results indicate that LBM is suited to fluid flow simulation of porous media due to its inherent theoretical advantages. The radius of sphere should have ten lattices at least and the media length along flow direction should be more than twenty radii. The force has no effect on the coefficient of permeability with the limitation of slow fluid flow. For mono spheres porous media sample, the relationship of permeability and porosity agrees well with the K-C equation, and the tortuosity decreases linearly with increasing porosity.

Lattice Boltzmann simulations of bubble formation in a microfluidic T-junction.

Science.gov (United States)

Amaya-Bower, Luz; Lee, Taehun

2011-06-28

A lattice Boltzmann equation method based on the Cahn-Hilliard diffuse interface theory is developed to investigate the bubble formation process in a microchannel with T-junction mixing geometry. The bubble formation process has different regimes, namely, squeezing, dripping and jetting regimes, which correspond to the primary forces acting on the system. Transition from regime to regime is generally dictated by the capillary number Ca, volumetric flow ratio Q and viscosity ratio λ. A systematic analysis is performed to evaluate these effects. The computations are performed in the range of 10(-4)

A numeric investigation of co-flowing liquid streams using the Lattice Boltzmann Method

Science.gov (United States)

Somogyi, Andy; Tagg, Randall

2007-11-01

We present a numerical investigation of co-flowing immiscible liquid streams using the Lattice Boltzmann Method (LBM) for multi component, dissimilar viscosity, immiscible fluid flow. When a liquid is injected into another immiscible liquid, the flow will eventually transition from jetting to dripping due to interfacial tension. Our implementation of LBM models the interfacial tension through a variety of techniques. Parallelization is also straightforward for both single and multi component models as only near local interaction is required. We compare the results of our numerical investigation using LBM to several recent physical experiments.

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

Science.gov (United States)

Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun

2012-01-01

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish. PMID:23564971

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

Science.gov (United States)

Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun

2011-08-01

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

Ultrafine particles dispersion modeling in a street canyon: development and evaluation of a composite lattice Boltzmann model.

Science.gov (United States)

Habilomatis, George; Chaloulakou, Archontoula

2013-10-01

Recently, a branch of particulate matter research concerns on ultrafine particles found in the urban environment, which originate, to a significant extent, from traffic sources. In urban street canyons, dispersion of ultrafine particles affects pedestrian's short term exposure and resident's long term exposure as well. The aim of the present work is the development and the evaluation of a composite lattice Boltzmann model to study the dispersion of ultrafine particles, in urban street canyon microenvironment. The proposed model has the potential to penetrate into the physics of this complex system. In order to evaluate the model performance against suitable experimental data, ultrafine particles levels have been monitored on an hourly basis for a period of 35 days, in a street canyon, in Athens area. The results of the comparative analysis are quite satisfactory. Furthermore, our modeled results are in a good agreement with the results of other computational and experimental studies. This work is a first attempt to study the dispersion of an air pollutant by application of the lattice Boltzmann method. Copyright © 2013 Elsevier B.V. All rights reserved.

Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows.

Science.gov (United States)

Li, Q; Luo, K H; Li, X J

2012-07-01

The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model.

Hamiltonian formalism of two-dimensional Vlasov kinetic equation.

Science.gov (United States)

Pavlov, Maxim V

2014-12-08

In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.

On d -Dimensional Lattice (co)sine n -Algebra

International Nuclear Information System (INIS)

Yao Shao-Kui; Zhang Chun-Hong; Zhao Wei-Zhong; Ding Lu; Liu Peng

2016-01-01

We present the (co)sine n-algebra which is indexed by the d-dimensional integer lattice. Due to the associative operators, this generalized (co)sine n-algebra is the higher order Lie algebra for the n even case. The particular cases are the d-dimensional lattice sine 3 and cosine 5-algebras with the special parameter values. We find that the corresponding d-dimensional lattice sine 3 and cosine 5-algebras are the Nambu 3-algebra and higher order Lie algebra, respectively. The limiting case of the d-dimensional lattice (co)sine n-algebra is also discussed. Moreover we construct the super sine n-algebra, which is the super higher order Lie algebra for the n even case. (paper)

A weighted multiple-relaxation-time lattice Boltzmann method for multiphase flows and its application to partial coalescence cascades

Science.gov (United States)

Fakhari, Abbas; Bolster, Diogo; Luo, Li-Shi

2017-07-01

We present a lattice Boltzmann method (LBM) with a weighted multiple-relaxation-time (WMRT) collision model and an adaptive mesh refinement (AMR) algorithm for direct numerical simulation of two-phase flows in three dimensions. The proposed WMRT model enhances the numerical stability of the LBM for immiscible fluids at high density ratios, particularly on the D3Q27 lattice. The effectiveness and efficiency of the proposed WMRT-LBM-AMR is validated through simulations of (a) buoyancy-driven motion and deformation of a gas bubble rising in a viscous liquid; (b) the bag-breakup mechanism of a falling drop; (c) crown splashing of a droplet on a wet surface; and (d) the partial coalescence mechanism of a liquid drop at a liquid-liquid interface. The numerical simulations agree well with available experimental data and theoretical approximations where applicable.

Lattice Boltzmann Simulation Optimization on Leading Multicore Platforms

Energy Technology Data Exchange (ETDEWEB)

Williams, Samuel; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine

2008-02-01

We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Clovertown, AMD Opteron X2, Sun Niagara2, STI Cell, as well as the single core Intel Itanium2. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned LBMHD application achieves up to a 14x improvement compared with the original code. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.

Lattice Boltzmann simulation optimization on leading multicore platforms

Energy Technology Data Exchange (ETDEWEB)

Williams, S. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States); Carter, J. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oliker, L. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Shalf, J. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Yelick, K. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)

2008-01-01

We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of searchbased performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Clovertown, AMD Opteron X2, Sun Niagara2, STI Cell, as well as the single core Intel Itanium2. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our autotuned LBMHD application achieves up to a 14 improvement compared with the original code. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.

Implementing the lattice Boltzmann method to electrohydrodynamics with the leaky dielectric theory

International Nuclear Information System (INIS)

Zhang, J.; Kwok, D.Y.

2004-01-01

The lattice Boltzmann method (LBM) and electrohydrodynamics are both active subjects in fluid mechanics research in recent years. In this paper, we present a method to apply a multicomponent LBM to electrohydrodynamics studies. A series of drop deformation simulations under the influence of an electric field were carried out and the results are in good agreement with other theoretical and experimental studies. Given that no special treatment of interfaces is required for LBM, our method could be an excellent alternative to electrohydrodynamics studies than traditional computational fluid dynamics methods. Further, our algorithm and simulation can be readily implemented to the more complex electrohydrodynamic systems. (author)

A dynamic mesh refinement technique for Lattice Boltzmann simulations on octree-like grids

KAUST Repository

Neumann, Philipp

2012-04-27

In this contribution, we present our new adaptive Lattice Boltzmann implementation within the Peano framework, with special focus on nanoscale particle transport problems. With the continuum hypothesis not holding anymore on these small scales, new physical effects - such as Brownian fluctuations - need to be incorporated. We explain the overall layout of the application, including memory layout and access, and shortly review the adaptive algorithm. The scheme is validated by different benchmark computations in two and three dimensions. An extension to dynamically changing grids and a spatially adaptive approach to fluctuating hydrodynamics, allowing for the thermalisation of the fluid in particular regions of interest, is proposed. Both dynamic adaptivity and adaptive fluctuating hydrodynamics are validated separately in simulations of particle transport problems. The application of this scheme to an oscillating particle in a nanopore illustrates the importance of Brownian fluctuations in such setups. © 2012 Springer-Verlag.

Lattice Boltzmann Simulation of Collision between 2D Circular Particles Suspension in Couette Flow

Directory of Open Access Journals (Sweden)

Li-Zhong Huang

2013-01-01

Full Text Available Collision between 2D circular particles suspension in Couette flow is simulated by using multiple-relaxation-time based lattice Boltzmann and direct forcing/fictitious domain method in this paper. The patterns of particle collisions are simulated and analyzed in detail by changing the velocity of top and bottom walls in the Couette flow. It can be seen from the simulation results that, while the velocity is large enough, the number of collisions between particles will change little as this velocity varies.

Downstream-Conditioned Maximum Entropy Method for Exit Boundary Conditions in the Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Javier A. Dottori

2015-01-01

Full Text Available A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.

Numerical simulation of jet breakup behavior by the lattice Boltzmann method

International Nuclear Information System (INIS)

Matsuo, Eiji; Koyama, Kazuya; Abe, Yutaka; Iwasawa, Yuzuru; Ebihara, Ken-ichi

2015-01-01

In order to understand the jet breakup behavior of the molten core material into coolant during a core disruptive accident (CDA) for a sodium-cooled fast reactor (SFR), we simulated the jet breakup due to the hydrodynamic interaction using the lattice Boltzmann method (LBM). The applicability of the LBM to the jet breakup simulation was validated by comparison with our experimental data. In addition, the influence of several dimensionless numbers such as Weber number and Froude number was examined using the LBM. As a result, we validated applicability of the LBM to the jet breakup simulation, and found that the jet breakup length is independent of Froude number and in good agreement with the Epstein's correlation when the jet interface becomes unstable. (author)

Large eddy simulation of rotating turbulent flows and heat transfer by the lattice Boltzmann method

Science.gov (United States)

Liou, Tong-Miin; Wang, Chun-Sheng

2018-01-01

Due to its advantage in parallel efficiency and wall treatment over conventional Navier-Stokes equation-based methods, the lattice Boltzmann method (LBM) has emerged as an efficient tool in simulating turbulent heat and fluid flows. To properly simulate the rotating turbulent flow and heat transfer, which plays a pivotal role in tremendous engineering devices such as gas turbines, wind turbines, centrifugal compressors, and rotary machines, the lattice Boltzmann equations must be reformulated in a rotating coordinate. In this study, a single-rotating reference frame (SRF) formulation of the Boltzmann equations is newly proposed combined with a subgrid scale model for the large eddy simulation of rotating turbulent flows and heat transfer. The subgrid scale closure is modeled by a shear-improved Smagorinsky model. Since the strain rates are also locally determined by the non-equilibrium part of the distribution function, the calculation process is entirely local. The pressure-driven turbulent channel flow with spanwise rotation and heat transfer is used for validating the approach. The Reynolds number characterized by the friction velocity and channel half height is fixed at 194, whereas the rotation number in terms of the friction velocity and channel height ranges from 0 to 3.0. A working fluid of air is chosen, which corresponds to a Prandtl number of 0.71. Calculated results are demonstrated in terms of mean velocity, Reynolds stress, root mean square (RMS) velocity fluctuations, mean temperature, RMS temperature fluctuations, and turbulent heat flux. Good agreement is found between the present LBM predictions and previous direct numerical simulation data obtained by solving the conventional Navier-Stokes equations, which confirms the capability of the proposed SRF LBM and subgrid scale relaxation time formulation for the computation of rotating turbulent flows and heat transfer.

Near-Integrability of Low-Dimensional Periodic Klein-Gordon Lattices

Directory of Open Access Journals (Sweden)

Ognyan Christov

2018-01-01

Full Text Available The low-dimensional periodic Klein-Gordon lattices are studied for integrability. We prove that the periodic lattice with two particles and certain nonlinear potential is nonintegrable. However, in the cases of up to six particles, we prove that their Birkhoff-Gustavson normal forms are integrable, which allows us to apply KAM theory in most cases.

Simulation of diffusion in a two-dimensional lattice gas cellular automaton: a test of mode-coupling theory

NARCIS (Netherlands)

Frenkel, D.; Ernst, M.H.

1989-01-01

We compute the velocity autocorrelation function of a tagged particle in a two-dimensional lattice-gas cellular automaton using a method that is about a million times more efficient than existing techniques. A t-1 algebraic tail in the tagged-particle velocity autocorrelation function is clearly

Two-Dimensional Tellurene as Excellent Thermoelectric Material

KAUST Repository

Sharma, Sitansh; Singh, Nirpendra; Schwingenschlö gl, Udo

2018-01-01

We study the thermoelectric properties of two-dimensional tellurene by first-principles calculations and semiclassical Boltzmann transport theory. The HSE06 hybrid functional results in a moderate direct band gap of 1.48 eV at the Γ point. A high

The Effect of Wettability Heterogeneity on Relative Permeability of Two-Phase Flow in Porous Media: A Lattice Boltzmann Study

Science.gov (United States)

Zhao, Jianlin; Kang, Qinjun; Yao, Jun; Viswanathan, Hari; Pawar, Rajesh; Zhang, Lei; Sun, Hai

2018-02-01

Relative permeability is a critical parameter characterizing multiphase flow in porous media and it is strongly dependent on the wettability. In many situations, the porous media are nonuniformly wet. To investigate the effect of wettability heterogeneity on relative permeability of two-phase flow in porous media, a multi-relaxation-time color-gradient lattice Boltzmann model is adopted to simulate oil/water two-phase flow in porous media with different oil-wet solid fractions. For the water phase, when the water saturation is high, the relative permeability of water increases with the increase of oil-wet solid fraction under a constant water saturation. However, as the water saturation decreases to an intermediate value (about 0.4-0.7), the relative permeability of water in fractionally wet porous media could be lower than that in purely water-wet porous media, meaning additional flow resistance exists in the fractionally wet porous media. For the oil phase, similar phenomenon is observed. This phenomenon is mainly caused by the wettability-related microscale fluid distribution. According to both our simulation results and theoretical analysis, it is found that the relative permeability of two-phase flow in porous media is strongly related to three parameters: the fluid saturation, the specific interfacial length of fluid, and the fluid tortuosity in the flow direction. The relationship between the relative permeability and these parameters under different capillary numbers is explored in this paper.

Direct numerical simulation of circular-cap bubbles in low viscous liquids using counter diffusion lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Ryu, Seungyeob, E-mail: syryu@kaeri.re.kr [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Kim, Youngin; Yoon, Juhyeon [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Ko, Sungho, E-mail: sunghoko@cnu.ac.kr [Department of Mechanical Design Engineering, Chungnam National University, 220 Gung-dong, Yuseong-gu, Daejeon 305-764 (Korea, Republic of)

2014-01-15

Highlights: • We directly simulate circular-cap bubbles in low viscous liquids. • The counter diffusion multiphase lattice Boltzmann method is proposed. • The present method is validated through benchmark tests and experimental results. • The high-Reynolds-number bubbles can be simulated without any turbulence models. • The present method is feasible for the direct simulation of bubbly flows. -- Abstract: The counter diffusion lattice Boltzmann method (LBM) is used to directly simulate rising circular-cap bubbles in low viscous liquids. A counter diffusion model for single phase flows has been extended to multiphase flows, and the implicit formulation is converted into an explicit one for easy calculation. Bubbles at high Reynolds numbers ranging from O(10{sup 2}) to O(10{sup 4}) are simulated successfully without any turbulence models, which cannot be done for the existing LBM versions. The characteristics of the circular-cap bubbles are studied for a wide range of Morton numbers and compared with the previous literature. Calculated results agree with the theoretical and experimental data. Consequently, the wake phenomena of circular-cap bubbles and bubble induced turbulence are presented.

Multiple-relaxation-time lattice Boltzmann model for incompressible miscible flow with large viscosity ratio and high Péclet number

Science.gov (United States)

Meng, Xuhui; Guo, Zhaoli

2015-10-01

A lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator is proposed for incompressible miscible flow with a large viscosity ratio as well as a high Péclet number in this paper. The equilibria in the present model are motivated by the lattice kinetic scheme previously developed by Inamuro et al. [Philos. Trans. R. Soc. London, Ser. A 360, 477 (2002), 10.1098/rsta.2001.0942]. The fluid viscosity and diffusion coefficient depend on both the corresponding relaxation times and additional adjustable parameters in this model. As a result, the corresponding relaxation times can be adjusted in proper ranges to enhance the performance of the model. Numerical validations of the Poiseuille flow and a diffusion-reaction problem demonstrate that the proposed model has second-order accuracy in space. Thereafter, the model is used to simulate flow through a porous medium, and the results show that the proposed model has the advantage to obtain a viscosity-independent permeability, which makes it a robust method for simulating flow in porous media. Finally, a set of simulations are conducted on the viscous miscible displacement between two parallel plates. The results reveal that the present model can be used to simulate, to a high level of accuracy, flows with large viscosity ratios and/or high Péclet numbers. Moreover, the present model is shown to provide superior stability in the limit of high kinematic viscosity. In summary, the numerical results indicate that the present lattice Boltzmann model is an ideal numerical tool for simulating flow with a large viscosity ratio and/or a high Péclet number.

Lattice Boltzmann Simulation of the Hydrodynamic Entrance Region of Rectangular Microchannels in the Slip Regime

Directory of Open Access Journals (Sweden)

Niya Ma

2018-02-01

Full Text Available Developing a three-dimensional laminar flow in the entrance region of rectangular microchannels has been investigated in this paper. When the hydrodynamic development length is the same magnitude as the microchannel length, entrance effects have to be taken into account, especially in relatively short ducts. Simultaneously, there are a variety of non-continuum or rarefaction effects, such as velocity slip and temperature jump. The available data in the literature appearing on this issue is quite limited, the available study is the semi-theoretical approximate model to predict pressure drop of developing slip flow in rectangular microchannels with different aspect ratios. In this paper, we apply the lattice Boltzmann equation method (LBE to investigate the developing slip flow through a rectangular microchannel. The effects of the Reynolds number (1 < Re < 1000, channel aspect ratio (0 < ε < 1, and Knudsen number (0.001 < Kn < 0.1 on the dimensionless hydrodynamic entrance length, and the apparent friction factor, and Reynolds number product, are examined in detail. The numerical solution of LBM can recover excellent agreement with the available data in the literature, which proves its accuracy in capturing fundamental fluid characteristics in the slip-flow regime.

Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

Science.gov (United States)

Farhat, Hassan

Colloids are ubiquitous in the food, medical, cosmetic, polymer, water purification and pharmaceutical industries. Colloids thermal, mechanical and storage properties are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a cheap and reliable virtual laboratory for the study of colloids. However efficiency is a major concern to address when using numerical methods for practical applications. This work introduces the main building-blocks for an improved lattice Boltzmann-based numerical tool designed for the study of colloidal rheology and interface morphology. The efficiency of the proposed model is enhanced by using the recently developed and validated migrating multi-block algorithms for the lattice Boltzmann method (LBM). The migrating multi-block was used to simulate single component, multi-component, multiphase and single component multiphase flows. Results were validated by experimental, numerical and analytical solutions. The contamination of the fluid-fluid interface influences the colloids morphology. This issue was addressed by the introduction of the hybrid LBM for surfactant-covered droplets. The module was used for the simulation of surfactant-covered droplet deformation under shear and uniaxial extensional flows respectively and under buoyancy. Validation with experimental and theoretical results was provided. Colloids are non-Newtonian fluids which exhibit rich rheological behavior. The suppression of coalescence module is the part of the proposed model which facilitates the study of colloids rheology. The model results for the relative viscosity were in agreement with some theoretical results. Biological suspensions such as blood are macro-colloids by nature. The study of the blood flow in the microvasculature was heuristically approached by assuming the red blood cells as surfactant covered droplets. The effects of interfacial tension on the flow velocity and the droplet exclusion from the walls

Coupled lattice Boltzmann method for numerical simulations of fully coupled heart and torso bidomain system in electrocardiology

OpenAIRE

Corre , Samuel; Belmiloudi , Aziz

2016-01-01

International audience; In this work, a modified coupling Lattice Boltzmann Model (LBM) in simulation of cardiac electrophysiology is developed in order to capture the detailed activities of macro- to micro-scale transport processes. The propagation of electrical activity in the human heart through torso is mathematically modeled by bidomain type systems. As transmembrane potential evolves, we take into account domain anisotropical properties using intracellular and extracellular conductivity...

Lattice Boltzmann heat transfer model for permeable voxels

Science.gov (United States)

Pereira, Gerald G.; Wu, Bisheng; Ahmed, Shakil

2017-12-01

We develop a gray-scale lattice Boltzmann (LB) model to study fluid flow combined with heat transfer for flow through porous media where voxels may be partially solid (or void). Heat transfer in rocks may lead to deformation, which in turn can modulate the fluid flow and so has significant contribution to rock permeability. The LB temperature field is compared to a finite difference solution of the continuum partial differential equations for fluid flow in a channel. Excellent quantitative agreement is found for both Poiseuille channel flow and Brinkman flow. The LB model is then applied to sample porous media such as packed beds and also more realistic sandstone rock sample, and both the convective and diffusive regimes are recovered when varying the thermal diffusivity. It is found that while the rock permeability can be comparatively small (order milli-Darcy), the temperature field can show significant variation depending on the thermal convection of the fluid. This LB method has significant advantages over other numerical methods such as finite and boundary element methods in dealing with coupled fluid flow and heat transfer in rocks which have irregular and nonsmooth pore spaces.

Modeling of MHD natural convection in a square enclosure having an adiabatic square shaped body using Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Ahmed Kadhim Hussein

2016-03-01

Full Text Available A steady laminar two-dimensional magneto-hydrodynamics (MHD natural convection flow in a square enclosure filled with an electrically conducting fluid is numerically investigated using Lattice Boltzmann Method (LBM. The left and right vertical sidewalls of the square enclosure are maintained at hot and cold temperatures respectively. The horizontal top and bottom walls are considered thermally insulated. An adiabatic square shaped body is located in the center of a square enclosure and an external magnetic field is applied parallel to the horizontal x-axis. In the present work, the following parametric ranges of the non-dimensional groups are utilized: Hartmann number is varied as 0 ⩽ Ha ⩽ 50, Rayleigh number is varied as 103 ⩽ Ra ⩽ 105, Prandtl number is varied 0.05 ⩽ Pr ⩽ 5. It is found that the Hartmann number, Rayleigh number, and Prandtl number have an important role on the flow and thermal characteristics. It is found that when the Hartmann number increases the average Nusselt number decreases. The results also explain that the effect of magnetic field on flow field increases by increasing Prandtl number. However, the Prandtl number effect on the average Nusselt number with a magnetic field is less than the case without a magnetic field. Comparisons with previously published numerical works are performed and good agreements between the results are observed.

Study of nonequilibrium work distributions from a fluctuating lattice Boltzmann model.

Science.gov (United States)

Nasarayya Chari, S Siva; Murthy, K P N; Inguva, Ramarao

2012-04-01

A system of ideal gas is switched from an initial equilibrium state to a final state not necessarily in equilibrium, by varying a macroscopic control variable according to a well-defined protocol. The distribution of work performed during the switching process is obtained. The equilibrium free energy difference, ΔF, is determined from the work fluctuation relation. Some of the work values in the ensemble shall be less than ΔF. We term these as ones that "violate" the second law of thermodynamics. A fluctuating lattice Boltzmann model has been employed to carry out the simulation of the switching experiment. Our results show that the probability of violation of the second law increases with the increase of switching time (τ) and tends to one-half in the reversible limit of τ→∞.

Lattice classification of the four-dimensional heterotic strings

International Nuclear Information System (INIS)

Balog, J.; Forgacs, P.; Vecsernyes, P.; Horvath, Z.

1987-06-01

A lattice slicing procedure is proposed which leads to the classification of all four-dimensional chiral heterotic strings based on Conway and Sloane's 22-dimensional self-dual Euclidean lattices. By reversing this procedure it is possible to construct all these theories. (author)

Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.

Science.gov (United States)

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chen, Jie; Yin, Linmao; Chew, Jia Wei

2017-04-01

Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.

Topological Quantum Phase Transitions in Two-Dimensional Hexagonal Lattice Bilayers

Science.gov (United States)

Zhai, Xuechao; Jin, Guojun

2013-09-01

Since the successful fabrication of graphene, two-dimensional hexagonal lattice structures have become a research hotspot in condensed matter physics. In this short review, we theoretically focus on discussing the possible realization of a topological insulator (TI) phase in systems of graphene bilayer (GBL) and boron nitride bilayer (BNBL), whose band structures can be experimentally modulated by an interlayer bias voltage. Under the bias, a band gap can be opened in AB-stacked GBL but is still closed in AA-stacked GBL and significantly reduced in AA- or AB-stacked BNBL. In the presence of spin-orbit couplings (SOCs), further demonstrations indicate whether the topological quantum phase transition can be realized strongly depends on the stacking orders and symmetries of structures. It is observed that a bulk band gap can be first closed and then reopened when the Rashba SOC increases for gated AB-stacked GBL or when the intrinsic SOC increases for gated AA-stacked BNBL. This gives a distinct signal for a topological quantum phase transition, which is further characterized by a jump of the ℤ2 topological invariant. At fixed SOCs, the TI phase can be well switched by the interlayer bias and the phase boundaries are precisely determined. For AA-stacked GBL and AB-stacked BNBL, no strong TI phase exists, regardless of the strength of the intrinsic or Rashba SOCs. At last, a brief overview is given on other two-dimensional hexagonal materials including silicene and molybdenum disulfide bilayers.

New Poisson–Boltzmann type equations: one-dimensional solutions

International Nuclear Information System (INIS)

Lee, Chiun-Chang; Lee, Hijin; Hyon, YunKyong; Lin, Tai-Chia; Liu, Chun

2011-01-01

The Poisson–Boltzmann (PB) equation is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. In this paper we study a new Poisson–Boltzmann type (PB n ) equation with a small dielectric parameter ε 2 and non-local nonlinearity which takes into consideration the preservation of the total amount of each individual ion. This equation can be derived from the original Poisson–Nernst–Planck system. Under Robin-type boundary conditions with various coefficient scales, we demonstrate the asymptotic behaviours of one-dimensional solutions of PB n equations as the parameter ε approaches zero. In particular, we show that in case of electroneutrality, i.e. α = β, solutions of 1D PB n equations have a similar asymptotic behaviour as those of 1D PB equations. However, as α ≠ β (non-electroneutrality), solutions of 1D PB n equations may have blow-up behaviour which cannot be found in 1D PB equations. Such a difference between 1D PB and PB n equations can also be verified by numerical simulations

Polar-coordinate lattice Boltzmann modeling of compressible flows

Science.gov (United States)

Lin, Chuandong; Xu, Aiguo; Zhang, Guangcai; Li, Yingjun; Succi, Sauro

2014-01-01

We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RM instability occurs. It is found that the macroscopic effects due to deviating from thermodynamic equilibrium around the material interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function. These results deepen our understanding of the mechanical and material interfaces from a more fundamental level, which is indicative for constructing macroscopic models and other kinds of kinetic models.

Diagnostic performance of a Lattice Boltzmann-based method for CT-based fractional flow reserve.

Science.gov (United States)

Giannopoulos, Andreas A; Tang, Anji; Ge, Yin; Cheezum, Michael K; Steigner, Michael L; Fujimoto, Shinichiro; Kumamaru, Kanako K; Chiappino, Dante; Della Latta, Daniele; Berti, Sergio; Chiappino, Sara; Rybicki, Frank J; Melchionna, Simone; Mitsouras, Dimitrios

2018-02-20

Fractional flow reserve (FFR) estimated from coronary computed tomography angiography (CT-FFR) offers non-invasive detection of lesion-specific ischaemia. We aimed to develop and validate a fast CT-FFR algorithm utilising the Lattice Boltzmann method for blood flow simulation (LBM CT-FFR). Sixty-four patients with clinically indicated CTA and invasive FFR measurement from three institutions were retrospectively analysed. CT-FFR was performed using an onsite tool interfacing with a commercial Lattice Boltzmann fluid dynamics cloud-based platform. Diagnostic accuracy of LBM CT-FFR ≤0.8 and percent diameter stenosis >50% by CTA to detect invasive FFR ≤0.8 were compared using area under the receiver operating characteristic curve (AUC). Sixty patients successfully underwent LBM CT-FFR analysis; 29 of 73 lesions in 69 vessels had invasive FFR ≤0.8. Total time to perform LBM CT-FFR was 40±10 min. Compared to invasive FFR, LBM CT-FFR had good correlation (r=0.64), small bias (0.009) and good limits of agreement (-0.223 to 0.206). The AUC of LBM CT-FFR (AUC=0.894, 95% confidence interval [CI]: 0.792-0.996) was significantly higher than CTA (AUC=0.685, 95% CI: 0.576-0.794) to detect FFR ≤0.8 (p=0.0021). Per-lesion specificity, sensitivity, and accuracy of LBM CT-FFR were 97.7%, 79.3%, and 90.4%, respectively. LBM CT-FFR has very good diagnostic accuracy to detect lesion-specific ischaemia (FFR ≤0.8) and can be performed in less than one hour.

Multiple-relaxation-time lattice Boltzmann model for compressible fluids

International Nuclear Information System (INIS)

Chen Feng; Xu Aiguo; Zhang Guangcai; Li Yingjun

2011-01-01

We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. The collision step is first calculated in the moment space and then mapped back to the velocity space. The moment space and corresponding transformation matrix are constructed according to the group representation theory. Equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapman-Enskog expansion. Numerical experiments showed that compressible flows with strong shocks can be well simulated by the present model. The new model works for both low and high speeds compressible flows. It contains more physical information and has better numerical stability and accuracy than its single-relaxation-time version. - Highlights: → We present an energy-conserving MRT finite-difference LB model. → The moment space is constructed according to the group representation theory. → The new model works for both low and high speeds compressible flows. → It has better numerical stability and wider applicable range than its SRT version.

From Lattice Boltzmann to hydrodynamics in dissipative relativistic fluids

Science.gov (United States)

Gabbana, Alessandro; Mendoza, Miller; Succi, Sauro; Tripiccione, Raffaele

2017-11-01

Relativistic fluid dynamics is currently applied to several fields of modern physics, covering many physical scales, from astrophysics, to atomic scales (e.g. in the study of effective 2D systems such as graphene) and further down to subnuclear scales (e.g. quark-gluon plasmas). This talk focuses on recent progress in the largely debated connection between kinetic transport coefficients and macroscopic hydrodynamic parameters in dissipative relativistic fluid dynamics. We use a new relativistic Lattice Boltzmann method (RLBM), able to handle from ultra-relativistic to almost non-relativistic flows, and obtain strong evidence that the Chapman-Enskog expansion provides the correct pathway from kinetic theory to hydrodynamics. This analysis confirms recently obtained theoretical results, which can be used to obtain accurate calibrations for RLBM methods applied to realistic physics systems in the relativistic regime. Using this calibration methodology, RLBM methods are able to deliver improved physical accuracy in the simulation of the physical systems described above. European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 642069.

Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices

International Nuclear Information System (INIS)

Rojas-Rojas, Santiago; Naether, Uta; Delgado, Aldo; Vicencio, Rodrigo A.

2016-01-01

Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.

Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices

Energy Technology Data Exchange (ETDEWEB)

Rojas-Rojas, Santiago, E-mail: srojas@cefop.cl [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Naether, Uta [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, 50009 Zaragoza (Spain); Delgado, Aldo [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Vicencio, Rodrigo A. [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago (Chile)

2016-09-16

Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.

Third sound in one and two dimensional modulated structures

International Nuclear Information System (INIS)

Komuro, T.; Kawashima, H., Shirahama, K.; Kono, K.

1996-01-01

An experimental technique is developed to study acoustic transmission in one and two dimensional modulated structures by employing third sound of a superfluid helium film. In particular, the Penrose lattice, which is a two dimensional quasiperiodic structure, is studied. In two dimensions, the scattering of third sound is weaker than in one dimension. Nevertheless, the authors find that the transmission spectrum in the Penrose lattice, which is a two dimensional prototype of the quasicrystal, is observable if the helium film thickness is chosen around 5 atomic layers. The transmission spectra in the Penrose lattice are explained in terms of dynamical theory of diffraction

THREE-DIMENSIONAL BOLTZMANN HYDRO CODE FOR CORE COLLAPSE IN MASSIVE STARS. I. SPECIAL RELATIVISTIC TREATMENTS

International Nuclear Information System (INIS)

Nagakura, Hiroki; Sumiyoshi, Kohsuke; Yamada, Shoichi

2014-01-01

We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled with hydrodynamics equations. This method is meant to be applied to simulations of core-collapse supernovae. We handle special relativity in a non-conventional way, taking account of all orders of v/c. Consistent treatment of the advection and collision terms in the Boltzmann equations has been a challenge, which we overcome by employing two different energy grids: Lagrangian remapped and laboratory fixed grids. We conduct a series of basic tests and perform a one-dimensional simulation of core-collapse, bounce, and shock-stall for a 15 M ☉ progenitor model with a minimum but essential set of microphysics. We demonstrate in the latter simulation that our new code is capable of handling all phases in core-collapse supernova. For comparison, a non-relativistic simulation is also conducted with the same code, and we show that they produce qualitatively wrong results in neutrino transfer. Finally, we discuss a possible incorporation of general relativistic effects into our method

Hydraulic fracture conductivity: effects of rod-shaped proppant from lattice-Boltzmann simulations and lab tests

Science.gov (United States)

Osiptsov, Andrei A.

2017-06-01

The goal of this study is to evaluate the conductivity of random close packings of non-spherical, rod-shaped proppant particles under the closure stress using numerical simulation and lab tests, with application to the conductivity of hydraulic fractures created in subterranean formation to stimulate production from oil and gas reservoirs. Numerical simulations of a steady viscous flow through proppant packs are carried out using the lattice Boltzmann method for the Darcy flow regime. The particle packings were generated numerically using the sequential deposition method. The simulations are conducted for packings of spheres, ellipsoids, cylinders, and mixtures of spheres with cylinders at various volumetric concentrations. It is demonstrated that cylinders provide the highest permeability among the proppants studied. The dependence of the nondimensional permeability (scaled by the equivalent particle radius squared) on porosity obtained numerically is well approximated by the power-law function: K /Rv2 = 0.204ϕ4.58 in a wide range of porosity: 0.3 ≤ ϕ ≤ 0.7. Lattice-Boltzmann simulations are cross-verified against finite-volume simulations using Navier-Stokes equations for inertial flow regime. Correlations for the normalized beta-factor as a function of porosity and normalized permeability are presented as well. These formulae are in a good agreement with the experimental measurements (including packings of rod-shaped particles) and existing laboratory data, available in the porosity range 0.3 ≤ ϕ ≤ 0.5. Comparison with correlations by other authors is also given.

Synchrotron 4-dimensional imaging of two-phase flow through porous media.

Science.gov (United States)

Kim, F H; Penumadu, D; Patel, P; Xiao, X; Garboczi, E J; Moylan, S P; Donmez, M A

2016-01-01

Near real-time visualization of complex two-phase flow in a porous medium was demonstrated with dynamic 4-dimensional (4D) (3D + time) imaging at the 2-BM beam line of the Advanced Photon Source (APS) at Argonne National Laboratory. Advancing fluid fronts through tortuous flow paths and their interactions with sand grains were clearly captured, and formations of air bubbles and capillary bridges were visualized. The intense X-ray photon flux of the synchrotron facility made 4D imaging possible, capturing the dynamic evolution of both solid and fluid phases. Computed Tomography (CT) scans were collected every 12 s with a pixel size of 3.25 µm. The experiment was carried out to improve understanding of the physics associated with two-phase flow. The results provide a source of validation data for numerical simulation codes such as Lattice-Boltzmann, which are used to model multi-phase flow through porous media.

An approach to higher dimensional theories based on lattice gauge theory

International Nuclear Information System (INIS)

Murata, M.; So, H.

2004-01-01

A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. We propose the new possibility to realize the continuum limit of a five-dimensional theory based on the property of the phase diagram

Eliminating cubic terms in the pseudopotential lattice Boltzmann model for multiphase flow

Science.gov (United States)

Huang, Rongzong; Wu, Huiying; Adams, Nikolaus A.

2018-05-01

It is well recognized that there exist additional cubic terms of velocity in the lattice Boltzmann (LB) model based on the standard lattice. In this work, elimination of these cubic terms in the pseudopotential LB model for multiphase flow is investigated, where the force term and density gradient are considered. By retaining high-order (≥3 ) Hermite terms in the equilibrium distribution function and the discrete force term, as well as introducing correction terms in the LB equation, the additional cubic terms of velocity are entirely eliminated. With this technique, the computational simplicity of the pseudopotential LB model is well maintained. Numerical tests, including stationary and moving flat and circular interface problems, are carried out to show the effects of such cubic terms on the simulation of multiphase flow. It is found that the elimination of additional cubic terms is beneficial to reduce the numerical error, especially when the velocity is relatively large. Numerical results also suggest that these cubic terms mainly take effect in the interfacial region and that the density-gradient-related cubic terms are more important than the other cubic terms for multiphase flow.

Simulation of Micro-Channel and Micro-Orifice Flow Using Lattice Boltzmann Method with Langmuir Slip Model

Directory of Open Access Journals (Sweden)

A. R. Rahmati

2016-12-01

Full Text Available Because of its kinetic nature and computational advantages, the Lattice Boltzmann method (LBM has been well accepted as a useful tool to simulate micro-scale flows. The slip boundary model plays a crucial role in the accuracy of solutions for micro-channel flow simulations. The most used slip boundary condition is the Maxwell slip model. The results of Maxwell slip model are affected by the accommodation coefficient significantly, but there is not an explicitly relationship between properties at wall and accommodation coefficient. In the present wok, Langmuir slip model is used beside LBM to simulate micro-channel and micro-orifice flows. Slip velocity and nonlinear pressure drop profiles are presented as two major effects in such flows. The results are in good agreement with existing results in the literature.

Simulation of natural convection in an inclined polar cavity using a finite-difference lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Yang, Fan; Yang, Haicheng; Guo, Xueyan; Ren Dai [University of Shanghai for Science and Technology, Shanghai (China); Yan, Yonghua [Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai (China); Liu, Chaoqun [University of Texas at Arlington, Arlington (United States)

2017-06-15

Natural convection heat transfer in an inclined polar cavity was studied using a Finite-difference lattice Boltzmann method (FDLBM) based on a double-population approach for body-fitted coordinates. A D2G9 model coupled with the simplest TD2Q4 lattice model was applied to determine the velocity field and temperature field. For both velocity and temperature fields, the discrete spatial derivatives were obtained by combining the upwind scheme with the central scheme, and the discrete temporal term is obtained using a fourth-order Runge-Kutta scheme. Studies were carried out for different Rayleigh numbers and different inclination angles. The results in terms of streamlines, isotherms, and Nusselt numbers explain the heat transfer mechanism of natural convection in an inclined polar cavity due to the change of Rayleigh number and inclination angle.

Two-dimensional melting of vortex lattices and the mutual vortex drag effect in a superconducting transformer

International Nuclear Information System (INIS)

Glazman, L.I.; Fogel', N.Y.

1984-01-01

A study is reported of the effect of two-dimensional melting of a vortex lattice on the current-voltage characteristic of a transformer, in the form of the dependence of the secondary voltage V 2 on the primary-circuit transport current J 1 . The motion of vortices in the melted lattice is described in the diffusion approximation, and their interaction in the self-consistent field approximation. The melting of even one lattice largely eliminates the vortex drag: V 2 1 for any current J 1 . The square-root singularity of the characteristics which is typical of the ordinary transformer operation no longer occurs in the critical temperature range. In the linear part of the characteristic, the ratio V 2 /V 1 is inversely proportional to the magnetic field H over a wide range of the latter. The temperature dependence of V 2 and the asymptotic function V 2 (J 1 ) for large J 1 are different, according as one or both lattices melt. The transformer current-voltage characteristic thus conveys information about the state of the vortex lattice and allows its melting to be investigated. The function V 2 (V 1 ) and V 2 (H) found here agree well with experiment, and the experimental results can thus be explained by the melting of a vortex lattice

Creating tuneable microwave media from a two-dimensional lattice of re-entrant posts

Energy Technology Data Exchange (ETDEWEB)

Goryachev, Maxim; Tobar, Michael E. [ARC Centre of Excellence for Engineered Quantum Systems, University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009 (Australia)

2015-11-28

The potential capabilities of resonators based on two dimensional arrays of re-entrant posts is demonstrated. Such posts may be regarded as magnetically coupled lumped element microwave harmonic oscillators, arranged in a 2D lattices structure, which is enclosed in a 3D cavity. By arranging these elements in certain 2D patterns, we demonstrate how to achieve certain requirements with respect to field localisation and device spectra. Special attention is paid to symmetries of the lattices, mechanical tuning, design of areas of high localisation of magnetic energy; this in turn creates unique discrete mode spectra. We demonstrate analogies between systems designed on the proposed platform and well known physical phenomena such as polarisation, frustration, and Whispering Gallery Modes. The mechanical tunability of the cavity with multiple posts is analysed, and its consequences to optomechanical applications is calculated. One particular application to quantum memory is demonstrated with a cavity design consisting of separate resonators analogous to discrete Fabry–Pérot resonators. Finally, we propose a generalised approach to a microwave system design based on the concept of Programmable Cavity Arrays.

Cross-Permeability of the Semisolid Region in Directional Solidification: A Combined Phase-Field and Lattice-Boltzmann Simulation Approach

Science.gov (United States)

Böttger, B.; Haberstroh, C.; Giesselmann, N.

2016-01-01

Based on the results of microstructure simulations, fluid flow through the semisolid region during directional solidification of the technical Ni-base alloy 718 has been studied. Three-dimensional microstructures at different positions in the semisolid region were obtained by using a multicomponent multiphase-field model that was online coupled to a commercial thermodynamic database. For the range of five different primary dendrite distances λ 1 between 50 µm and 250 µm, the flow velocity and the permeability perpendicular to the dendrite growth direction was evaluated by using a proprietary Lattice-Boltzmann model. The commercial CFD software ANSYS FLUENT was alternatively applied for reference. Consistent values of the average flow velocity along the dendrites were obtained for both methods. From the results of the fluid flow simulations, the cross-permeability was evaluated as a function of temperature and fraction liquid for each of the five different primary dendrite distances λ 1. The obtained permeability values can be approximated by a single analytical function of the fraction liquid and λ 1 and are discussed and compared with known relations from the literature.

Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem

Directory of Open Access Journals (Sweden)

Aizat Abas

2016-01-01

Full Text Available This paper simulates and predicts the laminar flow inside the 3D aneurysm geometry, since the hemodynamic situation in the blood vessels is difficult to determine and visualize using standard imaging techniques, for example, magnetic resonance imaging (MRI. Three different types of Lattice Boltzmann (LB models are computed, namely, single relaxation time (SRT, multiple relaxation time (MRT, and regularized BGK models. The results obtained using these different versions of the LB-based code will then be validated with ANSYS FLUENT, a commercially available finite volume- (FV- based CFD solver. The simulated flow profiles that include velocity, pressure, and wall shear stress (WSS are then compared between the two solvers. The predicted outcomes show that all the LB models are comparable and in good agreement with the FVM solver for complex blood flow simulation. The findings also show minor differences in their WSS profiles. The performance of the parallel implementation for each solver is also included and discussed in this paper. In terms of parallelization, it was shown that LBM-based code performed better in terms of the computation time required.

Hermite regularization of the lattice Boltzmann method for open source computational aeroacoustics.

Science.gov (United States)

Brogi, F; Malaspinas, O; Chopard, B; Bonadonna, C

2017-10-01

The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, which is of interest for aeroacoustic applications. Several solutions have been proposed but are often too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. An original regularized collision operator is proposed, based on the expansion of Hermite polynomials, that greatly improves the accuracy and stability of the LBM without significantly altering its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between this approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial software, while here the entire theoretical framework is implemented using an open source library (palabos).

Lattice Boltzmann model for free-surface flow and its application to filling process in casting

CERN Document Server

Ginzburg, I

2003-01-01

A generalized lattice Boltzmann model to simulate free-surface is constructed in both two and three dimensions. The proposed model satisfies the interfacial boundary conditions accurately. A distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid. To maintain a sharp interfacial front, the method includes an anti-diffusion algorithm. The unknown distribution functions at the interfacial region are constructed according to the first-order Chapman-Enskog analysis. The interfacial boundary conditions are satisfied exactly by the coefficients in the Chapman-Enskog expansion. The distribution functions are naturally expressed in the local interfacial coordinates. The macroscopic quantities at the interface are extracted from the least-square solutions of a locally linearized system obtained from the known distribution functions. The proposed method does not require any geometric front construction and is robust for any interfacial ...

Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method

Science.gov (United States)

Peng, Cheng; Geneva, Nicholas; Guo, Zhaoli; Wang, Lian-Ping

2017-01-01

In lattice Boltzmann simulations involving moving solid boundaries, the momentum exchange between the solid and fluid phases was recently found to be not fully consistent with the principle of local Galilean invariance (GI) when the bounce-back schemes (BBS) and the momentum exchange method (MEM) are used. In the past, this inconsistency was resolved by introducing modified MEM schemes so that the overall moving-boundary algorithm could be more consistent with GI. However, in this paper we argue that the true origin of this violation of Galilean invariance (VGI) in the presence of a moving solid-fluid interface is due to the BBS itself, as the VGI error not only exists in the hydrodynamic force acting on the solid phase, but also in the boundary force exerted on the fluid phase, according to Newton's Third Law. The latter, however, has so far gone unnoticed in previously proposed modified MEM schemes. Based on this argument, we conclude that the previous modifications to the momentum exchange method are incomplete solutions to the VGI error in the lattice Boltzmann method (LBM). An implicit remedy to the VGI error in the LBM and its limitation is then revealed. To address the VGI error for a case when this implicit remedy does not exist, a bounce-back scheme based on coordinate transformation is proposed. Numerical tests in both laminar and turbulent flows show that the proposed scheme can effectively eliminate the errors associated with the usual bounce-back implementations on a no-slip solid boundary, and it can maintain an accurate momentum exchange calculation with minimal computational overhead.

Stable lattice Boltzmann model for Maxwell equations in media

Science.gov (United States)

Hauser, A.; Verhey, J. L.

2017-12-01

The present work shows a method for stable simulations via the lattice Boltzmann (LB) model for electromagnetic waves (EM) transiting homogeneous media. LB models for such media were already presented in the literature, but they suffer from numerical instability when the media transitions are sharp. We use one of these models in the limit of pure vacuum derived from Liu and Yan [Appl. Math. Model. 38, 1710 (2014), 10.1016/j.apm.2013.09.009] and apply an extension that treats the effects of polarization and magnetization separately. We show simulations of simple examples in which EM waves travel into media to quantify error scaling, stability, accuracy, and time scaling. For conductive media, we use the Strang splitting and check the simulations accuracy at the example of the skin effect. Like pure EM propagation, the error for the static limits, which are constructed with a current density added in a first-order scheme, can be less than 1 % . The presented method is an easily implemented alternative for the stabilization of simulation for EM waves propagating in spatially complex structured media properties and arbitrary transitions.

Interacting Fermi gases in disordered one-dimensional lattices

International Nuclear Information System (INIS)

Xianlong, Gao; Polini, M.; Tosi, M. P.; Tanatar, B.

2006-01-01

Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subject to harmonic trapping exhibit intriguing compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a random potential on these ground-state phases. Within a density-functional scheme we show that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the compressibility at low density from quenching of percolation

On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

Directory of Open Access Journals (Sweden)

Nikolai N. Bogoliubov (Jr.

2007-01-01

Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

Multiple-Relaxation-Time Lattice Boltzmann Approach to Richtmyer-Meshkov Instability

International Nuclear Information System (INIS)

Chen Feng; Li Yingjun; Xu Aiguo; Zhang Guangcai

2011-01-01

The aims of the present paper are twofold. At first, we further study the Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) model proposed in [Europhys. Lett. 90 (2010) 54003]. We discuss the reason why the Gram-Schmidt orthogonalization procedure is not needed in the construction of transformation matrix M; point out a reason why the Kataoka-Tsutahara model [Phys. Rev. E 69 (2004) 035701 (R)] is only valid in subsonic flows. The von Neumann stability analysis is performed. Secondly, we carry out a preliminary quantitative study on the Richtmyer-Meshkov instability using the proposed MRT LB model. When a shock wave travels from a light medium to a heavy one, the simulated growth rate is in qualitative agreement with the perturbation model by Zhang-Sohn. It is about half of the predicted value by the impulsive model and is closer to the experimental result. When the shock wave travels from a heavy medium to a light one, our simulation results are also consistent with physical analysis. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Rahman Prize Lecture: Lattice Boltzmann simulation of complex states of flowing matter

Science.gov (United States)

Succi, Sauro

Over the last three decades, the Lattice Boltzmann (LB) method has gained a prominent role in the numerical simulation of complex flows across an impressively broad range of scales, from fully-developed turbulence in real-life geometries, to multiphase flows in micro-fluidic devices, all the way down to biopolymer translocation in nanopores and lately, even quark-gluon plasmas. After a brief introduction to the main ideas behind the LB method and its historical developments, we shall present a few selected applications to complex flow problems at various scales of motion. Finally, we shall discuss prospects for extreme-scale LB simulations of outstanding problems in the physics of fluids and its interfaces with material sciences and biology, such as the modelling of fluid turbulence, the optimal design of nanoporous gold catalysts and protein folding/aggregation in crowded environments.

Implementing the lattice Boltzmann model on commodity graphics hardware

International Nuclear Information System (INIS)

Kaufman, Arie; Fan, Zhe; Petkov, Kaloian

2009-01-01

Modern graphics processing units (GPUs) can perform general-purpose computations in addition to the native specialized graphics operations. Due to the highly parallel nature of graphics processing, the GPU has evolved into a many-core coprocessor that supports high data parallelism. Its performance has been growing at a rate of squared Moore's law, and its peak floating point performance exceeds that of the CPU by an order of magnitude. Therefore, it is a viable platform for time-sensitive and computationally intensive applications. The lattice Boltzmann model (LBM) computations are carried out via linear operations at discrete lattice sites, which can be implemented efficiently using a GPU-based architecture. Our simulations produce results comparable to the CPU version while improving performance by an order of magnitude. We have demonstrated that the GPU is well suited for interactive simulations in many applications, including simulating fire, smoke, lightweight objects in wind, jellyfish swimming in water, and heat shimmering and mirage (using the hybrid thermal LBM). We further advocate the use of a GPU cluster for large scale LBM simulations and for high performance computing. The Stony Brook Visual Computing Cluster has been the platform for several applications, including simulations of real-time plume dispersion in complex urban environments and thermal fluid dynamics in a pressurized water reactor. Major GPU vendors have been targeting the high performance computing market with GPU hardware implementations. Software toolkits such as NVIDIA CUDA provide a convenient development platform that abstracts the GPU and allows access to its underlying stream computing architecture. However, software programming for a GPU cluster remains a challenging task. We have therefore developed the Zippy framework to simplify GPU cluster programming. Zippy is based on global arrays combined with the stream programming model and it hides the low-level details of the

FULL GPU Implementation of Lattice-Boltzmann Methods with Immersed Boundary Conditions for Fast Fluid Simulations

Directory of Open Access Journals (Sweden)

G Boroni

2017-03-01

Full Text Available Lattice Boltzmann Method (LBM has shown great potential in fluid simulations, but performance issues and difficulties to manage complex boundary conditions have hindered a wider application. The upcoming of Graphic Processing Units (GPU Computing offered a possible solution for the performance issue, and methods like the Immersed Boundary (IB algorithm proved to be a flexible solution to boundaries. Unfortunately, the implicit IB algorithm makes the LBM implementation in GPU a non-trivial task. This work presents a fully parallel GPU implementation of LBM in combination with IB. The fluid-boundary interaction is implemented via GPU kernels, using execution configurations and data structures specifically designed to accelerate each code execution. Simulations were validated against experimental and analytical data showing good agreement and improving the computational time. Substantial reductions of calculation rates were achieved, lowering down the required time to execute the same model in a CPU to about two magnitude orders.

Phase-field-lattice Boltzmann study for lamellar eutectic growth in a natural convection melt

Directory of Open Access Journals (Sweden)

Ang Zhang

2017-11-01

Full Text Available In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions.

Lattice Boltzmann simulation of the convective heat transfer from a stream-wise oscillating circular cylinder

International Nuclear Information System (INIS)

Bao Sheng; Chen Sheng; Liu Zhaohui; Zheng Chuguang

2012-01-01

Highlights: ► Heat transfer is enhanced by small and slow stream-wise oscillation. ► The average Nu decreases with increasing oscillation frequency. ► The RMS Nu increases with increasing frequency. ► The mean and RMS Nu reach a local maximum value in locked regime. ► Similar frequency effect is found for different Reynolds numbers. - Abstract: In this paper, we studied the convective heat transfer from a stream-wise oscillating circular cylinder. Two dimensional numerical simulations are conducted at Re = 100–200, A = 0.1–0.4 and F = f o /f s = 0.2–3.0 with the aid of the lattice Boltzmann method. In particular, detailed attentions are paid on the extensive numerical results elucidating the influence of oscillation frequency, oscillation amplitude and Reynolds number on the time-average and RMS value of the Nusselt number. Over the ranges of conditions considered herein, the heat transfer characteristics are observed to be influenced in an intricate manner by the value of the oscillation frequency (F), oscillation amplitude (A) and Reynolds number (Re). Firstly, the heat transfer is enhanced when the cylinder oscillates stream-wise with small amplitude and low frequency, while it will be reduced by large amplitude and high frequency. Secondly, the average Nusselt number (Nu (ave)) decreases against the increasing value of oscillation frequency, while the RMS value of the Nusselt number, Nu (RMS), displays an opposite trend. Third, we obtained a similar frequency effect on the heat transfer over the range of Reynolds numbers investigated in this paper. In addition, detailed analyses on phase portraits, energy spectrum are also made.

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions

DEFF Research Database (Denmark)

Johannessen, Kim

2014-01-01

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...

Anisotropic ordering in a two-temperature lattice gas

DEFF Research Database (Denmark)

Szolnoki, Attila; Szabó, György; Mouritsen, Ole G.

1997-01-01

We consider a two-dimensional lattice gas model with repulsive nearest- and next-nearest-neighbor interactions that evolves in time according to anisotropic Kawasaki dynamics. The hopping of particles along the principal directions is governed by two heat baths at different temperatures T-x and T...

Ballistic magnetotransport in a suspended two-dimensional electron gas with periodic antidot lattices

Energy Technology Data Exchange (ETDEWEB)

Zhdanov, E. Yu., E-mail: zhdanov@isp.nsc.ru; Pogosov, A. G.; Budantsev, M. V.; Pokhabov, D. A.; Bakarov, A. K. [Siberian Branch of the Russian Academy of Sciences, Rzhanov Institute of Semiconductor Physics (Russian Federation)

2017-01-15

The magnetoresistance of suspended semiconductor nanostructures with a two-dimensional electron gas structured by periodic square antidot lattices is studied. It is shown that the ballistic regime of electron transport is retained after detaching the sample from the substrate. Direct comparative analysis of commensurability oscillations of magnetoresistance and their temperature dependences in samples before and after suspension is performed. It is found that the temperature dependences are almost identical for non-suspended and suspended samples, whereas significant differences are observed in the nonlinear regime, caused by direct current passage. Commensurability oscillations in the suspended samples are more stable with respect to exposure to direct current, which can be presumably explained by electron–electron interaction enhancement after detaching nanostructures from the high-permittivity substrate.

A shallow water model for the propagation of tsunami via Lattice Boltzmann method

Science.gov (United States)

Zergani, Sara; Aziz, Z. A.; Viswanathan, K. K.

2015-01-01

An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory.

A shallow water model for the propagation of tsunami via Lattice Boltzmann method

International Nuclear Information System (INIS)

Zergani, Sara; Aziz, Z A; Viswanathan, K K

2015-01-01

An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory

Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study

Science.gov (United States)

Kendon, Vivien M.; Cates, Michael E.; Pagonabarraga, Ignacio; Desplat, J.-C.; Bladon, Peter

2001-08-01

The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamically consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecedented range of length and time scales when expressed in reduced physical units. (These are the length and time units derived from fluid density, viscosity, and interfacial tension.) Using eight large (2563) runs, the resulting composite graph of reduced domain size l against reduced time t covers 1 [less, similar] l [less, similar] 105, 10 [less, similar] t [less, similar] 108. Our data are consistent with the dynamical scaling hypothesis that l(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields. Using the conventional definition of Reynolds number for this problem, Re[phi] = ldl/dt, we attain values approaching 350. At Re[phi] [greater, similar] 100 (which requires t [greater, similar] 106) we find clear evidence of Furukawa's inertial scaling (l [similar] t2/3), although the crossover from the viscous regime (l [similar] t) is both broad and late (102 [less, similar] t [less, similar] 106). Though it cannot be ruled out, we find no indication that Re[phi] is self-limiting (l [similar] t1/2) at late times, as recently proposed by Grant & Elder. Detailed study of the velocity fields confirms that, for our most inertial runs, the RMS ratio of nonlinear to viscous terms in the Navier Stokes equation, R2, is of order 10, with the fluid mixture showing incipient turbulent characteristics. However, we cannot go far enough into the inertial regime to obtain a clear length separation of domain size, Taylor microscale, and Kolmogorov scale, as would be needed to test a

Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos

Science.gov (United States)

Boozer, A. D.

2011-01-01

We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…

Lattice gas simulations of dynamical geometry in two dimensions.

Science.gov (United States)

Klales, Anna; Cianci, Donato; Needell, Zachary; Meyer, David A; Love, Peter J

2010-10-01

We present a hydrodynamic lattice gas model for two-dimensional flows on curved surfaces with dynamical geometry. This model is an extension to two dimensions of the dynamical geometry lattice gas model previously studied in one dimension. We expand upon a variation of the two-dimensional flat space Frisch-Hasslacher-Pomeau (FHP) model created by Frisch [Phys. Rev. Lett. 56, 1505 (1986)] and independently by Wolfram, and modified by Boghosian [Philos. Trans. R. Soc. London, Ser. A 360, 333 (2002)]. We define a hydrodynamic lattice gas model on an arbitrary triangulation whose flat space limit is the FHP model. Rules that change the geometry are constructed using the Pachner moves, which alter the triangulation but not the topology. We present results on the growth of the number of triangles as a function of time. Simulations show that the number of triangles grows with time as t(1/3), in agreement with a mean-field prediction. We also present preliminary results on the distribution of curvature for a typical triangulation in these simulations.

Simulation of Thermomagnetic Convection in a Cavity Using the Lattice Boltzmann Model

Directory of Open Access Journals (Sweden)

Mahshid Hadavand

2011-01-01

Full Text Available Thermomagnetic convection in a differentially heated square cavity with an infinitely long third dimension is numerically simulated using the single relaxation time lattice Boltzmann method (LBM. This problem is of considerable interest when dealing with cooling of microelectronic devices, in situations where natural convection does not meet the cooling requirements, and forced convection is not viable due to the difficulties associated with pumping a ferrofluid. Therefore, circulation is achieved by imposing a magnetic field, which is created and controlled by placing a dipole at the bottom of the enclosure. The magnitude of the magnetic force is controlled by changing the electrical current through the dipole. In this study, the effects of combined natural convection and magnetic convection, which is commonly known as “thermomagnetic convection,” are analysed in terms of the flow modes and heat transfer characteristics of a magnetic fluid.

Simulating Engineering Flows through Complex Porous Media via the Lattice Boltzmann Method

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Vesselin Krassimirov Krastev

2018-03-01

Full Text Available In this paper, recent achievements in the application of the lattice Boltzmann method (LBM to complex fluid flows are reported. More specifically, we focus on flows through reactive porous media, such as the flow through the substrate of a selective catalytic reactor (SCR for the reduction of gaseous pollutants in the automotive field; pulsed-flow analysis through heterogeneous catalyst architectures; and transport and electro-chemical phenomena in microbial fuel cells (MFC for novel waste-to-energy applications. To the authors’ knowledge, this is the first known application of LBM modeling to the study of MFCs, which represents by itself a highly innovative and challenging research area. The results discussed here essentially confirm the capabilities of the LBM approach as a flexible and accurate computational tool for the simulation of complex multi-physics phenomena of scientific and technological interest, across physical scales.

Effects of hydrostatic pressure on spin-lattice coupling in two-dimensional ferromagnetic Cr2Ge2Te6

Science.gov (United States)

Sun, Y.; Xiao, R. C.; Lin, G. T.; Zhang, R. R.; Ling, L. S.; Ma, Z. W.; Luo, X.; Lu, W. J.; Sun, Y. P.; Sheng, Z. G.

2018-02-01

Spin-lattice coupling plays an important role in both formation and understanding of the magnetism in two-dimensional magnetic semiconductors (2DMS). In this paper, the steady pressure effects on the lattice structure, Raman resonances, and magnetization of a 2DMS Cr2Ge2Te6 have been studied by both experiments and first principles calculations. It is found that the bond length of Cr-Cr decreases, the angle of Cr-Te-Cr diverges from 90°, and the Raman modes Eg3 and Ag1 show an increase with the application of external pressure. Consequently, the magnetic phase transition temperature TC decreases from 66.6 K to 60.6 K (˜9%) as the pressure increases from 0 to 1 GPa. These pressure effects not only confirm the existence of strong spin-lattice coupling but also reveal the detailed information about the lattice deformation effect on the magnetic properties in such 2DMS, which would be a benefit for the further understanding and manipulation of the magnetism in 2D materials.

Decoherence in two-dimensional quantum walks

International Nuclear Information System (INIS)

Oliveira, A. C.; Portugal, R.; Donangelo, R.

2006-01-01

We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk

Lattice Boltzmann analysis of effect of heating location and Rayleigh number on natural convection in partially heated open ended cavity

Energy Technology Data Exchange (ETDEWEB)

Gangawane, Krunal Madhukar; Bharti, Ram Prakash; Kumar, Surendra [Indian Institute of Technology Roorkee, Uttarakhand (India)

2015-08-15

Natural convection characteristics of a partially heated open ended square cavity have been investigated numerically by using an in-house computational flow solver based on the passive scalar thermal lattice Boltzmann method (PS-TLBM) with D2Q9 (two-dimensional and nine-velocity link) lattice model. The partial part of left wall of the cavity is heated isothermally at either of the three different (bottom, middle and top) locations for the fixed heating length as half of characteristic length (H/2) while the right wall is open to the ambient conditions. The other parts of the cavity are thermally isolated. In particular, the influences of partial heating locations and Rayleigh number (103≤ Ra≤106) in the laminar zone on the local and global natural convection characteristics (such as streamline, vorticity and isotherm contours; centerline variations of velocity and temperature; and local and average Nusselt numbers) have been presented and discussed for the fixed value of the Prandtl number (Pr=0.71). The streamline patterns show qualitatively similar nature for all the three heating cases and Rayleigh numbers, except the change in the recirculation zone which is found to be largest for middle heating case. Isotherm patterns are shifted towards a partially heated wall on increasing Rayleigh number and/or shifting of heating location from bottom to top. Both the local and average Nusselt numbers, as anticipated, shown proportional increase with Rayleigh number. The cavity with middle heating location shown higher heat transfer rate than that for the top and bottom heating cases. Finally, the functional dependence of the average Nusselt number on flow governing parameters is also presented as a closure relationship for the best possible utilization in engineering practices and design.

Study of the Dynamics of a Condensing Bubble Using Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Shahnawaz Ahmed

2015-06-01

Full Text Available Mesoscopic lattice Boltzmann method (LBM is used to discretize the governing equations for a steam bubble inside a tube filled with water. The bubbles are kept at higher temperature compared to its boiling point while the liquid is kept subcooled. Heat transfer is allowed to take place between the two phases by virtue of which the bubble will condense. Three separate probability distribution functions are used in LBM to handle continuity, momentum and energy equations separately. The interface is considered to be diffused within a narrow zone and it has been modeled using convective Cahn-Hillard equation. Combined diffused interface-LBM framework is adapted accordingly to handle complex interface separating two phases having high density ratio. Developed model is validated with respect to established correlations for instantaneous equivalent radius of a spherical condensing bubble. Numerical snapshots of the simulation depict that the bubble volume decreases faster for higher degree of superheat. The degrees of superheat are varied over a wide range to note its effect on bubble shape and size. Effect of initial volume of the bubble on the condensation rate is also studied. It has been observed that for a fixed degree of superheat, the condensation rate is not exactly proportional to its volume. Due to the variation in interfacial configuration for different sized bubbles, condensation rate changes drastically. Influence of gravity on the rate of condensation is also studied using the developed methodology.

LBflow: An extensible lattice Boltzmann framework for the simulation of geophysical flows. Part II: usage and validation

Science.gov (United States)

Llewellin, E. W.

2010-02-01

LBflow is a flexible, extensible implementation of the lattice Boltzmann method, developed with geophysical applications in mind. The theoretical basis for LBflow, and its implementation, are presented in the companion paper, 'Part I'. This article covers the practical usage of LBflow and presents guidelines for obtaining optimal results from available computing power. The relationships among simulation resolution, accuracy, runtime and memory requirements are investigated in detail. Particular attention is paid to the origin, quantification and minimization of errors. LBflow is validated against analytical, numerical and experimental results for a range of three-dimensional flow geometries. The fluid conductance of prismatic pipes with various cross sections is calculated with LBflow and found to be in excellent agreement with published results. Simulated flow along sinusoidally constricted pipes gives good agreement with experimental data for a wide range of Reynolds number. The permeability of packs of spheres is determined and shown to be in excellent agreement with analytical results. The accuracy of internal flow patterns within the investigated geometries is also in excellent quantitative agreement with published data. The development of vortices within a sinusoidally constricted pipe with increasing Reynolds number is shown, demonstrating the insight that LBflow can offer as a 'virtual laboratory' for fluid flow.

Boltzmann equations for a binary one-dimensional ideal gas.

Science.gov (United States)

Boozer, A D

2011-09-01

We consider a time-reversal invariant dynamical model of a binary ideal gas of N molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the N-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large N. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann's H theorem.

Generalized isothermic lattices

International Nuclear Information System (INIS)

Doliwa, Adam

2007-01-01

We study multi-dimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isothermic lattices using Steiner's projective structure of conics, and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two-dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem

Two Dimensional Super QCD on a Lattice

Energy Technology Data Exchange (ETDEWEB)

Catterall, Simon [Syracuse U.; Veernala, Aarti [Fermilab

2017-10-04

We construct a lattice theory with one exact supersymmetry which consists of fields transforming in both the adjoint and fundamental representations of a U(Nc) gauge group. In addition to gluons and gluinos, the theory contains Nf flavors of fermion in the fundamental representation along with their scalar partners and is invariant under a global U(Nf) flavor symmetry. The lattice action contains an additional Fayet-Iliopoulos term which can be used to generate a scalar potential. We perform numerical simulations that corroborate the theoretical expectation that supersymmetry is spontaneously broken for Nf

Lattice Boltzmann Study of Bubbles on a Patterned Superhydrophobic Surface under Shear Flow

Science.gov (United States)

Chen, Wei; Wang, Kai; Hou, Guoxiang; Leng, Wenjun

2018-01-01

This paper studies shear flow over a 2D patterned superhydrophobic surface using lattice Boltzmann method (LBM). Single component Shan-Chen multiphase model and Carnahan-Starling EOS are adopted to handle the liquid-gas flow on superhydrophobic surface with entrapped micro-bubbles. The shape of bubble interface and its influence on slip length under different shear rates are investigated. With increasing shear rate, the bubble interface deforms. Then the contact lines are depinned from the slot edges and move downstream. When the shear rate is high enough, a continuous gas layer forms. If the protrusion angle is small, the gas layer forms and collapse periodically, and accordingly the slip length changes periodically. While if the protrusion angle is large, the gas layer is steady and separates the solid wall from liquid, resulting in a very large slip length.

Fluctuating ideal-gas lattice Boltzmann method with fluctuation dissipation theorem for nonvanishing velocities.

Science.gov (United States)

Kaehler, G; Wagner, A J

2013-06-01

Current implementations of fluctuating ideal-gas descriptions with the lattice Boltzmann methods are based on a fluctuation dissipation theorem, which, while greatly simplifying the implementation, strictly holds only for zero mean velocity and small fluctuations. We show how to derive the fluctuation dissipation theorem for all k, which was done only for k=0 in previous derivations. The consistent derivation requires, in principle, locally velocity-dependent multirelaxation time transforms. Such an implementation is computationally prohibitively expensive but, with a small computational trick, it is feasible to reproduce the correct FDT without overhead in computation time. It is then shown that the previous standard implementations perform poorly for non vanishing mean velocity as indicated by violations of Galilean invariance of measured structure factors. Results obtained with the method introduced here show a significant reduction of the Galilean invariance violations.

Upscaled Lattice Boltzmann Method for Simulations of Flows in Heterogeneous Porous Media

Directory of Open Access Journals (Sweden)

Jun Li

2017-01-01

Full Text Available An upscaled Lattice Boltzmann Method (LBM for flow simulations in heterogeneous porous media at the Darcy scale is proposed in this paper. In the Darcy-scale simulations, the Shan-Chen force model is used to simplify the algorithm. The proposed upscaled LBM uses coarser grids to represent the average effects of the fine-grid simulations. In the upscaled LBM, each coarse grid represents a subdomain of the fine-grid discretization and the effective permeability with the reduced-order models is proposed as we coarsen the grid. The effective permeability is computed using solutions of local problems (e.g., by performing local LBM simulations on the fine grids using the original permeability distribution and used on the coarse grids in the upscaled simulations. The upscaled LBM that can reduce the computational cost of existing LBM and transfer the information between different scales is implemented. The results of coarse-grid, reduced-order, simulations agree very well with averaged results obtained using a fine grid.

Upscaled Lattice Boltzmann Method for Simulations of Flows in Heterogeneous Porous Media

KAUST Repository

Li, Jun

2017-02-16

An upscaled Lattice Boltzmann Method (LBM) for flow simulations in heterogeneous porous media at the Darcy scale is proposed in this paper. In the Darcy-scale simulations, the Shan-Chen force model is used to simplify the algorithm. The proposed upscaled LBM uses coarser grids to represent the average effects of the fine-grid simulations. In the upscaled LBM, each coarse grid represents a subdomain of the fine-grid discretization and the effective permeability with the reduced-order models is proposed as we coarsen the grid. The effective permeability is computed using solutions of local problems (e.g., by performing local LBM simulations on the fine grids using the original permeability distribution) and used on the coarse grids in the upscaled simulations. The upscaled LBM that can reduce the computational cost of existing LBM and transfer the information between different scales is implemented. The results of coarse-grid, reduced-order, simulations agree very well with averaged results obtained using a fine grid.

Two-dimensional nano-lattice in Fe-Co-Ni-Al-Cu alloys

International Nuclear Information System (INIS)

Kalanov, M.U.; Ibragimova, E.M.; Khamraeva, R.N.; Rustamova, V.M.; Ummatov, H.D.

2007-01-01

Full text: The high coercive strength of the dispersionally solidified alloys on the base of Fe-Co-Ni-Al-Cu system appears as a result of the special thermomagnetic annealing, when particles of the strong magnetic phase are distinguished in non-magnetic matrix along an external magnetic field direction. The neutron studying allows one to reveal the correlation between magnetization and inclusion axes, and also existence of magnetic microcell and perfectness of the lattice. This work presents results of neutron diffraction study with a double-crystal spectrometer (0.145 nm). Plate like samples of size 18 12 4 mm 3 were cut from a single crystal of alloy UNDK35 T5 along (100) plane. Magnetic field of 6 kOe was applied perpendicular to the neutron beam. Zero-field spectrum had only random variation of the background. Under the applied magnetic field two maxima appeared at the angles of 12 and 24 minute. In the case of the magnetic field directed in parallel to the scattering vector, the two maxima disappeared as expected. It is evidence that nuclear scattering is less than magnetic one and the observed maxima correspond to (10) and (20) reflections from a two dimensional ferro-magnetic microcell. The cell parameter of the magnetic microcell was found 40.6 nm. The coherent scattering region size was 120-160 nm. The ferro-magnetic rod diameter estimated from the peak widths was 16 nm. The diffraction pattern for the demagnetized sample strongly differs from the initial magnetized sample, where a diffuse reflection was observed near Bragg reflection and related with residual magnetization. So, the magnetic inclusions created in the Fe-Co-Ni-Al-Cu system at the thermomagnetic annealing by means of disintegration of the solid solution are strong ferro-magnetic and one-domain. These particles form the two-dimensional magnetic microcell and interact each to other within 3-4 periods of the cell. (authors)

Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues

International Nuclear Information System (INIS)

Maruno, Ken-ichi; Biondini, Gino

2004-01-01

We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)

Piecewise parabolic negative magnetoresistance of two-dimensional electron gas with triangular antidot lattice

International Nuclear Information System (INIS)

Budantsev, M. V.; Lavrov, R. A.; Pogosov, A. G.; Zhdanov, E. Yu.; Pokhabov, D. A.

2011-01-01

Extraordinary piecewise parabolic behavior of the magnetoresistance has been experimentally detected in the two-dimensional electron gas with a dense triangular lattice of antidots, where commensurability magnetoresistance oscillations are suppressed. The magnetic field range of 0–0.6 T can be divided into three wide regions, in each of which the magnetoresistance is described by parabolic dependences with high accuracy (comparable to the experimental accuracy) and the transition regions between adjacent regions are much narrower than the regions themselves. In the region corresponding to the weakest magnetic fields, the parabolic behavior becomes almost linear. The observed behavior is reproducible as the electron gas density changes, which results in a change in the resistance by more than an order of magnitude. Possible physical mechanisms responsible for the observed behavior, including so-called “memory effects,” are discussed.

Ultraviolet stability of three-dimensional lattice pure gauge field theories

International Nuclear Information System (INIS)

Balaban, T.

1985-01-01

We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on results of the previous papers on renormalization group method for lattice gauge theories. (orig.)

Simulation of condensation and liquid break-up on a micro-object with upper and lower movable walls using Lattice Boltzmann Method

Science.gov (United States)

Asadollahi, Arash; Esmaeeli, Asghar

2018-05-01

In this paper, two-dimensional condensation, liquid behavior on the micro-object with moving walls, and breaking up have been investigated by the Shan and Chen multiphase Lattice Boltzmann Method (LBM), which has the ability to incorporate interactions such as fluid-fluid, and also fluid-solid. Four test cases with low, medium, high, and very high Weber numbers are investigated considering the velocity control of walls in detail. Vertical spread fraction n / h (where n is the minimum liquid thickness after deformation and h is the maximum length of liquid deformation in each time) decreases quickly indicating the liquid tendency to breakup in all cases. Except for the case of a very high Weber number, the separation will not happen and finally after fluctuation the fixed bulk of condensed liquid will be placed on the side of the micro-object. The maximum value of reaction parameter h / d becomes larger as the Weber number increases. It is shown that an increase in the Weber number leads to liquid breakup and this mechanism provides an effective way for removing the condensed liquid from micro-devices surfaces. The results by LBM reveal the liquid evolutionary behavior and breaking up over time and show that it is a controllable situation by manipulating the walls velocity. Moreover, it can be used in order to centralize and aggregate all the liquid to a specific direction.

Lattice Boltzmann simulations for wall-flow dynamics in porous ceramic diesel particulate filters

Science.gov (United States)

Lee, Da Young; Lee, Gi Wook; Yoon, Kyu; Chun, Byoungjin; Jung, Hyun Wook

2018-01-01

Flows through porous filter walls of wall-flow diesel particulate filter are investigated using the lattice Boltzmann method (LBM). The microscopic model of the realistic filter wall is represented by randomly overlapped arrays of solid spheres. The LB simulation results are first validated by comparison to those from previous hydrodynamic theories and constitutive models for flows in porous media with simple regular and random solid-wall configurations. We demonstrate that the newly designed randomly overlapped array structures of porous walls allow reliable and accurate simulations for the porous wall-flow dynamics in a wide range of solid volume fractions from 0.01 to about 0.8, which is beyond the maximum random packing limit of 0.625. The permeable performance of porous media is scrutinized by changing the solid volume fraction and particle Reynolds number using Darcy's law and Forchheimer's extension in the laminar flow region.

Tracer sorption and macroscopic transport in clay nano-pores: a lattice-Boltzmann study

International Nuclear Information System (INIS)

Levesque, Maximilien; Rotenberg, Benjamin; Duvail, Magali; Benichou, Olivier; Voituriez, Raphael; Pagonabarraga, Ignacio; Frenkel, Daan

2012-01-01

followed by making their associated moment to propagate between nodes of a lattice with a probability defined by evolution equations. This evolution with time gives access to macroscopic transport properties like the tracer effective diffusion coefficient. For now, however, the evolution equations do not satisfactorily account for sorption effects as they do not capture their chemical-specific nature. This is our goal to overtake this lack. We have introduced the specific adsorption and desorption mechanisms in the description of tracers transport. This has been done for neutral tracers, as a first step, by introducing a new possible event during the moment propagation of particles standing at solid-liquid interfacial nodes: they may adsorb (desorb) with a probability related to the adsorption and desorption rates of the underlying mechanism occurring at the molecular scale. In order to validate the method and to determine its numerical limitations, we have compared the Lattice-Boltzmann results to an analytical solution developed purposely in the simple geometry consisting of two parallel walls. This last solution comes from a stochastic approach of the longitudinal dynamics of a particle assumed to be driven by a Langevin equation accounting for bulk diffusion and for the adsorption-desorption rates defined above. It is finally shown how sorption phenomena affect the macroscopic transport properties of neutral tracers in geometries and regimes compatible with water in clay nano-pores. (authors)

Perfect 3-dimensional lattice actions for 4-dimensional quantum field theories at finite temperature

International Nuclear Information System (INIS)

Kerres, U.; Mack, G.; Palma, G.

1994-12-01

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bololiubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for φ 4 -theory and scalar electrodynamics. The Balaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here. (orig.)

Applicability of the lattice Boltzmann method to determine the ohmic resistance in equivalent resistor connections

Science.gov (United States)

Espinoza-Andaluz, Mayken; Barzola, Julio; Guarochico-Moreira, Víctor H.; Andersson, Martin

2017-12-01

Knowing the ohmic resistance in the materials allow to know in advance its electrical behavior when a potential difference is applied, and therefore the prediction of the electrical performance can be achieved in a most certain manner. Although the Lattice Boltzmann method (LBM) has been applied to solve several physical phenomena in complex geometries, it has only been used to describe the fluid phase, but applicability studies of LBM on the solid-electric-conducting material have not been carried out yet. The purpose of this paper is to demonstrate the accuracy of calculating the equivalent resistor connections using LBM. Several series and parallel resistor connections are effected. All the computations are carried out with 3D models, and the domain materials are designed by the authors.

Simulation of Sound Waves Using the Lattice Boltzmann Method for Fluid Flow: Benchmark Cases for Outdoor Sound Propagation.

Science.gov (United States)

Salomons, Erik M; Lohman, Walter J A; Zhou, Han

2016-01-01

Propagation of sound waves in air can be considered as a special case of fluid dynamics. Consequently, the lattice Boltzmann method (LBM) for fluid flow can be used for simulating sound propagation. In this article application of the LBM to sound propagation is illustrated for various cases: free-field propagation, propagation over porous and non-porous ground, propagation over a noise barrier, and propagation in an atmosphere with wind. LBM results are compared with solutions of the equations of acoustics. It is found that the LBM works well for sound waves, but dissipation of sound waves with the LBM is generally much larger than real dissipation of sound waves in air. To circumvent this problem it is proposed here to use the LBM for assessing the excess sound level, i.e. the difference between the sound level and the free-field sound level. The effect of dissipation on the excess sound level is much smaller than the effect on the sound level, so the LBM can be used to estimate the excess sound level for a non-dissipative atmosphere, which is a useful quantity in atmospheric acoustics. To reduce dissipation in an LBM simulation two approaches are considered: i) reduction of the kinematic viscosity and ii) reduction of the lattice spacing.

Revisiting the use of the immersed-boundary lattice-Boltzmann method for simulations of suspended particles

Science.gov (United States)

Mountrakis, L.; Lorenz, E.; Hoekstra, A. G.

2017-07-01

The immersed-boundary lattice-Boltzmann method (IB-LBM) is increasingly being used in simulations of dense suspensions. These systems are computationally very expensive and can strongly benefit from lower resolutions that still maintain the desired accuracy for the quantities of interest. IB-LBM has a number of free parameters that have to be defined, often without exact knowledge of the tradeoffs, since their behavior in low resolutions is not well understood. Such parameters are the lattice constant Δ x , the number of vertices Nv, the interpolation kernel ϕ , and the LBM relaxation time τ . We investigate the effect of these IB-LBM parameters on a number of straightforward but challenging benchmarks. The systems considered are (a) the flow of a single sphere in shear flow, (b) the collision of two spheres in shear flow, and (c) the lubrication interaction of two spheres. All benchmarks are performed in three dimensions. The first two systems are used for determining two effective radii: the hydrodynamic radius rhyd and the particle interaction radius rinter. The last system is used to establish the numerical robustness of the lubrication forces, used to probe the hydrodynamic interactions in the limit of small gaps. Our results show that lower spatial resolutions result in larger hydrodynamic and interaction radii, while surface densities should be chosen above two vertices per LU2 result to prevent fluid penetration in underresolved meshes. Underresolved meshes also failed to produce the migration of particles toward the center of the domain due to lift forces in Couette flow, mostly noticeable for IBM-kernel ϕ2. Kernel ϕ4, despite being more robust toward mesh resolution, produces a notable membrane thickness, leading to the breakdown of the lubrication forces in larger gaps, and its use in dense suspensions where the mean particle distances are small can result in undesired behavior. rhyd is measured to be different from rinter, suggesting that there is

Periodic, quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein–Gordon lattice

International Nuclear Information System (INIS)

Quan, Xu; Qiang, Tian

2009-01-01

We study a two-dimensional (2D) diatomic lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DBs) can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein–Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers (QDBs) and chaotic discrete breathers (CDBs) by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom

Stable three-dimensional solitons in attractive Bose-Einstein condensates loaded in an optical lattice

International Nuclear Information System (INIS)

Mihalache, D.; Mazilu, D.; Lederer, F.; Malomed, B.A.; Crasovan, L.-C.; Kartashov, Y.V.; Torner, L.

2005-01-01

The existence and stability of solitons in Bose-Einstein condensates with attractive interatomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic form. We find a one-parameter family of stable 3D solitons in a certain interval of values of their norm, provided that the strength of the potential exceeds a threshold value. The minimum number of 7 Li atoms in the stable solitons is 60, and the energy of the soliton at the stability threshold is ≅6 recoil energies in the lattice. The respective energy versus norm diagram features two cuspidal points, resulting in a typical swallowtail pattern, which is a generic feature of 3D solitons supported by quasi-two-dimensional or fully dimensional lattice potentials

The Fundamental Structure and the Reproduction of Spiral Wave in a Two-Dimensional Excitable Lattice.

Science.gov (United States)

Qian, Yu; Zhang, Zhaoyang

2016-01-01

In this paper we have systematically investigated the fundamental structure and the reproduction of spiral wave in a two-dimensional excitable lattice. A periodically rotating spiral wave is introduced as the model to reproduce spiral wave artificially. Interestingly, by using the dominant phase-advanced driving analysis method, the fundamental structure containing the loop structure and the wave propagation paths has been revealed, which can expose the periodically rotating orbit of spiral tip and the charity of spiral wave clearly. Furthermore, the fundamental structure is utilized as the core for artificial spiral wave. Additionally, the appropriate parameter region, in which the artificial spiral wave can be reproduced, is studied. Finally, we discuss the robustness of artificial spiral wave to defects.

Simulation and detection of massive Dirac fermions with cold atoms in one-dimensional optical lattice

Energy Technology Data Exchange (ETDEWEB)

Yu Yafei, E-mail: yfyuks@hotmail.com [Laboratory of Nanophotonic Functional Materials and Devices, LQIT and SIPSE, South China Normal University, Guangzhou 510006 (China); Shan Chuanjia [Laboratory of Nanophotonic Functional Materials and Devices, LQIT and SIPSE, South China Normal University, Guangzhou 510006 (China); College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002 (China); Mei Feng; Zhang Zhiming [Laboratory of Nanophotonic Functional Materials and Devices, LQIT and SIPSE, South China Normal University, Guangzhou 510006 (China)

2012-09-15

We propose a simple but feasible experimental scheme to simulate and detect Dirac fermions with cold atoms trapped in one-dimensional optical lattice. In our scheme, through tuning the laser intensity, the one-dimensional optical lattice can have two sites in each unit cell and the atoms around the low energy behave as massive Dirac fermions. Furthermore, we show that these relativistic quasiparticles can be detected experimentally by using atomic density profile measurements and Bragg scattering.

Hovering and targeting flight simulations of a dragonfly-like flapping wing-body model by the immersed boundary-lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Hirohashi, Kensuke; Inamuro, Takaji, E-mail: inamuro@kuaero.kyoto-u.ac.jp [Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 615-8540 (Japan)

2017-08-15

Hovering and targeting flights of the dragonfly-like flapping wing-body model are numerically investigated by using the immersed boundary-lattice Boltzmann method. The governing parameters of the problem are the Reynolds number Re , the Froude number Fr , and the non-dimensional mass m . We set the parameters at Re = 200, Fr = 15 and m  = 51. First, we simulate free flights of the model for various values of the phase difference angle ϕ between the forewing and the hindwing motions and for various values of the stroke angle β between the stroke plane and the horizontal plane. We find that the vertical motion of the model depends on the phase difference angle ϕ , and the horizontal motion of the model depends on the stroke angle β . Secondly, using the above results we try to simulate the hovering flight by dynamically changing the phase difference angle ϕ and the stroke angle β . The hovering flight can be successfully simulated by a simple proportional controller of the phase difference angle and the stroke angle. Finally, we simulate a targeting flight by dynamically changing the stroke angle β . (paper)

Hovering and targeting flight simulations of a dragonfly-like flapping wing-body model by the immersed boundary-lattice Boltzmann method

International Nuclear Information System (INIS)

Hirohashi, Kensuke; Inamuro, Takaji

2017-01-01

Hovering and targeting flights of the dragonfly-like flapping wing-body model are numerically investigated by using the immersed boundary-lattice Boltzmann method. The governing parameters of the problem are the Reynolds number Re , the Froude number Fr , and the non-dimensional mass m . We set the parameters at Re = 200, Fr = 15 and m  = 51. First, we simulate free flights of the model for various values of the phase difference angle ϕ between the forewing and the hindwing motions and for various values of the stroke angle β between the stroke plane and the horizontal plane. We find that the vertical motion of the model depends on the phase difference angle ϕ , and the horizontal motion of the model depends on the stroke angle β . Secondly, using the above results we try to simulate the hovering flight by dynamically changing the phase difference angle ϕ and the stroke angle β . The hovering flight can be successfully simulated by a simple proportional controller of the phase difference angle and the stroke angle. Finally, we simulate a targeting flight by dynamically changing the stroke angle β . (paper)

Analysis of natural convection in nanofluid-filled H-shaped cavity by entropy generation and heatline visualization using lattice Boltzmann method

Science.gov (United States)

Rahimi, Alireza; Sepehr, Mohammad; Lariche, Milad Janghorban; Mesbah, Mohammad; Kasaeipoor, Abbas; Malekshah, Emad Hasani

2018-03-01

The lattice Boltzmann simulation of natural convection in H-shaped cavity filled with nanofluid is performed. The entropy generation analysis and heatline visualization are employed to analyze the considered problem comprehensively. The produced nanofluid is SiO2-TiO2/Water-EG (60:40) hybrid nanofluid, and the thermal conductivity and dynamic viscosity of used nanofluid are measured experimentally. To use the experimental data of thermal conductivity and dynamic viscosity, two sets of correlations based on temperature for six different solid volume fractions of 0.5, 1, 1.5, 2, 2.5 and 3 vol% are derived. The influences of different governing parameters such different aspect ratio, solid volume fractions of nanofluid and Rayleigh numbers on the fluid flow, temperature filed, average/local Nusselt number, total/local entropy generation and heatlines are presented.

Lattice Boltzmann model for thermal free surface flows with liquid-solid phase transition

International Nuclear Information System (INIS)

Attar, Elham; Koerner, Carolin

2011-01-01

Purpose: The main objective of this work is to develop an algorithm to use the Lattice Boltzmann method for solving free surface thermal flow problems with solid/liquid phase changes. Approach: A multi-distribution function model is applied to simulate hydrodynamic flow and the coupled thermal diffusion-convection problem. Findings: The free surface problem, i.e. the reconstruction of the missing distribution functions at the interface, can be solved by applying a physical transparent momentum and heat flux based methodology. The developed method is subsequently applied to some test cases in order to assess its computational potentials. Practical implications: Many industrial processes involve problems where non-isothermal motion and simultaneous solidification of fluids with free surface is important. Examples are all castings processes and especially foaming processes which are characterized by a huge and strongly changing surface. Value: A reconstruction algorithm to treat a thermal hydrodynamic problem with free surfaces is presented which is physically transparent and easy to implement.

GPU-accelerated Lattice Boltzmann method for anatomical extraction in patient-specific computational hemodynamics

Science.gov (United States)

Yu, H.; Wang, Z.; Zhang, C.; Chen, N.; Zhao, Y.; Sawchuk, A. P.; Dalsing, M. C.; Teague, S. D.; Cheng, Y.

2014-11-01

Existing research of patient-specific computational hemodynamics (PSCH) heavily relies on software for anatomical extraction of blood arteries. Data reconstruction and mesh generation have to be done using existing commercial software due to the gap between medical image processing and CFD, which increases computation burden and introduces inaccuracy during data transformation thus limits the medical applications of PSCH. We use lattice Boltzmann method (LBM) to solve the level-set equation over an Eulerian distance field and implicitly and dynamically segment the artery surfaces from radiological CT/MRI imaging data. The segments seamlessly feed to the LBM based CFD computation of PSCH thus explicit mesh construction and extra data management are avoided. The LBM is ideally suited for GPU (graphic processing unit)-based parallel computing. The parallel acceleration over GPU achieves excellent performance in PSCH computation. An application study will be presented which segments an aortic artery from a chest CT dataset and models PSCH of the segmented artery.

Influence of thermal fluctuations on ligament break-up: a fluctuating lattice Boltzmann study

Science.gov (United States)

Xue, Xiao; Biferale, Luca; Sbragaglia, Mauro; Toschi, Federico

2017-11-01

Thermal fluctuations are essential ingredients in a nanoscale system, driving Brownian motion of particles and capillary waves at non-ideal interfaces. Here we study the influence of thermal fluctuations on the breakup of liquid ligaments at the nanoscale. We offer quantitative characterization of the effects of thermal fluctuations on the Plateau-Rayleigh mechanism that drives the breakup process of ligaments. Due to thermal fluctuations, the droplet sizes after break-up need to be analyzed in terms of their distribution over an ensemble made of repeated experiments. To this aim, we make use of numerical simulations based on the fluctuating lattice Boltzmann method (FLBM) for multicomponent mixtures. The method allows an accurate and efficient simulation of the fluctuating hydrodynamics equations of a binary mixture, where both stochastic viscous stresses and diffusion fluxes are introduced. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No 642069.

Lattice Boltzmann simulations of droplet formation in confined channels with thermocapillary flows

Science.gov (United States)

Gupta, A.; Sbragaglia, M.; Belardinelli, D.; Sugiyama, K.

2016-12-01

Based on mesoscale lattice Boltzmann simulations with the "Shan-Chen" model, we explore the influence of thermocapillarity on the breakup properties of fluid threads in a microfluidic T-junction, where a dispersed phase is injected perpendicularly into a main channel containing a continuous phase, and the latter induces periodic breakup of droplets due to the cross-flowing. Temperature effects are investigated by switching on-off both positive-negative temperature gradients along the main channel direction, thus promoting a different thread dynamics with anticipated-delayed breakup. Numerical simulations are performed at changing the flow rates of both the continuous and dispersed phases, as well as the relative importance of viscous forces, surface tension forces, and thermocapillary stresses. The range of parameters is broad enough to characterize the effects of thermocapillarity on different mechanisms of breakup in the confined T-junction, including the so-called "squeezing" and "dripping" regimes, previously identified in the literature. Some simple scaling arguments are proposed to rationalize the observed behavior, and to provide quantitative guidelines on how to predict the droplet size after breakup.

Emergent dynamic structures and statistical law in spherical lattice gas automata

Science.gov (United States)

Yao, Zhenwei

2017-12-01

Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature-driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several nonequilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven nonequilibrium physics.

Emergent dynamic structures and statistical law in spherical lattice gas automata.

Science.gov (United States)

Yao, Zhenwei

2017-12-01

Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature-driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several nonequilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven nonequilibrium physics.

Tunable all-angle negative refraction and photonic band gaps in two-dimensional plasma photonic crystals with square-like Archimedean lattices

International Nuclear Information System (INIS)

Zhang, Hai-Feng; Liu, Shao-Bin; Jiang, Yu-Chi

2014-01-01

In this paper, the tunable all-angle negative refraction and photonic band gaps (PBGs) in two types of two-dimensional (2D) plasma photonic crystals (PPCs) composed of homogeneous plasma and dielectric (GaAs) with square-like Archimedean lattices (ladybug and bathroom lattices) for TM wave are theoretically investigated based on a modified plane wave expansion method. The type-1 structure is dielectric rods immersed in the plasma background, and the complementary structure is named as type-2 PPCs. Theoretical simulations demonstrate that the both types of PPCs with square-like Archimedean lattices have some advantages in obtaining the higher cut-off frequency, the larger PBGs, more number of PBGs, and the relative bandwidths compared to the conventional square lattices as the filling factor or radius of inserted rods is same. The influences of plasma frequency and radius of inserted rod on the properties of PBGs for both types of PPCs also are discussed in detail. The calculated results show that PBGs can be manipulated by the parameters as mentioned above. The possibilities of all-angle negative refraction in such two types of PPCs at low bands also are discussed. Our calculations reveal that the all-angle negative phenomena can be observed in the first two TM bands, and the frequency range of all-angle negative refraction can be tuned by changing plasma frequency. Those properties can be used to design the optical switching and sensor