Entropic Lattice Boltzmann Simulations of Turbulence

NASA Astrophysics Data System (ADS)

Keating, Brian; Vahala, George; Vahala, Linda; Soe, Min; Yepez, Jeffrey

2006-10-01

Because of its simplicity, nearly perfect parallelization and vectorization on supercomputer platforms, lattice Boltzmann (LB) methods hold great promise for simulations of nonlinear physics. Indeed, our MHD-LB code has the best sustained performance/PE of any code on the Earth Simulator. By projecting into the higher dimensional kinetic phase space, the solution trajectory is simpler and much easier to compute than standard CFD approach. However, simple LB -- with its simple advection and local BGK collisional relaxation -- does not impose positive definiteness of the distribution functions in the time evolution. This leads to numerical instabilities for very low transport coefficients. In Entropic LB (ELB) one determines a discrete H-theorem and the equilibrium distribution functions subject to the collisional invariants. The ELB algorithm is unconditionally stable to arbitrary small transport coefficients. Various choices of velocity discretization are examined: 15, 19 and 27-bit ELB models. The connection between Tsallis and Boltzmann entropies are clarified.

Lattice-Boltzmann simulations of microswimmer-tracer interactions

NASA Astrophysics Data System (ADS)

de Graaf, Joost; Stenhammar, Joakim

2017-02-01

Hydrodynamic interactions in systems composed of self-propelled particles, such as swimming microorganisms and passive tracers, have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force-counterforce-based lattice-Boltzmann (LB) algorithm [De Graaf et al., J. Chem. Phys. 144, 134106 (2016), 10.1063/1.4944962] in order to validate its ability to capture the relevant low-Reynolds-number physics. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The force-lattice coupling of the LB algorithm leads to a "smearing out" of the flow field, which strongly perturbs the tracer trajectories at close swimmer-tracer separations, and we analyze how this effect can be accurately captured using a simple renormalized hydrodynamic theory. Finally, we show that care must be taken when using LB algorithms to simulate systems of self-propelled particles, since its finite momentum transport time can lead to significant deviations from theoretical predictions based on Stokes flow. These insights should prove relevant to the future study of large-scale microswimmer suspensions using these methods.

Immersed boundary lattice Boltzmann model based on multiple relaxation times

NASA Astrophysics Data System (ADS)

Lu, Jianhua; Han, Haifeng; Shi, Baochang; Guo, Zhaoli

2012-01-01

As an alterative version of the lattice Boltzmann models, the multiple relaxation time (MRT) lattice Boltzmann model introduces much less numerical boundary slip than the single relaxation time (SRT) lattice Boltzmann model if some special relationship between the relaxation time parameters is chosen. On the other hand, most current versions of the immersed boundary lattice Boltzmann method, which was first introduced by Feng and improved by many other authors, suffer from numerical boundary slip as has been investigated by Le and Zhang. To reduce such a numerical boundary slip, an immerse boundary lattice Boltzmann model based on multiple relaxation times is proposed in this paper. A special formula is given between two relaxation time parameters in the model. A rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single-relaxation-time-based model.

Lattice Boltzmann simulation of antiplane shear loading of a stationary crack

NASA Astrophysics Data System (ADS)

Schlüter, Alexander; Kuhn, Charlotte; Müller, Ralf

2018-01-01

In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61-69, 2000) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu's work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.

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

NASA Astrophysics Data System (ADS)

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.

Multiple-Relaxation-Time Lattice Boltzmann Models in 3D

NASA Technical Reports Server (NTRS)

dHumieres, Dominique; Ginzburg, Irina; Krafczyk, Manfred; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

This article provides a concise exposition of the multiple-relaxation-time lattice Boltzmann equation, with examples of fifteen-velocity and nineteen-velocity models in three dimensions. Simulation of a diagonally lid-driven cavity flow in three dimensions at Re=500 and 2000 is performed. The results clearly demonstrate the superior numerical stability of the multiple-relaxation-time lattice Boltzmann equation over the popular lattice Bhatnagar-Gross-Krook equation.

Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.

PubMed

Keating, Brian; Vahala, George; Yepez, Jeffrey; Soe, Min; Vahala, Linda

2007-03-01

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.

Lattice Boltzmann Methods for Fluid Structure Interaction

DTIC Science & Technology

2012-09-01

MONTEREY, CALIFORNIA DISSERTATION LATTICE BOLTZMANN METHODS FOR FLUID STRUCTURE INTERACTION by Stuart R. Blair September 2012 Dissertation Supervisor...200 words) The use of lattice Boltzmann methods (LBM) for fluid flow and its coupling with finite element method (FEM) structural models for fluid... structure interaction (FSI) is investigated. A body of high performance LBM software that exploits graphic processing unit (GPU) and multiprocessor

Finite-element lattice Boltzmann simulations of contact line dynamics

NASA Astrophysics Data System (ADS)

Matin, Rastin; Krzysztof Misztal, Marek; Hernández-García, Anier; Mathiesen, Joachim

2018-01-01

The lattice Boltzmann method has become one of the standard techniques for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular lattices. Alternative off-lattice Boltzmann schemes exist for both single- and multiphase flows that decouple the velocity discretization from the underlying spatial grid. The current study extends the applicability of these off-lattice methods by introducing a finite element formulation that enables simulating contact line dynamics for partially wetting fluids. This work exemplifies the implementation of the scheme and furthermore presents benchmark experiments that show the scheme reduces spurious currents at the liquid-vapor interface by at least two orders of magnitude compared to a nodal implementation and allows for predicting the equilibrium states accurately in the range of moderate contact angles.

Two-dimensional lattice Boltzmann model for magnetohydrodynamics.

PubMed

Schaffenberger, Werner; Hanslmeier, Arnold

2002-10-01

We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.

Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

NASA Astrophysics Data System (ADS)

Chen, Z.; Shu, C.; Tan, D.

2018-05-01

An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

From the Boltzmann to the Lattice-Boltzmann Equation:. Beyond BGK Collision Models

NASA Astrophysics Data System (ADS)

Philippi, Paulo Cesar; Hegele, Luiz Adolfo; Surmas, Rodrigo; Siebert, Diogo Nardelli; Dos Santos, Luís Orlando Emerich

In this work, we present a derivation for the lattice-Boltzmann equation directly from the linearized Boltzmann equation, combining the following main features: multiple relaxation times and thermodynamic consistency in the description of non isothermal compressible flows. The method presented here is based on the discretization of increasingly order kinetic models of the Boltzmann equation. Following a Gross-Jackson procedure, the linearized collision term is developed in Hermite polynomial tensors and the resulting infinite series is diagonalized after a chosen integer N, establishing the order of approximation of the collision term. The velocity space is discretized, in accordance with a quadrature method based on prescribed abscissas (Philippi et al., Phys. Rev E 73, 056702, 2006). The problem of describing the energy transfer is discussed, in relation with the order of approximation of a two relaxation-times lattice Boltzmann model. The velocity-step, temperature-step and the shock tube problems are investigated, adopting lattices with 37, 53 and 81 velocities.

Maxwell iteration for the lattice Boltzmann method with diffusive scaling

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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 project. Here, we describe the theoretical basis of the algorithm as well as computational aspects of the implementation. The software package is validated against simulations of meso-phases resulting from self-assembly in ternary fluid mixtures comprising immiscible and amphiphilic components such as water-oil-surfactant systems. The impact of the surfactant species on the dynamics of spinodal decomposition are tested and quantitative measurement of the permeability of a body centred cubic (BCC) model porous medium for a simple binary mixture is described. Single-core performance and scaling behaviour of the code are reported for simulations on current supercomputer architectures.

Electroosmotic flow and mixing in microchannels with the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Tang, G. H.; Li, Zhuo; Wang, J. K.; He, Y. L.; Tao, W. Q.

2006-11-01

Understanding the electroosmotic flow in microchannels is of both fundamental and practical significance for the design and optimization of various microfluidic devices to control fluid motion. In this paper, a lattice Boltzmann equation, which recovers the nonlinear Poisson-Boltzmann equation, is used to solve the electric potential distribution in the electrolytes, and another lattice Boltzmann equation, which recovers the Navier-Stokes equation including the external force term, is used to solve the velocity fields. The method is validated by the electric potential distribution in the electrolytes and the pressure driven pulsating flow. Steady-state and pulsating electroosmotic flows in two-dimensional parallel uniform and nonuniform charged microchannels are studied with this lattice Boltzmann method. The simulation results show that the heterogeneous surface potential distribution and the electroosmotic pulsating flow can induce chaotic advection and thus enhance the mixing in microfluidic systems efficiently.

Lattice Boltzmann approach for complex nonequilibrium flows.

PubMed

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

2015-10-01

We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion.

High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

NASA Astrophysics Data System (ADS)

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.

An Immersed Boundary-Lattice Boltzmann Method for Simulating Particulate Flows

NASA Astrophysics Data System (ADS)

Zhang, Baili; Cheng, Ming; Lou, Jing

2013-11-01

A two-dimensional momentum exchange-based immersed boundary-lattice Boltzmann method developed by X.D. Niu et al. (2006) has been extended in three-dimensions for solving fluid-particles interaction problems. This method combines the most desirable features of the lattice Boltzmann method and the immersed boundary method by using a regular Eulerian mesh for the flow domain and a Lagrangian mesh for the moving particles in the flow field. The non-slip boundary conditions for the fluid and the particles are enforced by adding a force density term into the lattice Boltzmann equation, and the forcing term is simply calculated by the momentum exchange of the boundary particle density distribution functions, which are interpolated by the Lagrangian polynomials from the underlying Eulerian mesh. This method preserves the advantages of lattice Boltzmann method in tracking a group of particles and, at the same time, provides an alternative approach to treat solid-fluid boundary conditions. Numerical validations show that the present method is very accurate and efficient. The present method will be further developed to simulate more complex problems with particle deformation, particle-bubble and particle-droplet interactions.

A Lattice Boltzmann Method for Turbomachinery Simulations

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Lopez, I.

2003-01-01

Lattice Boltzmann (LB) Method is a relatively new method for flow simulations. The start point of LB method is statistic mechanics and Boltzmann equation. The LB method tries to set up its model at molecular scale and simulate the flow at macroscopic scale. LBM has been applied to mostly incompressible flows and simple geometry.

Entropic lattice Boltzmann model for compressible flows.

PubMed

Frapolli, N; Chikatamarla, S S; Karlin, I V

2015-12-01

We present a lattice Boltzmann model (LBM) that covers the entire range of fluid flows, from low Mach weakly compressible to transonic and supersonic flows. One of the most restrictive limitations of the lattice Boltzmann method, the low Mach number limit, is overcome here by three fundamental changes to the LBM scheme: use of an appropriately chosen multispeed lattice, accurate evaluation of the equilibrium, and the entropic relaxation for the collision. The range of applications is demonstrated through the simulation of a bow shock in front of an airfoil and the simulation of decaying compressible turbulence with shocklets.

Comment on ``Numerics of the lattice Boltzmann method: Effects of collision models on the lattice Boltzmann simulations''

NASA Astrophysics Data System (ADS)

Karlin, I. V.; Succi, S.; Chikatamarla, S. S.

2011-12-01

Critical comments on the entropic lattice Boltzmann equation (ELBE), by Li-Shi Luo, Wei Liao, Xingwang Chen, Yan Peng, and Wei Zhang in Ref. , are based on simulations, which make use of a model that, despite being referred to as the ELBE by the authors, is in fact equivalent to the standard lattice Bhatnagar-Gross-Krook equation for low Mach number simulations. In this Comment, a concise review of the ELBE is provided and illustrated by means of a three-dimensional turbulent flow simulation, which highlights the subgrid features of the ELBE.

Solitons of the Kadomtsev-Petviashvili equation based on lattice Boltzmann model

NASA Astrophysics Data System (ADS)

Wang, Huimin

2017-01-01

In this paper, a lattice Boltzmann model for the Kadomtsev-Petviashvili equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. Due to the asymmetry in x direction and y direction of the equation, the moments of the equilibrium distribution function are selected are asymmetric. The numerical results demonstrate the lattice Boltzmann method is an effective method to simulate the solitons of the Kadomtsev-Petviashvili equation.

New variational principles for locating periodic orbits of differential equations.

PubMed

Boghosian, Bruce M; Fazendeiro, Luis M; Lätt, Jonas; Tang, Hui; Coveney, Peter V

2011-06-13

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier-Stokes equations, simulated using the lattice Boltzmann equation.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Thermal, Microchannel, and Immersed Boundary Extension Validation for the Lattice-Boltzmann Method: Report 2 in Discrete Nano Scale Mechanics and Simulations Series

DTIC Science & Technology

2017-07-01

Lattice Boltzmann Method continues to garner interest in fluids research , particularly with its ability to accurately simulate laminar flows in the...Lattice- Boltzmann Method Report 2 in “Discrete Nano-Scale Mechanics and Simulations” Series In fo rm at io n Te ch no lo gy L ab or at or y...William P. England and Jeffrey B. Allen July 2017 Approved for public release; distribution is unlimited. The U.S. Army Engineer Research and

Dual FIB-SEM 3D imaging and lattice boltzmann modeling of porosimetry and multiphase flow in chalk.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rinehart, Alex; Petrusak, Robin; Heath, Jason E.

2010-12-01

Mercury intrusion porosimetry (MIP) is an often-applied technique for determining pore throat distributions and seal analysis of fine-grained rocks. Due to closure effects, potential pore collapse, and complex pore network topologies, MIP data interpretation can be ambiguous, and often biased toward smaller pores in the distribution. We apply 3D imaging techniques and lattice-Boltzmann modeling in interpreting MIP data for samples of the Cretaceous Selma Group Chalk. In the Mississippi Interior Salt Basin, the Selma Chalk is the apparent seal for oil and gas fields in the underlying Eutaw Fm., and, where unfractured, the Selma Chalk is one of the regional-scalemore » seals identified by the Southeast Regional Carbon Sequestration Partnership for CO2 injection sites. Dual focused ion - scanning electron beam and laser scanning confocal microscopy methods are used for 3D imaging of nanometer-to-micron scale microcrack and pore distributions in the Selma Chalk. A combination of image analysis software is used to obtain geometric pore body and throat distributions and other topological properties, which are compared to MIP results. 3D data sets of pore-microfracture networks are used in Lattice Boltzmann simulations of drainage (wetting fluid displaced by non-wetting fluid via the Shan-Chen algorithm), which in turn are used to model MIP procedures. Results are used in interpreting MIP results, understanding microfracture-matrix interaction during multiphase flow, and seal analysis for underground CO2 storage.« less

Simulation of gaseous diffusion in partially saturated porous media under variable gravity with lattice Boltzmann methods

NASA Technical Reports Server (NTRS)

Chau, Jessica Furrer; Or, Dani; Sukop, Michael C.; Steinberg, S. L. (Principal Investigator)

2005-01-01

Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents for different gravity conditions and measured gas diffusion through the media using a multicomponent lattice Boltzmann code. The relative diffusion coefficients (D rel) for simulations with and without gravity as functions of air-filled porosity were in good agreement with measured data and established models. We found significant differences in liquid configuration in porous media, leading to reductions in D rel of up to 25% under zero gravity. The study highlights potential applications of the lattice Boltzmann method for rapid and cost-effective evaluation of alternative plant growth media designs under variable gravity.

Counter-extrapolation method for conjugate interfaces in computational heat and mass transfer.

PubMed

Le, Guigao; Oulaid, Othmane; Zhang, Junfeng

2015-03-01

In this paper a conjugate interface method is developed by performing extrapolations along the normal direction. Compared to other existing conjugate models, our method has several technical advantages, including the simple and straightforward algorithm, accurate representation of the interface geometry, applicability to any interface-lattice relative orientation, and availability of the normal gradient. The model is validated by simulating the steady and unsteady convection-diffusion system with a flat interface and the steady diffusion system with a circular interface, and good agreement is observed when comparing the lattice Boltzmann results with respective analytical solutions. A more general system with unsteady convection-diffusion process and a curved interface, i.e., the cooling process of a hot cylinder in a cold flow, is also simulated as an example to illustrate the practical usefulness of our model, and the effects of the cylinder heat capacity and thermal diffusivity on the cooling process are examined. Results show that the cylinder with a larger heat capacity can release more heat energy into the fluid and the cylinder temperature cools down slower, while the enhanced heat conduction inside the cylinder can facilitate the cooling process of the system. Although these findings appear obvious from physical principles, the confirming results demonstrates the application potential of our method in more complex systems. In addition, the basic idea and algorithm of the counter-extrapolation procedure presented here can be readily extended to other lattice Boltzmann models and even other computational technologies for heat and mass transfer systems.

Quantitative phase-field lattice-Boltzmann study of lamellar eutectic growth under natural convection

NASA Astrophysics Data System (ADS)

Zhang, A.; Guo, Z.; Xiong, S.-M.

2018-05-01

The influence of natural convection on lamellar eutectic growth was determined by a comprehensive phase-field lattice-Boltzmann study for Al-Cu and CB r4-C2C l6 eutectic alloys. The mass differences resulting from concentration differences led to the fluid flow and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency. By means of carefully designed "numerical experiments", the eutectic growth under natural convection was explored and a simple analytical model was proposed to predict the adjustment of the lamellar spacing. Furthermore, by alternating the solute expansion coefficient, initial lamellar spacing, and undercooling, the microstructure evolution was presented and compared with the classical eutectic growth theory. Results showed that both interfacial solute distribution and average curvature were affected by the natural convection, the effect of which could be further quantified by adding a constant into the growth rule proposed by Jackson and Hunt [Jackson and Hunt, Trans. Metall. Soc. AIME 236, 1129 (1966)].

Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios

NASA Astrophysics Data System (ADS)

Fakhari, Abbas; Bolster, Diogo

2017-04-01

We introduce a simple and efficient lattice Boltzmann method for immiscible multiphase flows, capable of handling large density and viscosity contrasts. The model is based on a diffuse-interface phase-field approach. Within this context we propose a new algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. The proposed method has superior computational accuracy compared with the common approach of approximating curved boundaries with stair cases. We test the model by applying it to four benchmark problems: (i) wetting and dewetting of a droplet on a flat surface and (ii) on a cylindrical surface, (iii) multiphase flow past a circular cylinder at an intermediate Reynolds number, and (iv) a droplet falling on hydrophilic and superhydrophobic circular cylinders under differing conditions. Where available, our results show good agreement with analytical solutions and/or existing experimental data, highlighting strengths of this new approach.

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

NASA Astrophysics Data System (ADS)

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.

Towards a physical interpretation of the entropic lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Malaspinas, Orestis; Deville, Michel; Chopard, Bastien

2008-12-01

The entropic lattice Boltzmann method (ELBM) is one among several different versions of the lattice Boltzmann method for the simulation of hydrodynamics. The collision term of the ELBM is characterized by a nonincreasing H function, guaranteed by a variable relaxation time. We propose here an analysis of the ELBM using the Chapman-Enskog expansion. We show that it can be interpreted as some kind of subgrid model, where viscosity correction scales like the strain rate tensor. We confirm our analytical results by the numerical computations of the relaxation time modifications on the two-dimensional dipole-wall interaction benchmark.

Entropic multirelaxation lattice Boltzmann models for turbulent flows

NASA Astrophysics Data System (ADS)

Bösch, Fabian; Chikatamarla, Shyam S.; Karlin, Ilya V.

2015-10-01

We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014), 10.1103/PhysRevE.90.031302] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.

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

PubMed

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.

Topology optimisation of micro fluidic mixers considering fluid-structure interactions with a coupled Lattice Boltzmann algorithm

NASA Astrophysics Data System (ADS)

Munk, David J.; Kipouros, Timoleon; Vio, Gareth A.; Steven, Grant P.; Parks, Geoffrey T.

2017-11-01

Recently, the study of micro fluidic devices has gained much interest in various fields from biology to engineering. In the constant development cycle, the need to optimise the topology of the interior of these devices, where there are two or more optimality criteria, is always present. In this work, twin physical situations, whereby optimal fluid mixing in the form of vorticity maximisation is accompanied by the requirement that the casing in which the mixing takes place has the best structural performance in terms of the greatest specific stiffness, are considered. In the steady state of mixing this also means that the stresses in the casing are as uniform as possible, thus giving a desired operating life with minimum weight. The ultimate aim of this research is to couple two key disciplines, fluids and structures, into a topology optimisation framework, which shows fast convergence for multidisciplinary optimisation problems. This is achieved by developing a bi-directional evolutionary structural optimisation algorithm that is directly coupled to the Lattice Boltzmann method, used for simulating the flow in the micro fluidic device, for the objectives of minimum compliance and maximum vorticity. The needs for the exploration of larger design spaces and to produce innovative designs make meta-heuristic algorithms, such as genetic algorithms, particle swarms and Tabu Searches, less efficient for this task. The multidisciplinary topology optimisation framework presented in this article is shown to increase the stiffness of the structure from the datum case and produce physically acceptable designs. Furthermore, the topology optimisation method outperforms a Tabu Search algorithm in designing the baffle to maximise the mixing of the two fluids.

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

PubMed

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.

Simulation technique for slurries interacting with moving parts and deformable solids with applications

NASA Astrophysics Data System (ADS)

Mutabaruka, Patrick; Kamrin, Ken

2018-04-01

A numerical method for particle-laden fluids interacting with a deformable solid domain and mobile rigid parts is proposed and implemented in a full engineering system. The fluid domain is modeled with a lattice Boltzmann representation, the particles and rigid parts are modeled with a discrete element representation, and the deformable solid domain is modeled using a Lagrangian mesh. The main issue of this work, since separately each of these methods is a mature tool, is to develop coupling and model-reduction approaches in order to efficiently simulate coupled problems of this nature, as in various geological and engineering applications. The lattice Boltzmann method incorporates a large eddy simulation technique using the Smagorinsky turbulence model. The discrete element method incorporates spherical and polyhedral particles for stiff contact interactions. A neo-Hookean hyperelastic model is used for the deformable solid. We provide a detailed description of how to couple the three solvers within a unified algorithm. The technique we propose for rubber modeling/coupling exploits a simplification that prevents having to solve a finite-element problem at each time step. We also developed a technique to reduce the domain size of the full system by replacing certain zones with quasi-analytic solutions, which act as effective boundary conditions for the lattice Boltzmann method. The major ingredients of the routine are separately validated. To demonstrate the coupled method in full, we simulate slurry flows in two kinds of piston valve geometries. The dynamics of the valve and slurry are studied and reported over a large range of input parameters.

Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

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.

Exact diffusion constant in a lattice-gas wind-tree model on a Bethe lattice

NASA Astrophysics Data System (ADS)

Zhang, Guihua; Percus, J. K.

1992-02-01

Kong and Cohen [Phys. Rev. B 40, 4838 (1989)] obtained the diffusion constant of a lattice-gas wind-tree model in the Boltzmann approximation. The result is consistent with computer simulations for low tree concentration. In this Brief Report we find the exact diffusion constant of the model on a Bethe lattice, which turns out to be identical with the Kong-Cohen and Gunn-Ortuño results. Our interpretation is that the Boltzmann approximation is exact for this type of diffusion on a Bethe lattice in the same sense that the Bethe-Peierls approximation is exact for the Ising model on a Bethe lattice.

One-dimensional transient radiative transfer by lattice Boltzmann method.

PubMed

Zhang, Yong; Yi, Hongliang; Tan, Heping

2013-10-21

The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing scattering media subjected to a collimated short laser irradiation. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. The accuracy and computational efficiency of this algorithm are examined firstly. Afterwards, effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor, and the shapes of laser pulse on time-resolved signals of transmittance and reflectance are investigated. Results of the present method are found to compare very well with the data from the literature. For an oblique incidence, the LBM results in this paper are compared with those by Monte Carlo method generated by ourselves. In addition, transient radiative transfer in a two-Layer inhomogeneous media subjected to a short square pulse irradiation is investigated. At last, the LBM is further extended to study the transient radiative transfer in homogeneous medium with a refractive index discontinuity irradiated by the short pulse laser. Several trends on the time-resolved signals different from those for refractive index of 1 (i.e. refractive-index-matched boundary) are observed and analysed.

Extending a CAD-Based Cartesian Mesh Generator for the Lattice Boltzmann Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cantrell, J Nathan; Inclan, Eric J; Joshi, Abhijit S

2012-01-01

This paper describes the development of a custom preprocessor for the PaRAllel Thermal Hydraulics simulations using Advanced Mesoscopic methods (PRATHAM) code based on an open-source mesh generator, CartGen [1]. PRATHAM is a three-dimensional (3D) lattice Boltzmann method (LBM) based parallel flow simulation software currently under development at the Oak Ridge National Laboratory. The LBM algorithm in PRATHAM requires a uniform, coordinate system-aligned, non-body-fitted structured mesh for its computational domain. CartGen [1], which is a GNU-licensed open source code, already comes with some of the above needed functionalities. However, it needs to be further extended to fully support the LBM specificmore » preprocessing requirements. Therefore, CartGen is being modified to (i) be compiler independent while converting a neutral-format STL (Stereolithography) CAD geometry to a uniform structured Cartesian mesh, (ii) provide a mechanism for PRATHAM to import the mesh and identify the fluid/solid domains, and (iii) provide a mechanism to visually identify and tag the domain boundaries on which to apply different boundary conditions.« less

Entropy and Galilean Invariance of Lattice Boltzmann Theories

NASA Astrophysics Data System (ADS)

Chikatamarla, Shyam S.; Karlin, Iliya V.

2006-11-01

A theory of lattice Boltzmann (LB) models for hydrodynamic simulation is developed upon a novel relation between entropy construction and roots of Hermite polynomials. A systematic procedure is described for constructing numerically stable and complete Galilean invariant LB models. The stability of the new LB models is illustrated with a shock tube simulation.

Accuracy of the lattice Boltzmann method for describing the behavior of a gas in the continuum limit.

PubMed

Kataoka, Takeshi; Tsutahara, Michihisa

2010-11-01

The accuracy of the lattice Boltzmann method (LBM) for describing the behavior of a gas in the continuum limit is systematically investigated. The asymptotic analysis for small Knudsen numbers is carried out to derive the corresponding fluid-dynamics-type equations, and the errors of the LBM are estimated by comparing them with the correct fluid-dynamics-type equations. We discuss the following three important cases: (I) the Mach number of the flow is much smaller than the Knudsen number, (II) the Mach number is of the same order as the Knudsen number, and (III) the Mach number is finite. From the von Karman relation, the above three cases correspond to the flows of (I) small Reynolds number, (II) finite Reynolds number, and (III) large Reynolds number, respectively. The analysis is made with the information only of the fundamental properties of the lattice Boltzmann models without stepping into their detailed form. The results are therefore applicable to various lattice Boltzmann models that satisfy the fundamental properties used in the analysis.

An Implementation of Hydrostatic Boundary Conditions for Variable Density Lattice Boltzmann Methods

NASA Astrophysics Data System (ADS)

Bardsley, K. J.; Thorne, D. T.; Lee, J. S.; Sukop, M. C.

2006-12-01

Lattice Boltzmann Methods (LBMs) have been under development for the last two decades and have become another capable numerical method for simulating fluid flow. Recent advances in lattice Boltzmann applications involve simulation of density-dependent fluid flow in closed (Dixit and Babu, 2006; D'Orazio et al., 2004) or periodic (Guo and Zhao, 2005) domains. However, standard pressure boundary conditions (BCs) are incompatible with concentration-dependent density flow simulations that use a body force for gravity. An implementation of hydrostatic BCs for use under these conditions is proposed here. The basis of this new implementation is an additional term in the pressure BC. It is derived to account for the incorporation of gravity as a body force and the effect of varying concentration in the fluid. The hydrostatic BC expands the potential of density-dependent LBM to simulate domains with boundaries other than the closed or periodic boundaries that have appeared in previous literature on LBM simulations. With this new implementation, LBM will be able to simulate complex concentration-dependent density flows, such as salt water intrusion in the classic Henry and Henry-Hilleke problems. This is demonstrated using various examples, beginning with a closed box system, and ending with a system containing two solid walls, one velocity boundary and one pressure boundary, as in the Henry problem. References Dixit, H. N., V. Babu, (2006), Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, Int. J. Heat Mass Transfer, 49, 727-739. D'Orazio, A., M. Corcione, G.P. Celata, (2004), Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary conditions, Int. J. Thermal Sci., 43, 575-586. Gou, Z., T.S. Zhao, (2005), Lattice Boltzmann simulation of natural convection with temperature-dependant viscosity in a porous cavity, Numerical Heat Transfer, Part B, 47, 157-177.

Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media.

PubMed

Karani, Hamid; Huber, Christian

2015-02-01

In this paper, we propose an approach for studying conjugate heat transfer using the lattice Boltzmann method (LBM). The approach is based on reformulating the lattice Boltzmann equation for solving the conservative form of the energy equation. This leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components with different thermal properties. The proposed source term formulation conserves conductive and advective heat flux simultaneously, which makes it suitable for modeling conjugate heat transfer in general multiphase or multicomponent systems. The simple implementation of the source term approach avoids any correction of distribution functions neighboring the interface and provides an algorithm that is independent from the topology of the interface. Moreover, our approach is independent of the choice of lattice discretization and can be easily applied to different advection-diffusion LBM solvers. The model is tested against several benchmark problems including steady-state convection-diffusion within two fluid layers with parallel and normal interfaces with respect to the flow direction, unsteady conduction in a three-layer stratified domain, and steady conduction in a two-layer annulus. The LBM results are in excellent agreement with analytical solution. Error analysis shows that our model is first-order accurate in space, but an extension to a second-order scheme is straightforward. We apply our LBM model to heat transfer in a two-component heterogeneous medium with a random microstructure. This example highlights that the method we propose is independent of the topology of interfaces between the different phases and, as such, is ideally suited for complex natural heterogeneous media. We further validate the present LBM formulation with a study of natural convection in a porous enclosure. The results confirm the reliability of the model in simulating complex coupled fluid and thermal dynamics in complex geometries.

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

NASA Astrophysics Data System (ADS)

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.

Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement

DOE PAGES

Guzik, Stephen M.; Weisgraber, Todd H.; Colella, Phillip; ...

2013-12-10

A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examplesmore » highlighting the mesh adaptivity of this method are also provided.« less

Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows

NASA Astrophysics Data System (ADS)

Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan

2018-05-01

This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.

Simulation on Thermocapillary-Driven Drop Coalescence by Hybrid Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Xie, Haiqiong; Zeng, Zhong; Zhang, Liangqi; Yokota, Yuui; Kawazoe, Yoshiyuki; Yoshikawa, Akira

2016-04-01

A hybrid two-phase model, incorporating lattice Boltzmann method (LBM) and finite difference method (FDM), was developed to investigate the coalescence of two drops during their thermocapillary migration. The lattice Boltzmann method with a multi-relaxation-time (MRT) collision model was applied to solve the flow field for incompressible binary fluids, and the method was implemented in an axisymmetric form. The deformation of the drop interface was captured with the phase-field theory, and the continuum surface force model (CSF) was adopted to introduce the surface tension, which depends on the temperature. Both phase-field equation and the energy equation were solved with the finite difference method. The effects of Marangoni number and Capillary numbers on the drop's motion and coalescence were investigated.

Lattice Boltzmann method for rain-induced overland flow

NASA Astrophysics Data System (ADS)

Ding, Yu; Liu, Haifei; Peng, Yong; Xing, Liming

2018-07-01

Complex rainfall situations can generate overland flow with complex hydrodynamic characteristics, affecting the surface configuration (i.e. sheet erosion) and environment to varying degrees. Reliable numerical simulations can provide a scientific method for the optimization of environmental management. A mesoscopic numerical method, the lattice Boltzmann method, was employed to simulate overland flows. To deal with complex rainfall, two schemes were introduced to improve the lattice Boltzmann equation and the local equilibrium function, respectively. Four typical cases with differences in rainfall, bed roughness, and slopes were selected to test the accuracy and applicability of the proposed schemes. It was found that the simulated results were in good agreement with the experimental data, analytical values, and the results produced by other models.

Lattice Boltzmann method for weakly ionized isothermal plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Huayu; Ki, Hyungson

2007-12-15

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.

Human Signatures for Personnel Detection

DTIC Science & Technology

2010-09-14

work\\ TESIS \\prueba.avi’); switch videoinfo.ImageType case ’truecolor’ video=aviread(’C:\\MATLAB\\R2006a\\work\\ TESIS \\prueba.avi’); case...8217indexed’ video=aviread(’C:\\MATLAB\\R2006a\\work\\ TESIS \\prueba.avi’); video=ind2rgb(video); end 4.1.2 Color to Grayscale Converter The conversion from...algorithm. • Maximum errors for both GTSig and the lattice Boltzmann method were confined to the corners where fthe temperature is ill de ined Numerical

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

PubMed

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.

Numerical investigation of nonlinear fluid-structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-Finite Element method

NASA Astrophysics Data System (ADS)

Gong, Chun-Lin; Fang, Zhe; Chen, Gang

A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear finite element method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on Eulerian grid, the behaviors of flexible objects are calculated through nonlinear dynamic finite element method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-Finite Element method is first validated by a fluid-structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.

Evolution of a double-front Rayleigh-Taylor system using a graphics-processing-unit-based high-resolution thermal lattice-Boltzmann model.

PubMed

Ripesi, P; Biferale, L; Schifano, S F; Tripiccione, R

2014-04-01

We study the turbulent evolution originated from a system subjected to a Rayleigh-Taylor instability with a double density at high resolution in a two-dimensional geometry using a highly optimized thermal lattice-Boltzmann code for GPUs. Our investigation's initial condition, given by the superposition of three layers with three different densities, leads to the development of two Rayleigh-Taylor fronts that expand upward and downward and collide in the middle of the cell. By using high-resolution numerical data we highlight the effects induced by the collision of the two turbulent fronts in the long-time asymptotic regime. We also provide details on the optimized lattice-Boltzmann code that we have run on a cluster of GPUs.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

Chen, Lin-Jie; Ma, Chang-Feng

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 ut + αuux + βunux + γuxx + δuxxx + ζuxxxx = 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.

Lattice Boltzmann model for the compressible Navier-Stokes equations with flexible specific-heat ratio.

PubMed

Kataoka, Takeshi; Tsutahara, Michihisa

2004-03-01

We have developed a lattice Boltzmann model for the compressible Navier-Stokes equations with a flexible specific-heat ratio. Several numerical results are presented, and they agree well with the corresponding solutions of the Navier-Stokes equations. In addition, an explicit finite-difference scheme is proposed for the numerical calculation that can make a stable calculation with a large Courant number.

The lattice Boltzmann method and the problem of turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Djenidi, L.

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.

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

NASA Astrophysics Data System (ADS)

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 model has been found to perform better than the improved Z-S-C model in this aspect.

Hermite regularization of the lattice Boltzmann method for open source computational aeroacoustics.

PubMed

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).

New Developments of Computational Fluid Dynamics and Their Applications to Practical Engineering Problems

NASA Astrophysics Data System (ADS)

Chen, Hudong

2001-06-01

There have been considerable advances in Lattice Boltzmann (LB) based methods in the last decade. By now, the fundamental concept of using the approach as an alternative tool for computational fluid dynamics (CFD) has been substantially appreciated and validated in mainstream scientific research and in industrial engineering communities. Lattice Boltzmann based methods possess several major advantages: a) less numerical dissipation due to the linear Lagrange type advection operator in the Boltzmann equation; b) local dynamic interactions suitable for highly parallel processing; c) physical handling of boundary conditions for complicated geometries and accurate control of fluxes; d) microscopically consistent modeling of thermodynamics and of interface properties in complex multiphase flows. It provides a great opportunity to apply the method to practical engineering problems encountered in a wide range of industries from automotive, aerospace to chemical, biomedical, petroleum, nuclear, and others. One of the key challenges is to extend the applicability of this alternative approach to regimes of highly turbulent flows commonly encountered in practical engineering situations involving high Reynolds numbers. Over the past ten years, significant efforts have been made on this front at Exa Corporation in developing a lattice Boltzmann based commercial CFD software, PowerFLOW. It has become a useful computational tool for the simulation of turbulent aerodynamics in practical engineering problems involving extremely complex geometries and flow situations, such as in new automotive vehicle designs world wide. In this talk, we present an overall LB based algorithm concept along with certain key extensions in order to accurately handle turbulent flows involving extremely complex geometries. To demonstrate the accuracy of turbulent flow simulations, we provide a set of validation results for some well known academic benchmarks. These include straight channels, backward-facing steps, flows over a curved hill and typical NACA airfoils at various angles of attack including prediction of stall angle. We further provide numerous engineering cases, ranging from external aerodynamics around various car bodies to internal flows involved in various industrial devices. We conclude with a discussion of certain future extensions for complex fluids.

Lattice Boltzmann model for three-phase viscoelastic fluid flow

NASA Astrophysics Data System (ADS)

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.

Flow force and torque on submerged bodies in lattice-Boltzmann methods via momentum exchange.

PubMed

Giovacchini, Juan P; Ortiz, Omar E

2015-12-01

We review the momentum exchange method to compute the flow force and torque on a submerged body in lattice-Boltzmann methods by presenting an alternative derivation. Our derivation does not depend on a particular implementation of the boundary conditions at the body surface, and it relies on general principles. After the introduction of the momentum exchange method in lattice-Boltzmann methods, some formulations were introduced to compute the fluid force on static and moving bodies. These formulations were introduced in a rather intuitive, ad hoc way. In our derivation, we recover the proposals most frequently used, in some cases with minor corrections, gaining some insight into the two most used formulations. At the end, we present some numerical tests to compare different approaches on a well-known benchmark test that support the correctness of the formulas derived.

Galilean-invariant algorithm coupling immersed moving boundary conditions and Lees-Edwards boundary conditions

NASA Astrophysics Data System (ADS)

Zhou, Guofeng; Wang, Limin; Wang, Xiaowei; Ge, Wei

2011-12-01

Many investigators have coupled the Lees-Edwards boundary conditions (LEBCs) and suspension methods in the framework of the lattice Boltzmann method to study the pure bulk properties of particle-fluid suspensions. However, these suspension methods are all link-based and are more or less exposed to the disadvantages of violating Galilean invariance. In this paper, we have coupled LEBCs with a node-based suspension method, which is demonstrated to be Galilean invariant in benchmark simulations. We use the coupled algorithm to predict the viscosity of a particle-fluid suspension at very low Reynolds number, and the simulation results are in good agreement with the semiempirical Krieger-Dougherty formula.

Three-dimensional lattice Boltzmann model for compressible flows.

PubMed

Sun, Chenghai; Hsu, Andrew T

2003-07-01

A three-dimensional compressible lattice Boltzmann model is formulated on a cubic lattice. A very large particle-velocity set is incorporated in order to enable a greater variation in the mean velocity. Meanwhile, the support set of the equilibrium distribution has only six directions. Therefore, this model can efficiently handle flows over a wide range of Mach numbers and capture shock waves. Due to the simple form of the equilibrium distribution, the fourth-order velocity tensors are not involved in the formulation. Unlike the standard lattice Boltzmann model, no special treatment is required for the homogeneity of fourth-order velocity tensors on square lattices. The Navier-Stokes equations were recovered, using the Chapman-Enskog method from the Bhatnagar-Gross-Krook (BGK) lattice Boltzmann equation. The second-order discretization error of the fluctuation velocity in the macroscopic conservation equation was eliminated by means of a modified collision invariant. The model is suitable for both viscous and inviscid compressible flows with or without shocks. Since the present scheme deals only with the equilibrium distribution that depends only on fluid density, velocity, and internal energy, boundary conditions on curved wall are easily implemented by an extrapolation of macroscopic variables. To verify the scheme for inviscid flows, we have successfully simulated a three-dimensional shock-wave propagation in a box and a normal shock of Mach number 10 over a wedge. As an application to viscous flows, we have simulated a flat plate boundary layer flow, flow over a cylinder, and a transonic flow over a NACA0012 airfoil cascade.

Comment on ``Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation''

NASA Astrophysics Data System (ADS)

Lallemand, Pierre; Luo, Li-Shi

2008-12-01

Recently Reis and Phillips [Phys. Rev. E 77, 026702 (2008)] proposed a perturbative method to solve the dispersion equation derived from the linearized lattice Boltzmann equation. We will demonstrate that the method proposed by Reis and Phillips is a reinvention of an existing method. We would also like to refute a number of claims made by Reis and Phillips.

Mass-conserving advection-diffusion Lattice Boltzmann model for multi-species reacting flows

NASA Astrophysics Data System (ADS)

Hosseini, S. A.; Darabiha, N.; Thévenin, D.

2018-06-01

Given the complex geometries usually found in practical applications, the Lattice Boltzmann (LB) method is becoming increasingly attractive. In addition to the simple treatment of intricate geometrical configurations, LB solvers can be implemented on very large parallel clusters with excellent scalability. However, reacting flows and especially combustion lead to additional challenges and have seldom been studied by LB methods. Indeed, overall mass conservation is a pressing issue in modeling multi-component flows. The classical advection-diffusion LB model recovers the species transport equations with the generalized Fick approximation under the assumption of an incompressible flow. However, for flows involving multiple species with different diffusion coefficients and density fluctuations - as is the case with weakly compressible solvers like Lattice Boltzmann -, this approximation is known not to conserve overall mass. In classical CFD, as the Fick approximation does not satisfy the overall mass conservation constraint a diffusion correction velocity is usually introduced. In the present work, a local expression is first derived for this correction velocity in a LB framework. In a second step, the error due to the incompressibility assumption is also accounted for through a modified equilibrium distribution function. Theoretical analyses and simulations show that the proposed scheme performs much better than the conventional advection-diffusion Lattice Boltzmann model in terms of overall mass conservation.

A novel heterogeneous algorithm to simulate multiphase flow in porous media on multicore CPU-GPU systems

NASA Astrophysics Data System (ADS)

McClure, J. E.; Prins, J. F.; Miller, C. T.

2014-07-01

Multiphase flow implementations of the lattice Boltzmann method (LBM) are widely applied to the study of porous medium systems. In this work, we construct a new variant of the popular "color" LBM for two-phase flow in which a three-dimensional, 19-velocity (D3Q19) lattice is used to compute the momentum transport solution while a three-dimensional, seven velocity (D3Q7) lattice is used to compute the mass transport solution. Based on this formulation, we implement a novel heterogeneous GPU-accelerated algorithm in which the mass transport solution is computed by multiple shared memory CPU cores programmed using OpenMP while a concurrent solution of the momentum transport is performed using a GPU. The heterogeneous solution is demonstrated to provide speedup of 2.6 × as compared to multi-core CPU solution and 1.8 × compared to GPU solution due to concurrent utilization of both CPU and GPU bandwidths. Furthermore, we verify that the proposed formulation provides an accurate physical representation of multiphase flow processes and demonstrate that the approach can be applied to perform heterogeneous simulations of two-phase flow in porous media using a typical GPU-accelerated workstation.

Thermal lattice BGK models for fluid dynamics

NASA Astrophysics Data System (ADS)

Huang, Jian

1998-11-01

As an alternative in modeling fluid dynamics, the Lattice Boltzmann method has attracted considerable attention. In this thesis, we shall present a general form of thermal Lattice BGK. This form can handle large differences in density, temperature, and high Mach number. This generalized method can easily model gases with different adiabatic index values. The numerical transport coefficients of this model are estimated both theoretically and numerically. Their dependency on the sizes of integration steps in time and space, and on the flow velocity and temperature, are studied and compared with other established CFD methods. This study shows that the numerical viscosity of the Lattice Boltzmann method depends linearly on the space interval, and on the flow velocity as well for supersonic flow. This indicates this method's limitation in modeling high Reynolds number compressible thermal flow. On the other hand, the Lattice Boltzmann method shows promise in modeling micro-flows, i.e., gas flows in micron-sized devices. A two-dimensional code has been developed based on the conventional thermal lattice BGK model, with some modifications and extensions for micro- flows and wall-fluid interactions. Pressure-driven micro- channel flow has been simulated. Results are compared with experiments and simulations using other methods, such as a spectral element code using slip boundary condition with Navier-Stokes equations and a Direct Simulation Monte Carlo (DSMC) method.

Laser short-pulse heating of an aluminum thin film: Energy transfer in electron and lattice sub-systems

NASA Astrophysics Data System (ADS)

Bin Mansoor, Saad; Sami Yilbas, Bekir

2015-08-01

Laser short-pulse heating of an aluminum thin film is considered and energy transfer in the film is formulated using the Boltzmann equation. Since the heating duration is short and the film thickness is considerably small, thermal separation of electron and lattice sub-systems is incorporated in the analysis. The electron-phonon coupling is used to formulate thermal communication of both sub-systems during the heating period. Equivalent equilibrium temperature is introduced to account for the average energy of all phonons around a local point when they redistribute adiabatically to an equilibrium state. Temperature predictions of the Boltzmann equation are compared with those obtained from the two-equation model. It is found that temperature predictions from the Boltzmann equation differ slightly from the two-equation model results. Temporal variation of equivalent equilibrium temperature does not follow the laser pulse intensity in the electron sub-system. The time occurrence of the peak equivalent equilibrium temperature differs for electron and lattice sub-systems, which is attributed to phonon scattering in the irradiated field in the lattice sub-system. In this case, time shift is observed for occurrence of the peak temperature in the lattice sub-system.

Entropic Lattice Boltzmann Methods

DTIC Science & Technology

2001-12-10

model of fluid dynamics in one dimension, first considered by Renda et al. in 1997 [14]. Here the geometric picture involves a four dimensional polytope...convention of including constant terms in an extra column of the matrix, using the device of appending 1 to the column vector of unknowns. In general, there...we apply the entropic lattice Boltzmann method to a simple five-velocity model of fluid dynamics in one dimension, first considered by Renda et al

Simulating anomalous transport and multiphase segregation in porous media with the Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Matin, Rastin; Hernandez, Anier; Misztal, Marek; Mathiesen, Joachim

2015-04-01

Many hydrodynamic phenomena ranging from flows at micron scale in porous media, large Reynolds numbers flows, non-Newtonian and multiphase flows have been simulated on computers using the lattice Boltzmann (LB) method. By solving the Lattice Boltzmann Equation on unstructured meshes in three dimensions, we have developed methods to efficiently model the fluid flow in real rock samples. We use this model to study the spatio-temporal statistics of the velocity field inside three-dimensional real geometries and investigate its relation to the, in general, anomalous transport of passive tracers for a wide range of Peclet and Reynolds numbers. We extend this model by free-energy based method, which allows us to simulate binary systems with large-density ratios in a thermodynamically consistent way and track the interface explicitly. In this presentation we will present our recent results on both anomalous transport and multiphase segregation.

Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation.

PubMed

Zhang, Raoyang; Shan, Xiaowen; Chen, Hudong

2006-10-01

We present a further theoretical extension to the kinetic-theory-based formulation of the lattice Boltzmann method of Shan [J. Fluid Mech. 550, 413 (2006)]. In addition to the higher-order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to third-order hydrodynamic moments. Numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number Kn can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsen's minimum and the asymptotic behavior of flow flux at large Kn.

Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

PubMed

Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

2016-02-01

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Prediction of sound absorption in rigid porous media with the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

da Silva, Andrey Ricardo; Mareze, Paulo; Brandão, Eric

2016-02-01

In this work, sound absorption phenomena associated with the viscous shear stress within rigid porous media is investigated with a simple isothermal lattice Boltzmann BGK model. Simulations are conducted for different macroscopic material properties such as sample thickness and porosity and the results are compared with the exact analytical solution for materials with slit-like structure in terms of acoustic impedance and sound absorption coefficient. The numerical results agree very well with the exact solution, particularly for the sound absorption coefficient. The small deviations found in the low frequency limit for the real part of the acoustic impedance are attributed to the ratio between the thicknesses of the slit and the viscous boundary layer. The results suggest that the lattice Boltzmann method can be a very compelling numerical tool for simulating viscous sound absorption phenomena in the time domain, particularly due to its computational simplicity when compared to traditional continuum based techniques.

An effective lattice Boltzmann flux solver on arbitrarily unstructured meshes

NASA Astrophysics Data System (ADS)

Wu, Qi-Feng; Shu, Chang; Wang, Yan; Yang, Li-Ming

2018-05-01

The recently proposed lattice Boltzmann flux solver (LBFS) is a new approach for the simulation of incompressible flow problems. It applies the finite volume method (FVM) to discretize the governing equations, and the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. In the previous application of the LBFS, the structured meshes have been commonly employed, which may cause inconvenience for problems with complex geometries. In this paper, the LBFS is extended to arbitrarily unstructured meshes for effective simulation of incompressible flows. Two test cases, the lid-driven flow in a triangular cavity and flow around a circular cylinder, are carried out for validation. The obtained results are compared with the data available in the literature. Good agreement has been achieved, which demonstrates the effectiveness and reliability of the LBFS in simulating flows on arbitrarily unstructured meshes.

Combining cellular automata and Lattice Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and immune competition.

PubMed

Alemani, Davide; Pappalardo, Francesco; Pennisi, Marzio; Motta, Santo; Brusic, Vladimir

2012-02-28

In the last decades the Lattice Boltzmann method (LB) has been successfully used to simulate a variety of processes. The LB model describes the microscopic processes occurring at the cellular level and the macroscopic processes occurring at the continuum level with a unique function, the probability distribution function. Recently, it has been tried to couple deterministic approaches with probabilistic cellular automata (probabilistic CA) methods with the aim to model temporal evolution of tumor growths and three dimensional spatial evolution, obtaining hybrid methodologies. Despite the good results attained by CA-PDE methods, there is one important issue which has not been completely solved: the intrinsic stochastic nature of the interactions at the interface between cellular (microscopic) and continuum (macroscopic) level. CA methods are able to cope with the stochastic phenomena because of their probabilistic nature, while PDE methods are fully deterministic. Even if the coupling is mathematically correct, there could be important statistical effects that could be missed by the PDE approach. For such a reason, to be able to develop and manage a model that takes into account all these three level of complexity (cellular, molecular and continuum), we believe that PDE should be replaced with a statistic and stochastic model based on the numerical discretization of the Boltzmann equation: The Lattice Boltzmann (LB) method. In this work we introduce a new hybrid method to simulate tumor growth and immune system, by applying Cellular Automata Lattice Boltzmann (CA-LB) approach. Copyright © 2011 Elsevier B.V. All rights reserved.

Color-gradient lattice Boltzmann model for simulating droplet motion with contact-angle hysteresis.

PubMed

Ba, Yan; Liu, Haihu; Sun, Jinju; Zheng, Rongye

2013-10-01

Lattice Boltzmann method (LBM) is an effective tool for simulating the contact-line motion due to the nature of its microscopic dynamics. In contact-line motion, contact-angle hysteresis is an inherent phenomenon, but it is neglected in most existing color-gradient based LBMs. In this paper, a color-gradient based multiphase LBM is developed to simulate the contact-line motion, particularly with the hysteresis of contact angle involved. In this model, the perturbation operator based on the continuum surface force concept is introduced to model the interfacial tension, and the recoloring operator proposed by Latva-Kokko and Rothman is used to produce phase segregation and resolve the lattice pinning problem. At the solid surface, the color-conserving wetting boundary condition [Hollis et al., IMA J. Appl. Math. 76, 726 (2011)] is applied to improve the accuracy of simulations and suppress spurious currents at the contact line. In particular, we present a numerical algorithm to allow for the effect of the contact-angle hysteresis, in which an iterative procedure is used to determine the dynamic contact angle. Numerical simulations are conducted to verify the developed model, including the droplet partial wetting process and droplet dynamical behavior in a simple shear flow. The obtained results are compared with theoretical solutions and experimental data, indicating that the model is able to predict the equilibrium droplet shape as well as the dynamic process of partial wetting and thus permits accurate prediction of contact-line motion with the consideration of contact-angle hysteresis.

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

NASA Astrophysics Data System (ADS)

Ibrahem, Ahmed M.; El-Amin, Mohamed F.; Sun, Shuyu

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.

Lattice Boltzmann model for numerical relativity.

PubMed

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.

Dual FIB-SEM 3D Imaging and Lattice Boltzmann Modeling of Porosimetry and Multiphase Flow in Chalk

NASA Astrophysics Data System (ADS)

Rinehart, A. J.; Yoon, H.; Dewers, T. A.; Heath, J. E.; Petrusak, R.

2010-12-01

Mercury intrusion porosimetry (MIP) is an often-applied technique for determining pore throat distributions and seal analysis of fine-grained rocks. Due to closure effects, potential pore collapse, and complex pore network topologies, MIP data interpretation can be ambiguous, and often biased toward smaller pores in the distribution. We apply 3D imaging techniques and lattice-Boltzmann modeling in interpreting MIP data for samples of the Cretaceous Selma Group Chalk. In the Mississippi Interior Salt Basin, the Selma Chalk is the apparent seal for oil and gas fields in the underlying Eutaw Fm., and, where unfractured, the Selma Chalk is one of the regional-scale seals identified by the Southeast Regional Carbon Sequestration Partnership for CO2 injection sites. Dual focused ion - scanning electron beam and laser scanning confocal microscopy methods are used for 3D imaging of nanometer-to-micron scale microcrack and pore distributions in the Selma Chalk. A combination of image analysis software is used to obtain geometric pore body and throat distributions and other topological properties, which are compared to MIP results. 3D data sets of pore-microfracture networks are used in Lattice Boltzmann simulations of drainage (wetting fluid displaced by non-wetting fluid via the Shan-Chen algorithm), which in turn are used to model MIP procedures. Results are used in interpreting MIP results, understanding microfracture-matrix interaction during multiphase flow, and seal analysis for underground CO2 storage. This work was supported by the US Department of Energy, Office of Basic Energy Sciences as part of an Energy Frontier Research Center. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Company, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Theoretical and numerical study of axisymmetric lattice Boltzmann models

NASA Astrophysics Data System (ADS)

Huang, Haibo; Lu, Xi-Yun

2009-07-01

The forcing term in the lattice Boltzmann equation (LBE) is usually used to mimic Navier-Stokes equations with a body force. To derive axisymmetric model, forcing terms are incorporated into the two-dimensional (2D) LBE to mimic the additional axisymmetric contributions in 2D Navier-Stokes equations in cylindrical coordinates. Many axisymmetric lattice Boltzmann D2Q9 models were obtained through the Chapman-Enskog expansion to recover the 2D Navier-Stokes equations in cylindrical coordinates [I. Halliday , Phys. Rev. E 64, 011208 (2001); K. N. Premnath and J. Abraham, Phys. Rev. E 71, 056706 (2005); T. S. Lee, H. Huang, and C. Shu, Int. J. Mod. Phys. C 17, 645 (2006); T. Reis and T. N. Phillips, Phys. Rev. E 75, 056703 (2007); J. G. Zhou, Phys. Rev. E 78, 036701 (2008)]. The theoretical differences between them are discussed in detail. Numerical studies were also carried out by simulating two different flows to make a comparison on these models’ accuracy and τ sensitivity. It is found all these models are able to obtain accurate results and have the second-order spatial accuracy. However, the model C [J. G. Zhou, Phys. Rev. E 78, 036701 (2008)] is the most stable one in terms of τ sensitivity. It is also found that if density of fluid is defined in its usual way and not directly relevant to source terms, the lattice Boltzmann model seems more stable.

Lattice Boltzmann multi-phase simulations in porous media using Multiple GPUs

NASA Astrophysics Data System (ADS)

Toelke, J.; De Prisco, G.; Mu, Y.

2011-12-01

Ingrain's digital rock physics lab computes the physical properties and fluid flow characteristics of oil and gas reservoir rocks including shales, carbonates and sandstones. Ingrain uses advanced lattice Boltzmann methods (LBM) to simulate multiphase flow in the rocks (porous media). We present a very efficient implementation of these methods based on CUDA. Because LBM operates on a finite difference grid, is explicit in nature, and requires only next-neighbor interactions, it is suitable for implementation on GPUs. Since GPU hardware allows for very fine grain parallelism, every lattice site can be handled by a different core. Data has to be loaded from and stored to the device memory in such a way that dense access to the memory is ensured. This can be achieved by accessing the lattice nodes with respect to their contiguous memory locations [1,2]. The simulation engine uses a sparse data structure to represent the grid and advanced algorithms to handle the moving fluid-fluid interface. The simulations are accelerated on one GPU by one order of magnitude compared to a state of the art multicore desktop computer. The engine is parallelized using MPI and runs on multiple GPUs in the same node or across the Infiniband network. Simulations with up to 50 GPUs in parallel are presented. With this simulator using it is possible to perform pore scale multi-phase (oil-water-matrix) simulations in natural porous media in a commercial manner and to predict important rock properties like absolute permeability, relative permeabilites and capillary pressure [3,4]. Results and videos of these simulations in complex real world porous media and rocks are presented and discussed.

Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions

NASA Astrophysics Data System (ADS)

Asta, Adelchi J.; Levesque, Maximilien; Vuilleumier, Rodolphe; Rotenberg, Benjamin

2017-06-01

We use lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite-size effects induced by the use of periodic boundary conditions. These effects are inevitable in simulations at the molecular, mesoscopic, or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain the local velocity correlation function via linear response theory. This approach is validated by comparing the finite-size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time dependence of the local velocity autocorrelation function. We find at long times a crossover between the expected t-3 /2 hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the crossover time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite-size effects in bulk fluids, which arise regardless of the level of description and simulation algorithm, but also establishes the lattice-Boltzmann method as a suitable tool to investigate such effects in general.

Reply to ``Comment on `Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation' ''

NASA Astrophysics Data System (ADS)

Reis, T.; Phillips, T. N.

2008-12-01

In this reply to the comment by Lallemand and Luo, we defend our assertion that the alternative approach for the solution of the dispersion relation for a generalized lattice Boltzmann dispersion equation [T. Reis and T. N. Phillips, Phys. Rev. E 77, 026702 (2008)] is mathematically transparent, elegant, and easily justified. Furthermore, the rigorous perturbation analysis used by Reis and Phillips does not require the reciprocals of the relaxation parameters to be small.

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

PubMed

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.

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

PubMed

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.

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

PubMed

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.

Evaluation of the Performance of the Hybrid Lattice Boltzmann Based Numerical Flux

NASA Astrophysics Data System (ADS)

Zheng, H. W.; Shu, C.

2016-06-01

It is well known that the numerical scheme is a key factor to the stability and accuracy of a Navier-Stokes solver. Recently, a new hybrid lattice Boltzmann numerical flux (HLBFS) is developed by Shu's group. It combines two different LBFS schemes by a switch function. It solves the Boltzmann equation instead of the Euler equation. In this article, the main object is to evaluate the ability of this HLBFS scheme by our in-house cell centered hybrid mesh based Navier-Stokes code. Its performance is examined by several widely-used bench-mark test cases. The comparisons on results between calculation and experiment are conducted. They show that the scheme can capture the shock wave as well as the resolving of boundary layer.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Computational Research Division, Lawrence Berkeley National Laboratory; NERSC, Lawrence Berkeley National Laboratory; Computer Science Department, University of California, Berkeley

2009-05-04

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 permore » 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.« less

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

NASA Astrophysics Data System (ADS)

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.

Study on effective thermal conductivity of silicone/phosphor composite and its size effect by Lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Li, Lan; Zheng, Huai; Yuan, Chao; Hu, Run; Luo, Xiaobing

2016-12-01

The silicone/phosphor composite is widely used in light emitting diode (LED) packaging. The composite thermal properties, especially the effective thermal conductivity, strongly influence the LED performance. In this paper, a lattice Boltzmann model was presented to predict the silicone/phosphor composite effective thermal conductivity. Based on the present lattice Boltzmann model, a random generation method was established to describe the phosphor particle distribution in composite. Benchmarks were conducted by comparing the simulation results with theoretical solutions for simple cases. Then the model was applied to analyze the effective thermal conductivity of the silicone/phosphor composite and its size effect. The deviations between simulation and experimental results are <7 %, when the phosphor volume fraction varies from 0.038 to 0.45. The simulation results also indicate that effective thermal conductivity of the composite with larger particles is higher than that with small particles at the same volume fraction. While mixing these two sizes of phosphor particles provides an extra enhancement for the effective thermal conductivity.

A Lattice Boltzmann Fictitious Domain Method for Modeling Red Blood Cell Deformation and Multiple-Cell Hydrodynamic Interactions in Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Xing; Lin, Guang; Zou, Jianfeng

To model red blood cell (RBC) deformation in flow, the recently developed LBM-DLM/FD method ([Shi and Lim, 2007)29], derived from the lattice Boltzmann method and the distributed Lagrange multiplier/fictitious domain methodthe fictitious domain method, is extended to employ the mesoscopic network model for simulations of red blood cell deformation. The flow is simulated by the lattice Boltzmann method with an external force, while the network model is used for modeling red blood cell deformation and the fluid-RBC interaction is enforced by the Lagrange multiplier. To validate parameters of the RBC network model, sThe stretching numerical tests on both coarse andmore » fine meshes are performed and compared with the corresponding experimental data to validate the parameters of the RBC network model. In addition, RBC deformation in pipe flow and in shear flow is simulated, revealing the capacity of the current method for modeling RBC deformation in various flows.« less

Optimal preconditioning of lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

Izquierdo, Salvador; Fueyo, Norberto

2009-09-01

A preconditioning technique to accelerate the simulation of steady-state problems using the single-relaxation-time (SRT) lattice Boltzmann (LB) method was first proposed by Guo et al. [Z. Guo, T. Zhao, Y. Shi, Preconditioned lattice-Boltzmann method for steady flows, Phys. Rev. E 70 (2004) 066706-1]. The key idea in this preconditioner is to modify the equilibrium distribution function in such a way that, by means of a Chapman-Enskog expansion, a time-derivative preconditioner of the Navier-Stokes (NS) equations is obtained. In the present contribution, the optimal values for the free parameter γ of this preconditioner are searched both numerically and theoretically; the later with the aid of linear-stability analysis and with the condition number of the system of NS equations. The influence of the collision operator, single- versus multiple-relaxation-times (MRT), is also studied. Three steady-state laminar test cases are used for validation, namely: the two-dimensional lid-driven cavity, a two-dimensional microchannel and the three-dimensional backward-facing step. Finally, guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the Reynolds and Mach numbers. The new optimally preconditioned MRT method derived is shown to improve, simultaneously, the rate of convergence, the stability and the accuracy of the lattice Boltzmann simulations, when compared to the non-preconditioned methods and to the optimally preconditioned SRT one. Additionally, direct time-derivative preconditioning of the LB equation is also studied.

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

USGS Publications Warehouse

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.

Modeling and simulation of ocean wave propagation using lattice Boltzmann method

NASA Astrophysics Data System (ADS)

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.

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.

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

PubMed

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.

Applications of the Lattice Boltzmann Method to Complex and Turbulent Flows

NASA Technical Reports Server (NTRS)

Luo, Li-Shi; Qi, Dewei; Wang, Lian-Ping; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We briefly review the method of the lattice Boltzmann equation (LBE). We show the three-dimensional LBE simulation results for a non-spherical particle in Couette flow and 16 particles in sedimentation in fluid. We compare the LBE simulation of the three-dimensional homogeneous isotropic turbulence flow in a periodic cubic box of the size 1283 with the pseudo-spectral simulation, and find that the two results agree well with each other but the LBE method is more dissipative than the pseudo-spectral method in small scales, as expected.

Multicomponent lattice Boltzmann model from continuum kinetic theory.

PubMed

Shan, Xiaowen

2010-04-01

We derive from the continuum kinetic theory a multicomponent lattice Boltzmann model with intermolecular interaction. The resulting model is found to be consistent with the model previously derived from a lattice-gas cellular automaton [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] but applies in a much broader domain. A number of important insights are gained from the kinetic theory perspective. First, it is shown that even in the isothermal case, the energy equipartition principle dictates the form of the equilibrium distribution function. Second, thermal diffusion is shown to exist and the corresponding diffusivities are given in terms of macroscopic parameters. Third, the ordinary diffusion is shown to satisfy the Maxwell-Stefan equation at the ideal-gas limit.

Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer.

PubMed

Shi, Yong; Yap, Ying Wan; Sader, John E

2015-07-01

Ability to characterize the heat transfer in flowing gases is important for a wide range of applications involving micro- and nanoscale devices. Gas flows away from the continuum limit can be captured using the Boltzmann equation, whose analytical solution poses a formidable challenge. An efficient and accurate numerical simulation of the Boltzmann equation is thus highly desirable. In this article, the linearized Boltzmann Bhatnagar-Gross-Krook equation is used to develop a hierarchy of thermal lattice Boltzmann (LB) models based on half-space Gaussian-Hermite (GH) quadrature ranging from low to high algebraic precision, using double distribution functions. Simplified versions of the LB models in the continuum limit are also derived, and are shown to be consistent with existing thermal LB models for noncontinuum heat transfer reported in the literature. Accuracy of the proposed LB hierarchy is assessed by simulating thermal Couette flows for a wide range of Knudsen numbers. Effects of the underlying quadrature schemes (half-space GH vs full-space GH) and continuum-limit simplifications on computational accuracy are also elaborated. The numerical findings in this article provide direct evidence of improved computational capability of the proposed LB models for modeling noncontinuum flows and heat transfer at small length scales.

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

USGS Publications Warehouse

Michael Sukop,; Cunningham, Kevin J.

2014-01-01

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.

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

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann Equation On a 2D Rectangular Grid

NASA Technical Reports Server (NTRS)

Bouzidi, MHamed; DHumieres, Dominique; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.

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

PubMed

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.

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

NASA Astrophysics Data System (ADS)

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).

Simulation of mixed convection in a horizontal channel heated from below by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Sahraoui, Nassim M.; Houat, Samir; Saidi, Nawal

2017-05-01

We perform a contribution with a simulation study of the mixed convection in horizontal channel heated from below. The lattice Boltzmann method (LBM) is used with the Boussinesq approximation to solve the coupled phenomenon that governs the systems thermo-hydrodynamics. The double populations thermal lattice Boltzmann model (TLBM) is used with the D2Q5 for the thermal field and D2Q9 model for the dynamic field. A comparison of the results of the averaged Nusselt number obtained by the TLBM with other references is presented for an area stretching. The streamlines, the vortices, the isotherms, the velocity profiles and other parameters of the study, are presented at a certain time tT which is chosen arbitrarily. The results presented here are in good agreement with those reported in the scientific literature which gives us high expectations about the reliability of the TLBM to simulate this kind of physical phenomena. Contribution to the topical issue "Materials for Energy harvesting, conversion and storage II (ICOME 2016)", edited by Jean-Michel Nunzi, Rachid Bennacer and Mohammed El Ganaoui

Droplet flow along the wall of rectangular channel with gradient of wettability

NASA Astrophysics Data System (ADS)

Kupershtokh, A. L.

2018-03-01

The lattice Boltzmann equations (LBE) method (LBM) is applicable for simulating the multiphysics problems of fluid flows with free boundaries, taking into account the viscosity, surface tension, evaporation and wetting degree of a solid surface. Modeling of the nonstationary motion of a drop of liquid along a solid surface with a variable level of wettability is carried out. For the computer simulation of such a problem, the three-dimensional lattice Boltzmann equations method D3Q19 is used. The LBE method allows us to parallelize the calculations on multiprocessor graphics accelerators using the CUDA programming technology.

Fluid-structure interaction with the entropic lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Dorschner, B.; Chikatamarla, S. S.; Karlin, I. V.

2018-02-01

We propose a fluid-structure interaction (FSI) scheme using the entropic multi-relaxation time lattice Boltzmann (KBC) model for the fluid domain in combination with a nonlinear finite element solver for the structural part. We show the validity of the proposed scheme for various challenging setups by comparison to literature data. Beyond validation, we extend the KBC model to multiphase flows and couple it with a finite element method (FEM) solver. Robustness and viability of the entropic multi-relaxation time model for complex FSI applications is shown by simulations of droplet impact on elastic superhydrophobic surfaces.

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

NASA Astrophysics Data System (ADS)

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.

Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

NASA Astrophysics Data System (ADS)

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 in parabolic flows were in qualitative agreement with some experimental and numerical results. The Fahraeus and the Fahraeus-Lindqvist effects were reproduced. The proposed LBM model provides a flexible numerical platform consisting of various modules which could be used separately or in combination for the study of a variety of colloids and biological suspensions flow deformation problems.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fakhari, Abbas, E-mail: afakhari@nd.edu; Geier, Martin; Lee, Taehun

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 fastermore » 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 typical chaotic structure in the flow field is observed at a Reynolds number of 10000, which indicates that the proposed model is a promising tool for direct numerical simulation of two-phase flows.« less

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 themore » 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.« less

Discrete effect on the halfway bounce-back boundary condition of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations.

PubMed

Cui, Shuqi; Hong, Ning; Shi, Baochang; Chai, Zhenhua

2016-04-01

In this paper, we will focus on the multiple-relaxation-time (MRT) lattice Boltzmann model for two-dimensional convection-diffusion equations (CDEs), and analyze the discrete effect on the halfway bounce-back (HBB) boundary condition (or sometimes called bounce-back boundary condition) of the MRT model where three different discrete velocity models are considered. We first present a theoretical analysis on the discrete effect of the HBB boundary condition for the simple problems with a parabolic distribution in the x or y direction, and a numerical slip proportional to the second-order of lattice spacing is observed at the boundary, which means that the MRT model has a second-order convergence rate in space. The theoretical analysis also shows that the numerical slip can be eliminated in the MRT model through tuning the free relaxation parameter corresponding to the second-order moment, while it cannot be removed in the single-relaxation-time model or the Bhatnagar-Gross-Krook model unless the relaxation parameter related to the diffusion coefficient is set to be a special value. We then perform some simulations to confirm our theoretical results, and find that the numerical results are consistent with our theoretical analysis. Finally, we would also like to point out the present analysis can be extended to other boundary conditions of lattice Boltzmann models for CDEs.

Lattice Boltzmann model capable of mesoscopic vorticity computation

NASA Astrophysics Data System (ADS)

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.

Topology optimization of unsteady flow problems using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Nørgaard, Sebastian; Sigmund, Ole; Lazarov, Boyan

2016-02-01

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. The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves.

Lattice Boltzmann simulations of liquid crystal particulate flow in a channel with finite anchoring boundary conditions

NASA Astrophysics Data System (ADS)

Zhang, Rui; Roberts, Tyler; de Pablo, Juan; dePablo Team

2014-11-01

Liquid crystals (LC) posses anisotropic viscoelastic properties, and, as such, LC flow can be incredibly complicated. Here we employ a hybrid lattice Boltzmann method (pioneered by Deniston, Yeomans and Cates) to systematically study the hydrodynamics of nematic liquid crystals (LCs) with and without solid particles. This method evolves the velocity field through lattice Boltzmann and the LC-order parameter via a finite-difference solver of the Beris-Edwards equation. The evolution equation of the boundary points with finite anchoring is obtained through Poisson bracket formulation. Our method has been validated by matching the Ericksen-Leslie theory. We demonstrate two applications in the flow alignment regime. We first investigate a hybrid channel flow in which the top and bottom walls have different anchoring directions. By measuring the apparent shear viscosity in terms of Couette flow, we achieve a viscosity inhomogeneous system which may be applicable to nano particle processing. In the other example, we introduce a homeotropic spherical particle to the channel, and focus on the deformations of the defect ring due to anchorings and flow. The results are then compared to the molecular dynamics simulations of a colloid particle in an LC modeled by a Gay-Berne potential.

Cascaded lattice Boltzmann method with improved forcing scheme for large-density-ratio multiphase flow at high Reynolds and Weber numbers.

PubMed

Lycett-Brown, Daniel; Luo, Kai H

2016-11-01

A recently developed forcing scheme has allowed the pseudopotential multiphase lattice Boltzmann method to correctly reproduce coexistence curves, while expanding its range to lower surface tensions and arbitrarily high density ratios [Lycett-Brown and Luo, Phys. Rev. E 91, 023305 (2015)PLEEE81539-375510.1103/PhysRevE.91.023305]. Here, a third-order Chapman-Enskog analysis is used to extend this result from the single-relaxation-time collision operator, to a multiple-relaxation-time cascaded collision operator, whose additional relaxation rates allow a significant increase in stability. Numerical results confirm that the proposed scheme enables almost independent control of density ratio, surface tension, interface width, viscosity, and the additional relaxation rates of the cascaded collision operator. This allows simulation of large density ratio flows at simultaneously high Reynolds and Weber numbers, which is demonstrated through binary collisions of water droplets in air (with density ratio up to 1000, Reynolds number 6200 and Weber number 440). This model represents a significant improvement in multiphase flow simulation by the pseudopotential lattice Boltzmann method in which real-world parameters are finally achievable.

Modeling the Sedimentation of Red Blood Cells in Flow under Strong External Magnetic Body Force using a Lattice Boltzmann Fictitious Domain Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Xing; Lin, Guang

To model the sedimentation of the red blood cell (RBC) in a square duct and a circular pipe, the recently developed technique derived from the lattice Boltzmann method and the distributed Lagrange multiplier/fictitious domain method (LBM-DLM/FD) is extended to employ the mesoscopic network model for simulations of the sedimentation of the RBC in flow. The flow is simulated by the lattice Boltzmann method with a strong magnetic body force, while the network model is used for modeling RBC deformation. The fluid-RBC interactions are enforced by the Lagrange multiplier. The sedimentation of the RBC in a square duct and a circularmore » pipe is simulated, revealing the capacity of the current method for modeling the sedimentation of RBC in various flows. Numerical results illustrate that that the terminal setting velocity increases with the increment of the exerted body force. The deformation of the RBC has significant effect on the terminal setting velocity due to the change of the frontal area. The larger the exerted force is, the smaller the frontal area and the larger deformation of the RBC are.« less

Numerical investigation of the pseudopotential lattice Boltzmann modeling of liquid-vapor for multi-phase flows

NASA Astrophysics Data System (ADS)

Nemati, Maedeh; Shateri Najaf Abady, Ali Reza; Toghraie, Davood; Karimipour, Arash

2018-01-01

The incorporation of different equations of state into single-component multiphase lattice Boltzmann model is considered in this paper. The original pseudopotential model is first detailed, and several cubic equations of state, the Redlich-Kwong, Redlich-Kwong-Soave, and Peng-Robinson are then incorporated into the lattice Boltzmann model. A comparison of the numerical simulation achievements on the basis of density ratios and spurious currents is used for presentation of the details of phase separation in these non-ideal single-component systems. The paper demonstrates that the scheme for the inter-particle interaction force term as well as the force term incorporation method matters to achieve more accurate and stable results. The velocity shifting method is demonstrated as the force term incorporation method, among many, with accuracy and stability results. Kupershtokh scheme also makes it possible to achieve large density ratio (up to 104) and to reproduce the coexistence curve with high accuracy. Significant reduction of the spurious currents at vapor-liquid interface is another observation. High-density ratio and spurious current reduction resulted from the Redlich-Kwong-Soave and Peng-Robinson EOSs, in higher accordance with the Maxwell construction results.

Straight velocity boundaries in the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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 1,000 US dollars. The release of NVIDIA's CUDA architecture which includes both hardware and programming environment in 2007 makes GPU computing attractive. Due to its highly parallel nature, lattice Boltzmann method is successfully ported into GPU with a performance benefit during the recent years. In the current work, LBM CUDA code is developed for different fluid flow and heat transfer problems. In this dissertation, lattice Boltzmann method and immersed boundary method are used to study natural convection in an enclosure with an array of conduting obstacles, double-diffusive convection in a vertical cavity with Soret and Dufour effects, PCM melting process in a latent heat thermal energy storage system with internal fins, mixed convection in a lid-driven cavity with a sinusoidal cylinder, and AC electrothermal pumping in microfluidic systems on a CUDA computational platform. It is demonstrated that LBM is an efficient method to simulate complex heat transfer problems using GPU on CUDA.

Quantitative kinetic theory of active matter

NASA Astrophysics Data System (ADS)

Ihle, Thomas; Chou, Yen-Liang

2014-03-01

Models of self-driven agents similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] are studied by means of kinetic theory. In these models, particles try to align their travel directions with the average direction of their neighbours. At strong alignment a globally ordered state of collective motion forms. An Enskog-like kinetic theory is derived from the exact Chapman-Kolmogorov equation in phase space using Boltzmann's mean-field approximation of molecular chaos. The kinetic equation is solved numerically by a nonlocal Lattice-Boltzmann-like algorithm. Steep soliton-like waves are observed that lead to an abrupt jump of the global order parameter if the noise level is changed. The shape of the wave is shown to follow a novel scaling law and to quantitatively agree within 3 % with agent-based simulations at large particle speeds. This provides a mean-field mechanism to change the second-order character of the flocking transition to first order. Diagrammatic techniques are used to investigate small particle speeds, where the mean-field assumption of Molecular Chaos is invalid and where correlation effects need to be included.

Equation-free multiscale computation: algorithms and applications.

PubMed

Kevrekidis, Ioannis G; Samaey, Giovanni

2009-01-01

In traditional physicochemical modeling, one derives evolution equations at the (macroscopic, coarse) scale of interest; these are used to perform a variety of tasks (simulation, bifurcation analysis, optimization) using an arsenal of analytical and numerical techniques. For many complex systems, however, although one observes evolution at a macroscopic scale of interest, accurate models are only given at a more detailed (fine-scale, microscopic) level of description (e.g., lattice Boltzmann, kinetic Monte Carlo, molecular dynamics). Here, we review a framework for computer-aided multiscale analysis, which enables macroscopic computational tasks (over extended spatiotemporal scales) using only appropriately initialized microscopic simulation on short time and length scales. The methodology bypasses the derivation of macroscopic evolution equations when these equations conceptually exist but are not available in closed form-hence the term equation-free. We selectively discuss basic algorithms and underlying principles and illustrate the approach through representative applications. We also discuss potential difficulties and outline areas for future research.

Water Management In PEM Fuel Cell -“ A Lattice-Boltzmann Modeling Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Shiladitya; Cole, James Vernon; Jain, Kunal

2009-06-01

In Proton Exchange Membrane Fuel Cells (PEMFCs), water management and the effective transport of water through the gas-diffusion-layer (GDL) are key issues for improved performance at high power density and for durability during freeze-thaw cycles. The diffusion layer is a thin (~150-350{micro}m), porous material typically composed of a web of carbon fibers and particles, and is usually coated with hydrophobic Teflon to remove the excess water through capillary action. In-situ diagnostics of water movement and gas-reactant transport through this thin opaque substrate is challenging. Numerical analyses are typically based on simplified assumptions, such as Darcy's Law and Leverett functions formore » the capillary pressure. The objective of this work is to develop a high fidelity CFD modeling and analysis tool to capture the details of multiphase transport through the porous GDL. The tool can be utilized to evaluate GDL material design concepts and optimize systems based on the interactions between cell design, materials, and operating conditions. The flow modeling is based on the Lattice Boltzmann Method (LBM). LBM is a powerful modeling tool to simulate multiphase flows. Its strength is in its kinetic theory based foundation, which provides a fundamental basis for incorporating intermolecular forces that lead to liquid-gas phase separation and capillary effects without resorting to expensive or ad-hoc interface reconstruction schemes. At the heart of the solution algorithm is a discrete form of the well-known Boltzmann Transport Equation (BTE) for molecular distribution, tailored to recover the continuum Navier-Stokes flow. The solution advances by a streaming and collision type algorithm, mimicking actual molecular physics, which makes it suitable for porous media involving complex boundaries. We developed a numerical scheme to reconstruct various porous GDL microstructures including Teflon loading. Single and multiphase LBM models are implemented to compute permeability. Predicted values are in good agreement with measured data. The present modeling approach resolves the GDL microstructures and captures the influence of fiber orientation on permeability and the influence of Teflon loading on the development of preferential flow paths through the GDL. These observations can potentially guide the development of novel GDL materials designed for efficient removal of water.« less

Exploring cluster Monte Carlo updates with Boltzmann machines

NASA Astrophysics Data System (ADS)

Wang, Lei

2017-11-01

Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.

Generalized hydrodynamic transport in lattice-gas automata

NASA Technical Reports Server (NTRS)

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.

Large-scale parallel lattice Boltzmann-cellular automaton model of two-dimensional dendritic growth

NASA Astrophysics Data System (ADS)

Jelinek, Bohumir; Eshraghi, Mohsen; Felicelli, Sergio; Peters, John F.

2014-03-01

An extremely scalable lattice Boltzmann (LB)-cellular automaton (CA) model for simulations of two-dimensional (2D) dendritic solidification under forced convection is presented. The model incorporates effects of phase change, solute diffusion, melt convection, and heat transport. The LB model represents the diffusion, convection, and heat transfer phenomena. The dendrite growth is driven by a difference between actual and equilibrium liquid composition at the solid-liquid interface. The CA technique is deployed to track the new interface cells. The computer program was parallelized using the Message Passing Interface (MPI) technique. Parallel scaling of the algorithm was studied and major scalability bottlenecks were identified. Efficiency loss attributable to the high memory bandwidth requirement of the algorithm was observed when using multiple cores per processor. Parallel writing of the output variables of interest was implemented in the binary Hierarchical Data Format 5 (HDF5) to improve the output performance, and to simplify visualization. Calculations were carried out in single precision arithmetic without significant loss in accuracy, resulting in 50% reduction of memory and computational time requirements. The presented solidification model shows a very good scalability up to centimeter size domains, including more than ten million of dendrites. Catalogue identifier: AEQZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 29,767 No. of bytes in distributed program, including test data, etc.: 3131,367 Distribution format: tar.gz Programming language: Fortran 90. Computer: Linux PC and clusters. Operating system: Linux. Has the code been vectorized or parallelized?: Yes. Program is parallelized using MPI. Number of processors used: 1-50,000 RAM: Memory requirements depend on the grid size Classification: 6.5, 7.7. External routines: MPI (http://www.mcs.anl.gov/research/projects/mpi/), HDF5 (http://www.hdfgroup.org/HDF5/) Nature of problem: Dendritic growth in undercooled Al-3 wt% Cu alloy melt under forced convection. Solution method: The lattice Boltzmann model solves the diffusion, convection, and heat transfer phenomena. The cellular automaton technique is deployed to track the solid/liquid interface. Restrictions: Heat transfer is calculated uncoupled from the fluid flow. Thermal diffusivity is constant. Unusual features: Novel technique, utilizing periodic duplication of a pre-grown “incubation” domain, is applied for the scaleup test. Running time: Running time varies from minutes to days depending on the domain size and number of computational cores.

Simulation of plume dynamics by the Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

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.

Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation.

PubMed

Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji

2014-07-01

A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.

Effect of Rolling Massage on the Vortex Flow in Blood Vessels with Lattice Boltzmann Simulation

NASA Astrophysics Data System (ADS)

Yi, Hou Hui

The rolling massage manipulation is a classic Chinese Medical Massage, which is a nature therapy in eliminating many diseases. Here, the effect of the rolling massage on the cavity flows in blood vessel under the rolling manipulation is studied by the lattice Boltzmann simulation. The simulation results show that the vortex flows are fully disturbed by the rolling massage. The flow behavior depends on the rolling velocity and the rolling depth. Rolling massage has a better effect on the flows in the cavity than that of the flows in a planar blood vessel. The result is helpful to understand the mechanism of the massage and develop the rolling techniques.

Simulating condensation on microstructured surfaces using Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

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.

Consistent forcing scheme in the cascaded lattice Boltzmann method

NASA Astrophysics Data System (ADS)

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.

Fast Laplace solver approach to pore-scale permeability

NASA Astrophysics Data System (ADS)

Arns, C. H.; Adler, P. M.

2018-02-01

We introduce a powerful and easily implemented method to calculate the permeability of porous media at the pore scale using an approximation based on the Poiseulle equation to calculate permeability to fluid flow with a Laplace solver. The method consists of calculating the Euclidean distance map of the fluid phase to assign local conductivities and lends itself naturally to the treatment of multiscale problems. We compare with analytical solutions as well as experimental measurements and lattice Boltzmann calculations of permeability for Fontainebleau sandstone. The solver is significantly more stable than the lattice Boltzmann approach, uses less memory, and is significantly faster. Permeabilities are in excellent agreement over a wide range of porosities.

Mesoscopic modeling of multi-physicochemical transport phenomena in porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kang, Qinjin; Wang, Moran; Mukherjee, Partha P

2009-01-01

We present our recent progress on mesoscopic modeling of multi-physicochemical transport phenomena in porous media based on the lattice Boltzmann method. Simulation examples include injection of CO{sub 2} saturated brine into a limestone rock, two-phase behavior and flooding phenomena in polymer electrolyte fuel cells, and electroosmosis in homogeneously charged porous media. It is shown that the lattice Boltzmann method can account for multiple, coupled physicochemical processes in these systems and can shed some light on the underlying physics occuning at the fundamental scale. Therefore, it can be a potential powerful numerical tool to analyze multi-physicochemical processes in various energy, earth,more » and environmental systems.« less

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

PubMed

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.

Volumetric Lattice Boltzmann Simulation for Fluid dynamics and Turbulence in Practical Syringes

NASA Astrophysics Data System (ADS)

Lima, Everton; Deep, Debanjan; Yu, Huidan (Whitney)

2012-11-01

We conduct numerical experiments to study fluid dynamics and turbulence in syringes using volumetric lattice Boltzmann method (VLBM) that is developed for dealing with arbitrary moving boundaries. Several common used medical syringes are used to predict the efficiency and safety of syringes experiencing low flow infusion rates. It is found that smaller size syringes reach a steady flow rate much sooner than larger ones, which are in quantitative agreement with experimental results. The relation between the syringe size and its steady flow rate is revealed. At low flow rates, corner vortices are observed. We explore conditions that lead to turbulent flow aiming to aid safer syringe application in nursing practices.

Numerical simulation of three-component multiphase flows at high density and viscosity ratios using lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

Haghani Hassan Abadi, Reza; Fakhari, Abbas; Rahimian, Mohammad Hassan

2018-03-01

In this paper, we propose a multiphase lattice Boltzmann model for numerical simulation of ternary flows at high density and viscosity ratios free from spurious velocities. The proposed scheme, which is based on the phase-field modeling, employs the Cahn-Hilliard theory to track the interfaces among three different fluid components. Several benchmarks, such as the spreading of a liquid lens, binary droplets, and head-on collision of two droplets in binary- and ternary-fluid systems, are conducted to assess the reliability and accuracy of the model. The proposed model can successfully simulate both partial and total spreadings while reducing the parasitic currents to the machine precision.

Study on an antagonist differentiated heated lid driven-cavity enclosing a tube: lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Ma, Xiaoyan; Pellerin, Nicolas; Reggio, Marcelo; Bennacer, Rachid

2017-05-01

The method of lattice-Boltzmann multiple relaxation time (MRT) is commonly applied to study the conversion system consisting in a combination of forced convection and natural convection occurred in a cavity. Moving the top surface horizontally at a fixed speed, while two vertical walls are applied with constant different temperatures, assuming adiabatic case on both bottom and top walls. We consider a "non-cooperating" situation, where dynamics and buoyancy forces counterbalance. The cavity contains a circular cylinder placed at various positions. Boundary conditions for velocity and temperature have been applied to handle the non-Cartesian boundary of the cylinder. In lattice Boltzmann methods we adopt the double distribution model for calculating both the thermal and hydrodynamic fields. The D2Q5 and D2Q9 lattice are chosen to perform the simulations for a wide range of Reynolds and Rayleigh numbers. By calculating the average Nusselt number, we also investigated the influence of different obstacle positions on characteristics of flow and heat transfer. The results show the influence of the obstacle position on the dimensionless numbers, so as to effect the heat transfer behaviors inside the cavity. It is also indicates that the governing parameters are also related to driven power for the upper surface sliding. Contribution to the topical issue "Materials for Energy harvesting, conversion and storage II (ICOME 2016)", edited by Jean-Michel Nunzi, Rachid Bennacer and Mohammed El Ganaoui

Mass-conserved volumetric lattice Boltzmann method for complex flows with willfully moving boundaries.

PubMed

Yu, Huidan; Chen, Xi; Wang, Zhiqiang; Deep, Debanjan; Lima, Everton; Zhao, Ye; Teague, Shawn D

2014-06-01

In this paper, we develop a mass-conserved volumetric lattice Boltzmann method (MCVLBM) for numerically solving fluid dynamics with willfully moving arbitrary boundaries. In MCVLBM, fluid particles are uniformly distributed in lattice cells and the lattice Boltzmann equations deal with the time evolution of the particle distribution function. By introducing a volumetric parameter P(x,y,z,t) defined as the occupation of solid volume in the cell, we distinguish three types of lattice cells in the simulation domain: solid cell (pure solid occupation, P=1), fluid cell (pure fluid occupation, P=0), and boundary cell (partial solid and partial fluid, 0

Large-Eddy/Lattice Boltzmann Simulations of Micro-blowing Strategies for Subsonic and Supersonic Drag Control

NASA Technical Reports Server (NTRS)

Menon, Suresh

2003-01-01

This report summarizes the progress made in the first 8 to 9 months of this research. The Lattice Boltzmann Equation (LBE) methodology for Large-eddy Simulations (LES) of microblowing has been validated using a jet-in-crossflow test configuration. In this study, the flow intake is also simulated to allow the interaction to occur naturally. The Lattice Boltzmann Equation Large-eddy Simulations (LBELES) approach is capable of capturing not only the flow features associated with the flow, such as hairpin vortices and recirculation behind the jet, but also is able to show better agreement with experiments when compared to previous RANS predictions. The LBELES is shown to be computationally very efficient and therefore, a viable method for simulating the injection process. Two strategies have been developed to simulate multi-hole injection process as in the experiment. In order to allow natural interaction between the injected fluid and the primary stream, the flow intakes for all the holes have to be simulated. The LBE method is computationally efficient but is still 3D in nature and therefore, there may be some computational penalty. In order to study a large number or holes, a new 1D subgrid model has been developed that will simulate a reduced form of the Navier-Stokes equation in these holes.

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

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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.

Crystallographic Lattice Boltzmann Method

PubMed Central

Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh

2016-01-01

Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098

On the dispute between Boltzmann and Gibbs entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buonsante, Pierfrancesco; Franzosi, Roberto, E-mail: roberto.franzosi@ino.it; Smerzi, Augusto

2016-12-15

The validity of the concept of negative temperature has been recently challenged by arguing that the Boltzmann entropy (that allows negative temperatures) is inconsistent from a mathematical and statistical point of view, whereas the Gibbs entropy (that does not admit negative temperatures) provides the correct definition for the microcanonical entropy. Here we prove that the Boltzmann entropy is thermodynamically and mathematically consistent. Analytical results on two systems supporting negative temperatures illustrate the scenario we propose. In addition we numerically study a lattice system to show that negative temperature equilibrium states are accessible and obey standard statistical mechanics prediction.

Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels

NASA Astrophysics Data System (ADS)

Fang, Haiping; Wang, Zuowei; Lin, Zhifang; Liu, Muren

2002-05-01

A lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries. The mass conservation for the boundary condition is tested in detail. The viscous flow in elastic vessels is simulated with a pressure-radius relationship similar to that of the pulmonary blood vessels. The numerical results for steady flow agree with the analytical prediction to very high accuracy, and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally. The model is expected to find many applications for studying blood flows in large distensible arteries, especially in those suffering from atherosclerosis, stenosis, aneurysm, etc.

LUMA: A many-core, Fluid-Structure Interaction solver based on the Lattice-Boltzmann Method

NASA Astrophysics Data System (ADS)

Harwood, Adrian R. G.; O'Connor, Joseph; Sanchez Muñoz, Jonathan; Camps Santasmasas, Marta; Revell, Alistair J.

2018-01-01

The Lattice-Boltzmann Method at the University of Manchester (LUMA) project was commissioned to build a collaborative research environment in which researchers of all abilities can study fluid-structure interaction (FSI) problems in engineering applications from aerodynamics to medicine. It is built on the principles of accessibility, simplicity and flexibility. The LUMA software at the core of the project is a capable FSI solver with turbulence modelling and many-core scalability as well as a wealth of input/output and pre- and post-processing facilities. The software has been validated and several major releases benchmarked on supercomputing facilities internationally. The software architecture is modular and arranged logically using a minimal amount of object-orientation to maintain a simple and accessible software.

Role of Correlations in the Collective Behavior of Microswimmer Suspensions

NASA Astrophysics Data System (ADS)

Stenhammar, Joakim; Nardini, Cesare; Nash, Rupert W.; Marenduzzo, Davide; Morozov, Alexander

2017-07-01

In this Letter, we study the collective behavior of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedentedly large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is nonperturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its nontrivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.

Ternary Free-Energy Entropic Lattice Boltzmann Model with a High Density Ratio

NASA Astrophysics Data System (ADS)

Wöhrwag, M.; Semprebon, C.; Mazloomi Moqaddam, A.; Karlin, I.; Kusumaatmaja, H.

2018-06-01

A thermodynamically consistent free energy model for fluid flows comprised of one gas and two liquid components is presented and implemented using the entropic lattice Boltzmann scheme. The model allows a high density ratio, up to the order of O (103), between the liquid and gas phases, and a broad range of surface tension ratios, covering partial wetting states where Neumann triangles are formed, and full wetting states where complete encapsulation of one of the fluid components is observed. We further demonstrate that we can capture the bouncing, adhesive, and insertive regimes for the binary collisions between immiscible droplets suspended in air. Our approach opens up a vast range of multiphase flow applications involving one gas and several liquid components.

Navier-Stokes Dynamics by a Discrete Boltzmann Model

NASA Technical Reports Server (NTRS)

Rubinstein, Robet

2010-01-01

This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

Etude d'un modele de Boltzmann sur reseau pour la simulation assistee par ordinateur des fluides a plusieurs phases immiscibles

NASA Astrophysics Data System (ADS)

Leclaire, Sebastien

The computer assisted simulation of the dynamics of fluid flow has been a highly rewarding topic of research for several decades now, in terms of the number of scientific problems that have been solved as a result, both in the academic world and in industry. In the fluid dynamics field, simulating multiphase immiscible fluid flow remains a challenge, because of the complexity of the interactions at the flow phase interfaces. Various numerical methods are available to study these phenomena, and, the lattice Boltzmann method has been shown in recent years to be well adapted to solving this type of complex flow. In this thesis, a lattice Boltzmann model for the simulation of two-phase immiscible flows is studied. The main objective of the thesis is to develop this promising method further, with a view to enhancing its validity. To achieve this objective, the research is divided into five distinct themes. The first two focus on correcting some of the deficiencies of the original model. The third generalizes the model to support the simulation of N-phase immiscible fluid flows. The fourth is aimed at modifying the model itself, to enable the simulation of immiscible fluid flows in which the density of the phases varies. With the lattice Boltzmann class of models studied here, this density variation has been inadequately modeled, and, after 20 years, the issue still has not been resolved. The fifth, which complements this thesis, is connected with the lattice Boltzmann method, in that it generalizes the theory of 2D and 3D isotropic gradients for a high order of spatial precision. These themes have each been the subject of a scientific article, as listed in the appendix to this thesis, and together they constitute a synthesis that explains the links between the articles, as well as their scientific contributions, and satisfy the main objective of this research. Globally, a number of qualitative and quantitative test cases based on the theory of multiphase fluid flows have highlighted issues plaguing the simulation model. These test cases have resulted in various modifications to the model, which have reduced or eliminated some numerical artifacts that were problematic. They also allowed us to validate the extensions that were applied to the original model.

Random Walk Particle Tracking For Multiphase Heat Transfer

NASA Astrophysics Data System (ADS)

Lattanzi, Aaron; Yin, Xiaolong; Hrenya, Christine

2017-11-01

As computing capabilities have advanced, direct numerical simulation (DNS) has become a highly effective tool for quantitatively predicting the heat transfer within multiphase flows. Here we utilize a hybrid DNS framework that couples the lattice Boltzmann method (LBM) to the random walk particle tracking (RWPT) algorithm. The main challenge of such a hybrid is that discontinuous fields pose a significant challenge to the RWPT framework and special attention must be given to the handling of interfaces. We derive a method for addressing discontinuities in the diffusivity field, arising at the interface between two phases. Analytical means are utilized to develop an interfacial tracer balance and modify the RWPT algorithm. By expanding the modulus of the stochastic (diffusive) step and only allowing a subset of the tracers within the high diffusivity medium to undergo a diffusive step, the correct equilibrium state can be restored (globally homogeneous tracer distribution). The new RWPT algorithm is implemented within the SUSP3D code and verified against a variety of systems: effective diffusivity of a static gas-solids mixture, hot sphere in unbounded diffusion, cooling sphere in unbounded diffusion, and uniform flow past a hot sphere.

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

PubMed

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.

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

NASA Astrophysics Data System (ADS)

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 evolution of the system are reported.

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

NASA Astrophysics Data System (ADS)

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.

Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

PubMed

Garcia, Alejandro L; Wagner, Wolfgang

2003-11-01

In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

Modeling adsorption with lattice Boltzmann equation

PubMed Central

Guo, Long; Xiao, Lizhi; Shan, Xiaowen; Zhang, Xiaoling

2016-01-01

The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied. PMID:27256325

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

NASA Astrophysics Data System (ADS)

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 Method for 3-D Flows with Curved Boundary

NASA Technical Reports Server (NTRS)

Mei, Renwei; Shyy, Wei; Yu, Dazhi; Luo, Li-Shi

2002-01-01

In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamics applications of the lattice, Boltzmann equation (LBE): (1) Computational stability and accuracy of different lattice Boltzmann models and (2) the treatment of the boundary conditions on curved solid boundaries and their 3-D implementations. Three athermal 3-D LBE models (D3QI5, D3Ql9, and D3Q27) are studied and compared in terms of efficiency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hanel and Met et al. in 2-D is extended to and implemented for 3-D. The convergence, stability, and computational efficiency of the 3-D LBE models with the boundary treatment for curved boundaries were tested in simulations of four 3-D flows: (1) Fully developed flows in a square duct, (2) flow in a 3-D lid-driven cavity, (3) fully developed flows in a circular pipe, and (4) a uniform flow over a sphere. We found that while the fifteen-velocity 3-D (D3Ql5) model is more prone to numerical instability and the D3Q27 is more computationally intensive, the 63Q19 model provides a balance between computational reliability and efficiency. Through numerical simulations, we demonstrated that the boundary treatment for 3-D arbitrary curved geometry has second-order accuracy and possesses satisfactory stability characteristics.

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

PubMed Central

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

Deformation of a Capsule in a Power-Law Shear Flow

PubMed Central

2016-01-01

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values. PMID:27840656

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Li; He, Ya-Ling; Kang, Qinjun

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 whichmore » 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.« less

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

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann methods for global linear instability analysis

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann simulations of flapping wings: The flock effect and the lateral wind effect

NASA Astrophysics Data System (ADS)

de Rosis, Alessandro

2014-02-01

In this paper, numerical analysis aiming at simulating biological organisms immersed in a fluid are carried out. The fluid domain is modeled through the lattice Boltzmann (LB) method, while the immersed boundary method is used to account for the position of the organisms idealized as rigid bodies. The time discontinuous Galerkin method is employed to compute body motion. An explicit coupling strategy to combine the adopted numerical methods is proposed. The vertical take-off of a couple of butterflies is numerically simulated in different scenarios, showing the mutual interaction that a butterfly exerts on the other one. Moreover, the effect of lateral wind is investigated. A critical threshold value of the lateral wind is defined, thus corresponding to an increasing arduous take-off.

An Absorbing Boundary Condition for the Lattice Boltzmann Method Based on the Perfectly Matched Layer

PubMed Central

Najafi-Yazdi, A.; Mongeau, L.

2012-01-01

The Lattice Boltzmann Method (LBM) is a well established computational tool for fluid flow simulations. This method has been recently utilized for low Mach number computational aeroacoustics. Robust and nonreflective boundary conditions, similar to those used in Navier-Stokes solvers, are needed for LBM-based aeroacoustics simulations. The goal of the present study was to develop an absorbing boundary condition based on the perfectly matched layer (PML) concept for LBM. The derivation of formulations for both two and three dimensional problems are presented. The macroscopic behavior of the new formulation is discussed. The new formulation was tested using benchmark acoustic problems. The perfectly matched layer concept appears to be very well suited for LBM, and yielded very low acoustic reflection factor. PMID:23526050

Lattice Boltzmann Simulation of Blood Flow in Blood Vessels with the Rolling Massage

NASA Astrophysics Data System (ADS)

Yi, Hou-Hui; Xu, Shi-Xiong; Qian, Yue-Hong; Fang, Hai-Ping

2005-12-01

The rolling massage manipulation is a classic Chinese massage, which is expected to improve the circulation by pushing, pulling and kneading of the muscle. A model for the rolling massage manipulation is proposed and the lattice Boltzmann method is applied to study the blood flow in the blood vessels. The simulation results show that the blood flux is considerably modified by the rolling massage and the explicit value depends on the rolling frequency, the rolling depth, and the diameter of the vessel. The smaller the diameter of the blood vessel, the larger the enhancement of the blood flux by the rolling massage. The model, together with the simulation results, is expected to be helpful to understand the mechanism and further development of rolling massage techniques.

A lattice Boltzmann model for the Burgers-Fisher equation.

PubMed

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.

Applicability of the lattice Boltzmann method to determine the ohmic resistance in equivalent resistor connections

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann Simulation of Electroosmotic Micromixing by Heterogeneous Surface Charge

NASA Astrophysics Data System (ADS)

Tang, G. H.; Wang, F. F.; Tao, W. Q.

Microelectroosmotic flow is usually restricted to low Reynolds number regime, and mixing in these microfluidic systems becomes problematic due to the negligible inertial effects. To gain an improved understanding of mixing enhancement in microchannels patterned with heterogeneous surface charge, the lattice Boltzmann method has been employed to obtain the electric potential distribution in the electrolyte, the flow field, and the species concentration distribution, respectively. The simulation results show that heterogeneous surfaces can significantly disturb the streamlines leading to apparently substantial improvements in mixing. However, the introduction of such a feature can reduce the mass flow rate in the channel. The reduction in flow rate effectively prolongs the available mixing time when the flow passes through the channel and the observed mixing enhancement by heterogeneous surfaces partly results from longer mixing time.

Large-scale lattice-Boltzmann simulations over lambda networks

NASA Astrophysics Data System (ADS)

Saksena, R.; Coveney, P. V.; Pinning, R.; Booth, S.

Amphiphilic molecules are of immense industrial importance, mainly due to their tendency to align at interfaces in a solution of immiscible species, e.g., oil and water, thereby reducing surface tension. Depending on the concentration of amphiphiles in the solution, they may assemble into a variety of morphologies, such as lamellae, micelles, sponge and cubic bicontinuous structures exhibiting non-trivial rheological properties. The main objective of this work is to study the rheological properties of very large, defect-containing gyroidal systems (of up to 10243 lattice sites) using the lattice-Boltzmann method. Memory requirements for the simulation of such large lattices exceed that available to us on most supercomputers and so we use MPICH-G2/MPIg to investigate geographically distributed domain decomposition simulations across HPCx in the UK and TeraGrid in the US. Use of MPICH-G2/MPIg requires the port-forwarder to work with the grid middleware on HPCx. Data from the simulations is streamed to a high performance visualisation resource at UCL (London) for rendering and visualisation. Lighting the Blue Touchpaper for UK e-Science - Closing Conference of ESLEA Project March 26-28 2007 The George Hotel, Edinburgh, UK

Corner-transport-upwind lattice Boltzmann model for bubble cavitation

NASA Astrophysics Data System (ADS)

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 .

Effective Simulation Strategy of Multiscale Flows using a Lattice Boltzmann model with a Stretched Lattice

NASA Astrophysics Data System (ADS)

Yahia, Eman; Premnath, Kannan

2017-11-01

Resolving multiscale flow physics (e.g. for boundary layer or mixing layer flows) effectively generally requires the use of different grid resolutions in different coordinate directions. Here, we present a new formulation of a multiple relaxation time (MRT)-lattice Boltzmann (LB) model for anisotropic meshes. It is based on a simpler and more stable non-orthogonal moment basis while the use of MRT introduces additional flexibility, and the model maintains a stream-collide procedure; its second order moment equilibria are augmented with additional velocity gradient terms dependent on grid aspect ratio that fully restores the required isotropy of the transport coefficients of the normal and shear stresses. Furthermore, by introducing additional cubic velocity corrections, it maintains Galilean invariance. The consistency of this stretched lattice based LB scheme with the Navier-Stokes equations is shown via a Chapman-Enskog expansion. Numerical study for a variety of benchmark flow problems demonstrate its ability for accurate and effective simulations at relatively high Reynolds numbers. The MRT-LB scheme is also shown to be more stable compared to prior LB models for rectangular grids, even for grid aspect ratios as small as 0.1 and for Reynolds numbers of 10000.

Numerical study of active control of mixing in electro-osmotic flows by temperature difference using lattice Boltzmann methods.

PubMed

Alizadeh, A; Wang, J K; Pooyan, S; Mirbozorgi, S A; Wang, M

2013-10-01

In this paper, the effect of temperature difference between inlet flow and walls on the electro-osmotic flow through a two-dimensional microchannel is investigated. The main objective is to study the effect of temperature variations on the distribution of ions and consequently internal electric potential field, electric body force, and velocity fields in an electro-osmotic flow. We assume constant temperature and zeta potential on walls and use the mean temperature of each cross section to characterize the Boltzmann ion distribution across the channel. Based on these assumptions, the multiphysical transports are still able to be described by the classical Poisson-Boltzmann model. In this work, the Navier-Stokes equation for fluid flow, the Poisson-Boltzmann equation for ion distribution, and the energy equation for heat transfer are solved by a couple lattice Boltzmann method. The modeling results indicate that the temperature difference between walls and the inlet solution may lead to two symmetrical vortices at the entrance region of the microchannel which is appropriate for mixing enhancements. The advantage of this phenomenon for active control of mixing in electro-osmotic flow is the manageability of the vortex scale without extra efforts. For instance, the effective domain of this pattern could broaden by the following modulations: decreasing the external electric potential field, decreasing the electric double layer thickness, or increasing the temperature difference between inlet flow and walls. This work may provide a novel strategy for design or optimization of microsystems. Copyright © 2013 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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.

Numerical simulation of a lattice polymer model at its integrable point

NASA Astrophysics Data System (ADS)

Bedini, A.; Owczarek, A. L.; Prellberg, T.

2013-07-01

We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Blöte and Nienhuis (1989 J. Phys. A: Math. Gen. 22 1415) and it describes polymers with some attraction, providing thus a model for the polymer collapse transition. At a particular set of Boltzmann weights the model is integrable and the exponents ν = 12/23 ≈ 0.522 and γ = 53/46 ≈ 1.152 have been computed via identification of the scaling dimensions xt = 1/12 and xh = -5/48. We directly investigate the polymer scaling exponents via Monte Carlo simulations using the pruned-enriched Rosenbluth method algorithm. By simulating this polymer model for walks up to length 4096 we find ν = 0.576(6) and γ = 1.045(5), which are clearly different from the predicted values. Our estimate for the exponent ν is compatible with the known θ-point value of 4/7 and in agreement with very recent numerical evaluation by Foster and Pinettes (2012 J. Phys. A: Math. Theor. 45 505003).

Detection of Cheating by Decimation Algorithm

NASA Astrophysics Data System (ADS)

Yamanaka, Shogo; Ohzeki, Masayuki; Decelle, Aurélien

2015-02-01

We expand the item response theory to study the case of "cheating students" for a set of exams, trying to detect them by applying a greedy algorithm of inference. This extended model is closely related to the Boltzmann machine learning. In this paper we aim to infer the correct biases and interactions of our model by considering a relatively small number of sets of training data. Nevertheless, the greedy algorithm that we employed in the present study exhibits good performance with a few number of training data. The key point is the sparseness of the interactions in our problem in the context of the Boltzmann machine learning: the existence of cheating students is expected to be very rare (possibly even in real world). We compare a standard approach to infer the sparse interactions in the Boltzmann machine learning to our greedy algorithm and we find the latter to be superior in several aspects.

An improved gray lattice Boltzmann model for simulating fluid flow in multi-scale porous media

NASA Astrophysics Data System (ADS)

Zhu, Jiujiang; Ma, Jingsheng

2013-06-01

A lattice Boltzmann (LB) model is proposed for simulating fluid flow in porous media by allowing the aggregates of finer-scale pores and solids to be treated as 'equivalent media'. This model employs a partially bouncing-back scheme to mimic the resistance of each aggregate, represented as a gray node in the model, to the fluid flow. Like several other lattice Boltzmann models that take the same approach, which are collectively referred to as gray lattice Boltzmann (GLB) models in this paper, it introduces an extra model parameter, ns, which represents a volume fraction of fluid particles to be bounced back by the solid phase rather than the volume fraction of the solid phase at each gray node. The proposed model is shown to conserve the mass even for heterogeneous media, while this model and that model of Walsh et al. (2009) [1], referred to the WBS model thereafter, are shown analytically to recover Darcy-Brinkman's equations for homogenous and isotropic porous media where the effective viscosity and the permeability are related to ns and the relaxation parameter of LB model. The key differences between these two models along with others are analyzed while their implications are highlighted. An attempt is made to rectify the misconception about the model parameter ns being the volume fraction of the solid phase. Both models are then numerically verified against the analytical solutions for a set of homogenous porous models and compared each other for another two sets of heterogeneous porous models of practical importance. It is shown that the proposed model allows true no-slip boundary conditions to be incorporated with a significant effect on reducing errors that would otherwise heavily skew flow fields near solid walls. The proposed model is shown to be numerically more stable than the WBS model at solid walls and interfaces between two porous media. The causes to the instability in the latter case are examined. The link between these two GLB models and a generalized Navier-Stokes model [2] for heterogeneous but isotropic porous media are explored qualitatively. A procedure for estimating model parameter ns is proposed.

Lattice Boltzmann simulations of liquid CO2 displacing water in a 2D heterogeneous micromodel at reservoir pressure conditions.

PubMed

Chen, Yu; Li, Yaofa; Valocchi, Albert J; Christensen, Kenneth T

2018-05-01

We employed the color-fluid lattice Boltzmann multiphase model to simulate liquid CO 2 displacing water documented in experiments in a 2D heterogeneous micromodel at reservoir pressure conditions. The main purpose is to investigate whether lattice Boltzmann simulation can reproduce the CO 2 invasion patterns observed in these experiments for a range of capillary numbers. Although the viscosity ratio used in the simulation matches the experimental conditions, the viscosity of the fluids in the simulation is higher than that of the actual fluids used in the experiments. Doing so is required to enhance numerical stability, and is a common strategy employed in the literature when using the lattice Boltzmann method to simulate CO 2 displacing water. The simulations reproduce qualitatively similar trends of changes in invasion patterns as the capillary number is increased. However, the development of secondary CO 2 pathways, a key feature of the invasion patterns in the simulations and experiments, is found to occur at a much higher capillary number in the simulations compared with the experiments. Additional numerical simulations were conducted to investigate the effect of the absolute value of viscosity on the invasion patterns while maintaining the viscosity ratio and capillary number fixed. These results indicate that the use of a high viscosity (which significantly reduces the inertial effect in the simulations) suppresses the development of secondary CO 2 pathways, leading to a different fluid distribution compared with corresponding experiments at the same capillary number. Therefore, inertial effects are not negligible in drainage process with liquid CO 2 and water despite the low Reynolds number based on the average velocity, as the local velocity can be much higher due to Haines jump events. These higher velocities, coupled with the low viscosity of CO 2 , further amplifies the inertial effect. Therefore, we conclude that caution should be taken when using proxy fluids that only rely on the capillary number and viscosity ratio in both experiment and simulation. Copyright © 2017 Elsevier B.V. All rights reserved.

A free software for pore-scale modelling: solving Stokes equation for velocity fields and permeability values in 3D pore geometries

NASA Astrophysics Data System (ADS)

Gerke, Kirill; Vasilyev, Roman; Khirevich, Siarhei; Karsanina, Marina; Collins, Daniel; Korost, Dmitry; Mallants, Dirk

2015-04-01

In this contribution we introduce a novel free software which solves the Stokes equation to obtain velocity fields for low Reynolds-number flows within externally generated 3D pore geometries. Provided with velocity fields, one can calculate permeability for known pressure gradient boundary conditions via Darcy's equation. Finite-difference schemes of 2nd and 4th order of accuracy are used together with an artificial compressibility method to iteratively converge to a steady-state solution of Stokes' equation. This numerical approach is much faster and less computationally demanding than the majority of open-source or commercial softwares employing other algorithms (finite elements/volumes, lattice Boltzmann, etc.) The software consists of two parts: 1) a pre and post-processing graphical interface, and 2) a solver. The latter is efficiently parallelized to use any number of available cores (the speedup on 16 threads was up to 10-12 depending on hardware). Due to parallelization and memory optimization our software can be used to obtain solutions for 300x300x300 voxels geometries on modern desktop PCs. The software was successfully verified by testing it against lattice Boltzmann simulations and analytical solutions. To illustrate the software's applicability for numerous problems in Earth Sciences, a number of case studies have been developed: 1) identifying the representative elementary volume for permeability determination within a sandstone sample, 2) derivation of permeability/hydraulic conductivity values for rock and soil samples and comparing those with experimentally obtained values, 3) revealing the influence of the amount of fine-textured material such as clay on filtration properties of sandy soil. This work was partially supported by RSF grant 14-17-00658 (pore-scale modelling) and RFBR grants 13-04-00409-a and 13-05-01176-a.

Recursive regularization step for high-order lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann approach for hydro-acoustic waves generated by tsunamigenic sea bottom displacement

NASA Astrophysics Data System (ADS)

Prestininzi, P.; Abdolali, A.; Montessori, A.; Kirby, J. T.; La Rocca, Michele

2016-11-01

Tsunami waves are generated by sea bottom failures, landslides and faults. The concurrent generation of hydro-acoustic waves (HAW), which travel much faster than the tsunami, has received much attention, motivated by their possible exploitation as precursors of tsunamis. This feature makes the detection of HAW particularly well-suited for building an early-warning system. Accuracy and efficiency of the modeling approaches for HAW thus play a pivotal role in the design of such systems. Here, we present a Lattice Boltzmann Method (LBM) for the generation and propagation of HAW resulting from tsunamigenic ground motions and verify it against commonly employed modeling solutions. LBM is well known for providing fast and accurate solutions to both hydrodynamics and acoustics problems, thus it naturally becomes a candidate as a comprehensive computational tool for modeling generation and propagation of HAW.

Lattice Boltzmann Study of Bubbles on a Patterned Superhydrophobic Surface under Shear Flow

NASA Astrophysics Data System (ADS)

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.

A shallow water model for the propagation of tsunami via Lattice Boltzmann method

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann Modeling of Complex Flows for Engineering Applications

NASA Astrophysics Data System (ADS)

Montessori, Andrea; Falcucci, Giacomo

2018-01-01

Nature continuously presents a huge number of complex and multiscale phenomena, which in many cases, involve the presence of one or more fluids flowing, merging and evolving around us. Since the very first years of the third millennium, the Lattice Boltzmann method (LB) has seen an exponential growth of applications, especially in the fields connected with the simulation of complex and soft matter flows. LB, in fact, has shown a remarkable versatility in different fields of applications from nanoactive materials, free surface flows, and multiphase and reactive flows to the simulation of the processes inside engines and fluid machinery. In this book, the authors present the most recent advances of the application of the LB to complex flow phenomena of scientific and technical interest with focus on the multiscale modeling of heterogeneous catalysis within nano-porous media and multiphase, multicomponent flows.

Rahman Prize Lecture: Lattice Boltzmann simulation of complex states of flowing matter

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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 Boltzmann simulations of immiscible displacement process with large viscosity ratios

NASA Astrophysics Data System (ADS)

Rao, Parthib; Schaefer, Laura

2017-11-01

Immiscible displacement is a key physical mechanism involved in enhanced oil recovery and carbon sequestration processes. This multiphase flow phenomenon involves a complex interplay of viscous, capillary, inertial and wettability effects. The lattice Boltzmann (LB) method is an accurate and efficient technique for modeling and simulating multiphase/multicomponent flows especially in complex flow configurations and media. In this presentation we present numerical simulation results of displacement process in thin long channels. The results are based on a new psuedo-potential multicomponent LB model with multiple relaxation time collision (MRT) model and explicit forcing scheme. We demonstrate that the proposed model is capable of accurately simulating the displacement process involving fluids with a wider range of viscosity ratios (>100) and which also leads to viscosity-independent interfacial tension and reduction of some important numerical artifacts.

Coupling LAMMPS with Lattice Boltzmann fluid solver: theory, implementation, and applications

NASA Astrophysics Data System (ADS)

Tan, Jifu; Sinno, Talid; Diamond, Scott

2016-11-01

Studying of fluid flow coupled with solid has many applications in biological and engineering problems, e.g., blood cell transport, particulate flow, drug delivery. We present a partitioned approach to solve the coupled Multiphysics problem. The fluid motion is solved by the Lattice Boltzmann method, while the solid displacement and deformation is simulated by Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The coupling is achieved through the immersed boundary method so that the expensive remeshing step is eliminated. The code can model both rigid and deformable solids. The code also shows very good scaling results. It was validated with classic problems such as migration of rigid particles, ellipsoid particle's orbit in shear flow. Examples of the applications in blood flow, drug delivery, platelet adhesion and rupture are also given in the paper. NIH.

Fluctuating ideal-gas lattice Boltzmann method with fluctuation dissipation theorem for nonvanishing velocities.

PubMed

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.

Hydraulic fracture conductivity: effects of rod-shaped proppant from lattice-Boltzmann simulations and lab tests

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

Maquignon, Nicolas; Duchateau, Julien; Roussel, Gilles; Rousselle, François; Renaud, Christophe

2014-10-01

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 & Chen [1] [2] (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 [4] [5]. Multi-range interactions have been used for SC model [8], 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 & Cheng [6] [7]. 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.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maquignon, Nicolas; Duchateau, Julien; Roussel, Gilles

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 tomore » 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.« less

Higher Order Thermal Lattice Boltzmann Model

NASA Astrophysics Data System (ADS)

Sorathiya, Shahajhan; Ansumali, Santosh

2013-03-01

Lattice Boltzmann method (LBM) modelling of thermal flows, compressible and micro flows requires an accurate velocity space discretization. The sub optimality of Gauss-Hermite quadrature in this regard is well known. Most of the thermal LBM in the past have suffered from instability due to lack of proper H-theorem and accuracy. Motivated from these issues, the present work develops along the two works and and imposes an eighth higher order moment to get correct thermal physics. We show that this can be done by adding just 6 more velocities to D3Q27 model and obtain a ``multi-speed on lattice thermal LBM'' with 33 velocities in 3D and calO (u4) and calO (T4) accurate fieq with a consistent H-theorem and inherent numerical stability. Simulations for Rayleigh-Bernard as well as velocity and temperature slip in micro flows matches with analytical results. Lid driven cavity set up for grid convergence is studied. Finally, a novel data structure is developed for HPC. The authors express their gratitude for computational resources and financial support provide by Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore, India.

Three-dimensional Cascaded Lattice Boltzmann Model for Thermal Convective Flows

NASA Astrophysics Data System (ADS)

Hajabdollahi, Farzaneh; Premnath, Kannan

2017-11-01

Fluid motion driven by thermal effects, such as due to buoyancy in differentially heated enclosures arise in several natural and industrial settings, whose understanding can be achieved via numerical simulations. Lattice Boltzmann (LB) methods are efficient kinetic computational approaches for coupled flow physics problems. In this study, we develop three-dimensional (3D) LB models based on central moments and multiple relaxation times for D3Q7 and D3Q15 lattices to solve the energy transport equations in a double distribution function approach. Their collision operators lead to a cascaded structure involving higher order terms resulting in improved stability. This is coupled to a central moment based LB flow solver with source terms. The new 3D cascaded LB models for the convective flows are first validated for natural convection of air driven thermally on two vertically opposite faces in a cubic cavity at different Rayleigh numbers against prior numerical and experimental data, which show good quantitative agreement. Then, the detailed structure of the 3D flow and thermal fields and the heat transfer rates at different Rayleigh numbers are analyzed and interpreted.

Eliminating cubic terms in the pseudopotential lattice Boltzmann model for multiphase flow

NASA Astrophysics Data System (ADS)

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.

Recurrent procedure for constructing nonisotropic matrix elements of the collision integral of the nonlinear Boltzmann equation

NASA Astrophysics Data System (ADS)

Ender, I. A.; Bakaleinikov, L. A.; Flegontova, E. Yu.; Gerasimenko, A. B.

2017-08-01

We have proposed an algorithm for the sequential construction of nonisotropic matrix elements of the collision integral, which are required to solve the nonlinear Boltzmann equation using the moments method. The starting elements of the matrix are isotropic and assumed to be known. The algorithm can be used for an arbitrary law of interactions for any ratio of the masses of colliding particles.

Development of a Prototype Lattice Boltzmann Code for CFD of Fusion Systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pattison, Martin J; Premnath, Kannan N; Banerjee, Sanjoy

2007-02-26

Designs of proposed fusion reactors, such as the ITER project, typically involve the use of liquid metals as coolants in components such as heat exchangers, which are generally subjected to strong magnetic fields. These fields induce electric currents in the fluids, resulting in magnetohydrodynamic (MHD) forces which have important effects on the flow. The objective of this SBIR project was to develop computational techniques based on recently developed lattice Boltzmann techniques for the simulation of these MHD flows and implement them in a computational fluid dynamics (CFD) code for the study of fluid flow systems encountered in fusion engineering. Themore » code developed during this project, solves the lattice Boltzmann equation, which is a kinetic equation whose behaviour represents fluid motion. This is in contrast to most CFD codes which are based on finite difference/finite volume based solvers. The lattice Boltzmann method (LBM) is a relatively new approach which has a number of advantages compared with more conventional methods such as the SIMPLE or projection method algorithms that involve direct solution of the Navier-Stokes equations. These are that the LBM is very well suited to parallel processing, with almost linear scaling even for very large numbers of processors. Unlike other methods, the LBM does not require solution of a Poisson pressure equation leading to a relatively fast execution time. A particularly attractive property of the LBM is that it can handle flows in complex geometries very easily. It can use simple rectangular grids throughout the computational domain -- generation of a body-fitted grid is not required. A recent advance in the LBM is the introduction of the multiple relaxation time (MRT) model; the implementation of this model greatly enhanced the numerical stability when used in lieu of the single relaxation time model, with only a small increase in computer time. Parallel processing was implemented using MPI and demonstrated the ability of the LBM to scale almost linearly. The equation for magnetic induction was also solved using a lattice Boltzmann method. This approach has the advantage that it fits in well to the framework used for the hydrodynamic equations, but more importantly that it preserves the ability of the code to run efficiently on parallel architectures. Since the LBM is a relatively recent model, a number of new developments were needed to solve the magnetic induction equation for practical problems. Existing methods were only suitable for cases where the fluid viscosity and the magnetic resistivity are of the same order, and a preconditioning method was used to allow the simulation of liquid metals, where these properties differ by several orders of magnitude. An extension of this method to the hydrodynamic equations allowed faster convergence to steady state. A new method of imposing boundary conditions using an extrapolation technique was derived, enabling the magnetic field at a boundary to be specified. Also, a technique by which the grid can be stretched was formulated to resolve thin layers at high imposed magnetic fields, allowing flows with Hartmann numbers of several thousand to be quickly and efficiently simulated. In addition, a module has been developed to calculate the temperature field and heat transfer. This uses a total variation diminishing scheme to solve the equations and is again very amenable to parallelisation. Although, the module was developed with thermal modelling in mind, it can also be applied to passive scalar transport. The code is fully three dimensional and has been applied to a wide variety of cases, including both laminar and turbulent flows. Validations against a series of canonical problems involving both MHD effects and turbulence have clearly demonstrated the ability of the LBM to properly model these types of flow. As well as applications to fusion engineering, the resulting code is flexible enough to be applied to a wide range of other flows, in particular those requiring parallel computations with many processors. For example, at present it is being used for studies in aerodynamics and acoustics involving flows at high Reynolds numbers. It is anticipated that it will be used for multiphase flow applications in the near future.« less

Performance of flapping airfoil propulsion with LBM method and DMD analysis

NASA Astrophysics Data System (ADS)

Li, Bing-Hua; Huang, Xian-Wen; Zheng, Yao; Xie, Fang-Fang; Wang, Jing; Zou, Jian-Feng

2018-05-01

In this work, the performance of flapping airfoil propulsion at low Reynolds number of Re = 100-400 is studied numerically with the lattice Boltzmann method (LBM). Combined with immersed boundary method (IBM), the LBM has been widely used to simulate moving boundary problems. The influences of the reduced frequency on the plunging and pitching airfoil are explored. It is found that the leading-edge vertex separation and inverted wake structures are two main coherent structures, which dominate the flapping airfoil propulsion. However, the two structures play different roles in the flow and the combination effects on the propulsion need to be clarified. To do so, we adopt the dynamic mode decomposition (DMD) algorithm to reveal the underlying physics. The DMD has been proven to be very suitable for analyzing the complex transient systems like the vortex structure of flapping flight.

OpenMP performance for benchmark 2D shallow water equations using LBM

NASA Astrophysics Data System (ADS)

Sabri, Khairul; Rabbani, Hasbi; Gunawan, Putu Harry

2018-03-01

Shallow water equations or commonly referred as Saint-Venant equations are used to model fluid phenomena. These equations can be solved numerically using several methods, like Lattice Boltzmann method (LBM), SIMPLE-like Method, Finite Difference Method, Godunov-type Method, and Finite Volume Method. In this paper, the shallow water equation will be approximated using LBM or known as LABSWE and will be simulated in performance of parallel programming using OpenMP. To evaluate the performance between 2 and 4 threads parallel algorithm, ten various number of grids Lx and Ly are elaborated. The results show that using OpenMP platform, the computational time for solving LABSWE can be decreased. For instance using grid sizes 1000 × 500, the speedup of 2 and 4 threads is observed 93.54 s and 333.243 s respectively.

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

NASA Astrophysics Data System (ADS)

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.

Lattice-Boltzmann-based simulations of diffusiophoresis of colloids and cells

NASA Astrophysics Data System (ADS)

Kreft Pearce, Jennifer; Castigliego, Joshua

Increasing environmental degradation due to plastic pollutants requires innovative solutions that facilitate the extraction of pollutants without harming local biota. We present results from a lattice-Boltzmann-base Brownian Dynamics simulation on diffusiophoresis and the separation of particles within the system. A gradient in viscosity that simulates a concentration gradient in a dissolved polymer allows us to separate various types of particles based on their deformability. As seen in previous experiments, simulated particles that have a higher deformability react differently to the polymer matrix than those with a lower deformability. Therefore, the particles can be separated from each other. The system described above was simulated with various concentration gradients as well as various Soret coefficients in order to optimize the separation of the particles. This simulation, in particular, was intended to model an oceanic system where the particles of interest were motile and nonmotile plankton and microplastics. The separation of plankton from the microplastics was achieved.

Effect of volumetric radiation on natural convection in a cavity with a horizontal fin using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Tighchi, Hashem Ahmadi; Sobhani, Masoud; Esfahani, Javad Abolfazli

2018-01-01

The lattice Boltzmann method (LBM) is presented for the effects of volumetric radiation on laminar natural convection in a square cavity with a horizontal fin on the hot wall containing an absorbing, emitting and scattering medium. Accordingly, the flow, energy and radiative equations are solved by separate distribution functions in the LBM. A parametric study is performed: the effects of Rayleigh number and radiative parameters, such as extinction coefficient and scattering albedo on the flow and temperature fields are investigated. It is found that the isotherms become dense near the cold wall, due to highly participating properties and Rayleigh number. Also, the Nusselt number ratio (NNR) on the clod wall is examined for values of fin length and height. The maximum NNR is found at the longest fin length and near top wall for a given Rayleigh number.

CLASSICAL AREAS OF PHENOMENOLOGY: Lattice Boltzmann simulation of behaviour of particles moving in blood vessels under the rolling massage

NASA Astrophysics Data System (ADS)

Yi, Hou-Hui; Yang, Xiao-Feng; Wang, Cai-Feng; Li, Hua-Bing

2009-07-01

The rolling massage is one of the most important manipulations in Chinese massage, which is expected to eliminate many diseases. Here, the effect of the rolling massage on a pair of particles moving in blood vessels under rolling massage manipulation is studied by the lattice Boltzmann simulation. The simulated results show that the motion of each particle is considerably modified by the rolling massage, and it depends on the relative rolling velocity, the rolling depth, and the distance between particle position and rolling position. Both particles' translational average velocities increase almost linearly as the rolling velocity increases, and obey the same law. The increment of the average relative angular velocity for the leading particle is smaller than that of the trailing one. The result is helpful for understanding the mechanism of the massage and to further develop the rolling techniques.

Viscous dissipation effects on MHD slip flow and heat transfer in porous micro duct with LTNE assumptions using modified lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Rabhi, R.; Amami, B.; Dhahri, H.; Mhimid, A.

2017-11-01

This paper deals with heat transfer and fluid flow in a porous micro duct under local thermal non equilibrium conditions subjected to an external oriented magnetic field. The considered sample is a micro duct filled with porous media assumed to be homogenous, isotropic and saturated. The slip velocity and the temperature jump were uniformly imposed to the wall. In modeling the flow, the Brinkmann-Forchheimer extended Darcy model was incorporated into the momentum equations. In the energy equation, the local thermal non equilibrium between the two phases was adopted. A modified axisymmetric lattice Boltzmann method was used to solve the obtained governing equation system. Attention was focused on the influence of the emerging parameters such as Knudsen number, Kn, Hartmann number, Ha, Eckert number, Ec, Biot number, Bi and the magnetic field inclination γ on flow and heat transfer throughout this paper.

Predictive wind turbine simulation with an adaptive lattice Boltzmann method for moving boundaries

NASA Astrophysics Data System (ADS)

Deiterding, Ralf; Wood, Stephen L.

2016-09-01

Operating horizontal axis wind turbines create large-scale turbulent wake structures that affect the power output of downwind turbines considerably. The computational prediction of this phenomenon is challenging as efficient low dissipation schemes are necessary that represent the vorticity production by the moving structures accurately and that are able to transport wakes without significant artificial decay over distances of several rotor diameters. We have developed a parallel adaptive lattice Boltzmann method for large eddy simulation of turbulent weakly compressible flows with embedded moving structures that considers these requirements rather naturally and enables first principle simulations of wake-turbine interaction phenomena at reasonable computational costs. The paper describes the employed computational techniques and presents validation simulations for the Mexnext benchmark experiments as well as simulations of the wake propagation in the Scaled Wind Farm Technology (SWIFT) array consisting of three Vestas V27 turbines in triangular arrangement.

A new 3D immersed boundary method for non-Newtonian fluid-structure-interaction with application

NASA Astrophysics Data System (ADS)

Zhu, Luoding

2017-11-01

Motivated by fluid-structure-interaction (FSI) phenomena in life sciences (e.g., motions of sperm and cytoskeleton in complex fluids), we introduce a new immersed boundary method for FSI problems involving non-Newtonian fluids in three dimensions. The non-Newtonian fluids are modelled by the FENE-P model (including the Oldroyd-B model as an especial case) and numerically solved by a lattice Boltzmann scheme (the D3Q7 model). The fluid flow is modelled by the lattice Boltzmann equations and numerically solved by the D3Q19 model. The deformable structure and the fluid-structure-interaction are handled by the immersed boundary method. As an application, we study a FSI toy problem - interaction of an elastic plate (flapped at its leading edge and restricted nowhere else) with a non-Newtonian fluid in a 3D flow. Thanks to the support of NSF-DMS support under research Grant 1522554.

Analysis of natural convection in nanofluid-filled H-shaped cavity by entropy generation and heatline visualization using lattice Boltzmann method

NASA Astrophysics Data System (ADS)

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 simulations for wall-flow dynamics in porous ceramic diesel particulate filters

NASA Astrophysics Data System (ADS)

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.

Accuracy and Numerical Stabilty Analysis of Lattice Boltzmann Method with Multiple Relaxation Time for Incompressible Flows

NASA Astrophysics Data System (ADS)

Pradipto; Purqon, Acep

2017-07-01

Lattice Boltzmann Method (LBM) is the novel method for simulating fluid dynamics. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. The common collision model of LBM is the BGK with a constant single relaxation time τ. However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity. The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. The tests concluded that LBM with MRT are more stable than BGK, and have a similar accuracy. The maximum Reynolds number that converges for BGK is 3200 and 7500 for MRT respectively.

On the application of the lattice Boltzmann method to the investigation of glottal flow

PubMed Central

Kucinschi, Bogdan R.; Afjeh, Abdollah A.; Scherer, Ronald C.

2008-01-01

The production of voice is directly related to the vibration of the vocal folds, which is generated by the interaction between the glottal flow and the tissue of the vocal folds. In the current study, the aerodynamics of the symmetric glottis is investigated numerically for a number of static configurations. The numerical investigation is based on the lattice Boltzmann method (LBM), which is an alternative approach within computational fluid dynamics. Compared to the traditional Navier–Stokes computational fluid dynamics methods, the LBM is relatively easy to implement and can deal with complex geometries without requiring a dedicated grid generator. The multiple relaxation time model was used to improve the numerical stability. The results obtained with LBM were compared to the results provided by a traditional Navier–Stokes solver and experimental data. It was shown that LBM results are satisfactory for all the investigated cases. PMID:18646995

Lattice Boltzmann and Navier-Stokes Cartesian CFD Approaches for Airframe Noise Predictions

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Kocheemoolayil, Joseph G.; Kiris, Cetin C.

2017-01-01

Lattice Boltzmann (LB) and compressible Navier-Stokes (NS) equations based computational fluid dynamics (CFD) approaches are compared for simulating airframe noise. Both LB and NS CFD approaches are implemented within the Launch Ascent and Vehicle Aerodynamics (LAVA) framework. Both schemes utilize the same underlying Cartesian structured mesh paradigm with provision for local adaptive grid refinement and sub-cycling in time. We choose a prototypical massively separated, wake-dominated flow ideally suited for Cartesian-grid based approaches in this study - The partially-dressed, cavity-closed nose landing gear (PDCC-NLG) noise problem from AIAA's Benchmark problems for Airframe Noise Computations (BANC) series of workshops. The relative accuracy and computational efficiency of the two approaches are systematically compared. Detailed comments are made on the potential held by LB to significantly reduce time-to-solution for a desired level of accuracy within the context of modeling airframes noise from first principles.

Multiple-relaxation-time lattice Boltzmann method for immiscible fluids at high Reynolds numbers.

PubMed

Fakhari, Abbas; Lee, Taehun

2013-02-01

The lattice Boltzmann method for immiscible multiphase flows with large density ratio is extended to high Reynolds number flows using a multiple-relaxation-time (MRT) collision operator, and its stability and accuracy are assessed by simulating the Kelvin-Helmholtz instability. The MRT model is successful at damping high-frequency oscillations in the kinetic energy emerging from traveling waves generated by the inclusion of curvature. Numerical results are shown to be in good agreement with prior studies using adaptive mesh refinement techniques applied to the Navier-Stokes equations. Effects of viscosity and surface tension, as well as density ratio, are investigated in terms of the Reynolds and Weber numbers. It is shown that increasing the Reynolds number results in a more chaotic interface evolution and eventually shattering of the interface, while surface tension is shown to have a stabilizing effect.

Estimation of Reynolds number for flows around cylinders with lattice Boltzmann methods and artificial neural networks.

PubMed

Carrillo, Mauricio; Que, Ulices; González, José A

2016-12-01

The present work investigates the application of artificial neural networks (ANNs) to estimate the Reynolds (Re) number for flows around a cylinder. The data required to train the ANN was generated with our own implementation of a lattice Boltzmann method (LBM) code performing simulations of a two-dimensional flow around a cylinder. As results of the simulations, we obtain the velocity field (v[over ⃗]) and the vorticity (∇[over ⃗]×v[over ⃗]) of the fluid for 120 different values of Re measured at different distances from the obstacle and use them to teach the ANN to predict the Re. The results predicted by the networks show good accuracy with errors of less than 4% in all the studied cases. One of the possible applications of this method is the development of an efficient tool to characterize a blocked flowing pipe.

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions.

PubMed

Rivas, Nicolas; Frijters, Stefan; Pagonabarraga, Ignacio; Harting, Jens

2018-04-14

A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a Bhatnagar-Gross-Krook collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics through appropriate boundary conditions. We present the first full integration of these three elements. The model is validated by comparing with known analytic solutions of ionic distributions at fluid interfaces, dielectric droplet deformations, and the electrophoretic mobility of colloidal suspensions. Its possibilities are explored by considering various physical systems, such as breakup of charged and neutral droplets and colloidal dynamics at either planar or spherical fluid interfaces.

Three-dimensional morphologies of inclined equiaxed dendrites growing under forced convection by phase-field-lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Sakane, Shinji; Takaki, Tomohiro; Ohno, Munekazu; Shibuta, Yasushi; Shimokawabe, Takashi; Aoki, Takayuki

2018-02-01

Three-dimensional growth morphologies of equiaxed dendrites growing under forced convection, with their preferred growth direction inclined from the flow direction, were investigated by performing large-scale phase-field lattice Boltzmann simulations on a graphical-processing-unit supercomputer. The tip velocities of the dendrite arms with their preferred growth directions inclined toward the upstream and downstream directions increased and decreased, respectively, as a result of forced convection. In addition, the tip velocities decreased monotonically as the angle between the preferred growth direction and the upstream direction increased. Here, the degree of acceleration of the upstream tips was larger than the degree of deceleration of the downstream tips. The angles between the actual tip growth directions and the preferred growth direction of the dendrite arms exhibited a characteristic change with two local maxima and two local minima.

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions

NASA Astrophysics Data System (ADS)

Rivas, Nicolas; Frijters, Stefan; Pagonabarraga, Ignacio; Harting, Jens

2018-04-01

A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a Bhatnagar-Gross-Krook collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics through appropriate boundary conditions. We present the first full integration of these three elements. The model is validated by comparing with known analytic solutions of ionic distributions at fluid interfaces, dielectric droplet deformations, and the electrophoretic mobility of colloidal suspensions. Its possibilities are explored by considering various physical systems, such as breakup of charged and neutral droplets and colloidal dynamics at either planar or spherical fluid interfaces.

Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

NASA Technical Reports Server (NTRS)

Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q

2015-01-01

A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments is based upon a novel approach that relies on the global momentum conservation of the closed fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. A numerical example illustrates the method's application to prediction of bulk fluid behavior during a spacecraft ullage settling maneuver.

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

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

NASA Technical Reports Server (NTRS)

Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q.

2015-01-01

A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments relies upon the global momentum conservation of the fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. Numerical examples illustrate the method's application to predicting bulk fluid motion including lateral propellant slosh in low-g conditions.

Coupling lattice Boltzmann and continuum equations for flow and reactive transport in porous media.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coon, Ethan; Porter, Mark L.; Kang, Qinjun

2012-06-18

In spatially and temporally localized instances, capturing sub-reservoir scale information is necessary. Capturing sub-reservoir scale information everywhere is neither necessary, nor computationally possible. The lattice Boltzmann Method for solving pore-scale systems. At the pore-scale, LBM provides an extremely scalable, efficient way of solving Navier-Stokes equations on complex geometries. Coupling pore-scale and continuum scale systems via domain decomposition. By leveraging the interpolations implied by pore-scale and continuum scale discretizations, overlapping Schwartz domain decomposition is used to ensure continuity of pressure and flux. This approach is demonstrated on a fractured medium, in which Navier-Stokes equations are solved within the fracture while Darcy'smore » equation is solved away from the fracture Coupling reactive transport to pore-scale flow simulators allows hybrid approaches to be extended to solve multi-scale reactive transport.« less

Evaluation of the Lattice-Boltzmann Equation Solver PowerFLOW for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Lockard, David P.; Luo, Li-Shi; Singer, Bart A.; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

A careful comparison of the performance of a commercially available Lattice-Boltzmann Equation solver (Power-FLOW) was made with a conventional, block-structured computational fluid-dynamics code (CFL3D) for the flow over a two-dimensional NACA-0012 airfoil. The results suggest that the version of PowerFLOW used in the investigation produced solutions with large errors in the computed flow field; these errors are attributed to inadequate resolution of the boundary layer for reasons related to grid resolution and primitive turbulence modeling. The requirement of square grid cells in the PowerFLOW calculations limited the number of points that could be used to span the boundary layer on the wing and still keep the computation size small enough to fit on the available computers. Although not discussed in detail, disappointing results were also obtained with PowerFLOW for a cavity flow and for the flow around a generic helicopter configuration.

A Hermite-based lattice Boltzmann model with artificial viscosity for compressible viscous flows

NASA Astrophysics Data System (ADS)

Qiu, Ruofan; Chen, Rongqian; Zhu, Chenxiang; You, Yancheng

2018-05-01

A lattice Boltzmann model on Hermite basis for compressible viscous flows is presented in this paper. The model is developed in the framework of double-distribution-function approach, which has adjustable specific-heat ratio and Prandtl number. It contains a density distribution function for the flow field and a total energy distribution function for the temperature field. The equilibrium distribution function is determined by Hermite expansion, and the D3Q27 and D3Q39 three-dimensional (3D) discrete velocity models are used, in which the discrete velocity model can be replaced easily. Moreover, an artificial viscosity is introduced to enhance the model for capturing shock waves. The model is tested through several cases of compressible flows, including 3D supersonic viscous flows with boundary layer. The effect of artificial viscosity is estimated. Besides, D3Q27 and D3Q39 models are further compared in the present platform.

Shear viscosity of a two-dimensional emulsion of drops using a multiple-relaxation-time-step lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Halliday, I.; Xu, X.; Burgin, K.

2017-02-01

An extended Benzi-Dellar lattice Boltzmann equation scheme [R. Benzi, S. Succi, and M. Vergassola, Europhys. Lett. 13, 727 (1990), 10.1209/0295-5075/13/8/010; R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145 (1992), 10.1016/0370-1573(92)90090-M; P. J. Dellar, Phys. Rev. E 65, 036309 (2002), 10.1103/PhysRevE.65.036309] is developed and applied to the problem of confirming, at low Re and drop fluid concentration, c , the variation of effective shear viscosity, ηeff=η1[1 +f (η1,η2) c ] , with respect to c for a sheared, two-dimensional, initially crystalline emulsion [here η1 (η2) is the fluid (drop fluid) shear viscosity]. Data obtained with our enhanced multicomponent lattice Boltzmann method, using average shear stress and hydrodynamic dissipation, agree well once appropriate corrections to Landau's volume average shear stress [L. Landau and E. M. Lifshitz, Fluid Mechanics, 6th ed. (Pergamon, London, 1966)] are applied. Simulation results also confirm the expected form for f (ηi,η2) , and they provide a reasonable estimate of its parameters. Most significantly, perhaps, the generality of our data supports the validity of Taylor's disputed simplification [G. I. Taylor, Proc. R. Soc. London, Ser. A 138, 133 (1932), 10.1098/rspa.1932.0175] to reduce the effect of one hydrodynamic boundary condition (on the continuity of the normal contraction of stress) to an assumption that interfacial tension is sufficiently strong to maintain a spherical drop shape.

Effect of the electric field ratio on electroosmotic flow patterns in cross-shaped microchannels by the lattice-Boltzmann Method

NASA Astrophysics Data System (ADS)

Socias, Alvaro; Oyarzun, Diego; Guzman, Amador

2014-11-01

The electroosmotic flow (EOF) pattern characteristics in cross-shaped microchannels flow are important features when either suppressing or enhancing flow features for injection and separation or mixing of multiple species are the wanted objectives. There are situations in EOF in cross-shaped microchannels where the fluid flows toward unexpected and unwanted directions under a given external electric field that depends of both the applied electric field and lengths of the different channels. This article describes the effect of the electric field ratio, defined as the ratio between longitudinal nominal electric field ELong = (VE-VW) /(LW + LE) and the nominal electric field E a = (VS-VE) /(VS + VE) , where E, S and W define the east, south and west directions of the cross-shaped microchannel; V is the externally applied voltage and L is the length, on the EOF characteristics in a cross-shaped microchannel. We use the lattice-Boltzmann method (LBM) for solving the discretized Boltzmann Transport Equation (BTE) describing the coupled processes of hydrodynamics and electrodynamic. Our numerical simulations allow us to determine the EOF pattern for a wide range of the electric field ratio and Ea such that inverted flow features are captured and described, which are very important to determine for flow separation or mixing.

Lattice Boltzmann simulation of nonequilibrium effects in oscillatory gas flow.

PubMed

Tang, G H; Gu, X J; Barber, R W; Emerson, D R; Zhang, Y H

2008-08-01

Accurate evaluation of damping in laterally oscillating microstructures is challenging due to the complex flow behavior. In addition, device fabrication techniques and surface properties will have an important effect on the flow characteristics. Although kinetic approaches such as the direct simulation Monte Carlo (DSMC) method and directly solving the Boltzmann equation can address these challenges, they are beyond the reach of current computer technology for large scale simulation. As the continuum Navier-Stokes equations become invalid for nonequilibrium flows, we take advantage of the computationally efficient lattice Boltzmann method to investigate nonequilibrium oscillating flows. We have analyzed the effects of the Stokes number, Knudsen number, and tangential momentum accommodation coefficient for oscillating Couette flow and Stokes' second problem. Our results are in excellent agreement with DSMC data for Knudsen numbers up to Kn=O(1) and show good agreement for Knudsen numbers as large as 2.5. In addition to increasing the Stokes number, we demonstrate that increasing the Knudsen number or decreasing the accommodation coefficient can also expedite the breakdown of symmetry for oscillating Couette flow. This results in an earlier transition from quasisteady to unsteady flow. Our paper also highlights the deviation in velocity slip between Stokes' second problem and the confined Couette case.

Accuracy of the lattice-Boltzmann method using the Cell processor

NASA Astrophysics Data System (ADS)

Harvey, M. J.; de Fabritiis, G.; Giupponi, G.

2008-11-01

Accelerator processors like the new Cell processor are extending the traditional platforms for scientific computation, allowing orders of magnitude more floating-point operations per second (flops) compared to standard central processing units. However, they currently lack double-precision support and support for some IEEE 754 capabilities. In this work, we develop a lattice-Boltzmann (LB) code to run on the Cell processor and test the accuracy of this lattice method on this platform. We run tests for different flow topologies, boundary conditions, and Reynolds numbers in the range Re=6 350 . In one case, simulation results show a reduced mass and momentum conservation compared to an equivalent double-precision LB implementation. All other cases demonstrate the utility of the Cell processor for fluid dynamics simulations. Benchmarks on two Cell-based platforms are performed, the Sony Playstation3 and the QS20/QS21 IBM blade, obtaining a speed-up factor of 7 and 21, respectively, compared to the original PC version of the code, and a conservative sustained performance of 28 gigaflops per single Cell processor. Our results suggest that choice of IEEE 754 rounding mode is possibly as important as double-precision support for this specific scientific application.

Modelling viscoacoustic wave propagation with the lattice Boltzmann method.

PubMed

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.

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

PubMed

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

Chapman-Enskog Analyses on the Gray Lattice Boltzmann Equation Method for Fluid Flow in Porous Media

NASA Astrophysics Data System (ADS)

Chen, Chen; Li, Like; Mei, Renwei; Klausner, James F.

2018-03-01

The gray lattice Boltzmann equation (GLBE) method has recently been used to simulate fluid flow in porous media. It employs a partial bounce-back of populations (through a fractional coefficient θ, which represents the fraction of populations being reflected by the solid phase) in the evolution equation to account for the linear drag of the medium. Several particular GLBE schemes have been proposed in the literature and these schemes are very easy to implement; but there exists uncertainty about the need for redefining the macroscopic velocity as there has been no systematic analysis to recover the Brinkman equation from the various GLBE schemes. Rigorous Chapman-Enskog analyses are carried out to show that the momentum equation recovered from these schemes can satisfy Brinkman equation to second order in ɛ only if θ = O( ɛ ) in which ɛ is the ratio of the lattice spacing to the characteristic length of physical dimension. The need for redefining macroscopic velocity is shown to be scheme-dependent. When a body force is encountered such as the gravitational force or that caused by a pressure gradient, different forms of forcing redefinitions are required for each GLBE scheme.

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

NASA Astrophysics Data System (ADS)

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.

Lattice-Boltzmann simulation of coalescence-driven island coarsening

USGS Publications Warehouse

Basagaoglu, H.; Green, C.T.; Meakin, P.; McCoy, B.J.

2004-01-01

The first-order phase separation in a thin fluid film was simulated using a two-dimensional lattice-Boltzman model (LBM) with fluid-fluid interactions. The effects of the domain size on the intermediate asymptotic island size distribution were also discussed. It was observed that the overall process is dominated by coalescence which is independent of island mass. The results show that the combined effects of growth, coalescence, and Ostwald ripening control the phase transition process in the LBM simulations.

Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices

NASA Astrophysics Data System (ADS)

Ming, Yi; Ye, Liu; Chen, Han-Shuang; Mao, Shi-Feng; Li, Hui-Min; Ding, Ze-Jun

2018-01-01

Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-β lattices and the asymmetric Fermi-Pasta-Ulam-α β lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.

Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Priimak, Dmitri

2014-12-01

We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

A fast Laplace solver approach to pore scale permeability

NASA Astrophysics Data System (ADS)

Arns, Christoph; Adler, Pierre

2017-04-01

The permeability of a porous medium can be derived by solving the Stokes equations in the pore space with no slip at the walls. The resulting velocity averaged over the pore volume yields the permeability KS by application of the Darcy law. The Stokes equations can be solved by a number of different techniques such as finite differences, finite volume, Lattice Boltzmann, but whatever the technique it remains a heavy task since there are four unknowns at each node (the three velocity components and the pressure) which necessitate the solution of four equations (the projection of Newton's law on each axis and mass conservation). By comparison, the Laplace equation is scalar with a single unknown at each node. The objective of this work is to replace the Stokes equations by an elliptical equation with a space dependent permeability. More precisely, the local permeability k is supposed to be proportional to (r-alpha)**2 where r is the distance of the voxel to the closest wall, and alpha a constant; k is zero in the solid phase. The elliptical equation is div(k gradp)=0. A macroscopic pressure gradient is assumed to be exerted on the medium and again the resulting velocity averaged over space yields a permeability K_L. In order to validate this method, systematic calculations have been performed. First, elementary shapes (plane channel, circular pipe, rectangular channels) were studied for which flow occurs along parallel lines in which case KL is the arithmetic average of the k's. KL was calculated for various discretizations of the pore space and various values of alpha. For alpha=0.5, the agreement with the exact analytical value of KS is excellent for the plane and rectangular channels while it is only approximate for circular pipes. Second, the permeability KL of channels with sinusoidal walls was calculated and compared with analytical results and numerical ones provided by a Lattice Boltzmann algorithm. Generally speaking, the discrepancy does not exceed 25% when alpha=0.5. Third, the most important test was performed on two types of real media that were used for previous studies. A fracture network measured by FIB/SEM in a low permeability sandstone was used for that purpose; the two dimensionless permeabilities KS and KL are equal to 9.3d-3 and 8.5d-3. Similar calculations were performed on 256 samples of Fontainebleau sandstones and the agreement was in general excellent, except may be for very low permeabilities. To conclude, the Laplace solver is significantly more stable than the lattice Boltzmann approach, uses less memory, and is significantly faster. Permeabilities are in excellent agreement over a wide range of porosities.

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

PubMed

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.

Towards Full Aircraft Airframe Noise Prediction: Lattice Boltzmann Simulations

NASA Technical Reports Server (NTRS)

Khorrami, Mehdi R.; Fares, Ehab; Casalino, Damiano

2014-01-01

Computational results for an 18%-scale, semi-span Gulfstream aircraft model are presented. Exa Corporation's lattice Boltzmann PowerFLOW(trademark) solver was used to perform time-dependent simulations of the flow field associated with this high-fidelity aircraft model. The simulations were obtained for free-air at a Mach number of 0.2 with the flap deflected at 39 deg (landing configuration). We focused on accurately predicting the prominent noise sources at the flap tips and main landing gear for the two baseline configurations, namely, landing flap setting without and with gear deployed. Capitalizing on the inherently transient nature of the lattice Boltzmann formulation, the complex time-dependent flow features associated with the flap were resolved very accurately and efficiently. To properly simulate the noise sources over a broad frequency range, the tailored grid was very dense near the flap inboard and outboard tips. Extensive comparison of the computed time-averaged and unsteady surface pressures with wind tunnel measurements showed excellent agreement for the global aerodynamic characteristics and the local flow field at the flap inboard and outboard tips and the main landing gear. In particular, the computed fluctuating surface pressure field for the flap agreed well with the measurements in both amplitude and frequency content, indicating that the prominent airframe noise sources at the tips were captured successfully. Gear-flap interaction effects were remarkably well predicted and were shown to affect only the inboard flap tip, altering the steady and unsteady pressure fields in that region. The simulated farfield noise spectra for both baseline configurations, obtained using a Ffowcs-Williams and Hawkings acoustic analogy approach, were shown to be in close agreement with measured values.

Lattice Boltzmann method simulations of Stokes number effects on particle motion in a channel flow

NASA Astrophysics Data System (ADS)

Zhang, Lenan; Jebakumar, Anand Samuel; Abraham, John

2016-06-01

In a recent experimental study by Lau and Nathan ["Influence of Stokes number on the velocity and concentration distributions in particle-laden jets," J. Fluid Mech. 757, 432 (2014)], it was found that particles in a turbulent pipe flow tend to migrate preferentially toward the wall or the axis depending on their Stokes number (St). Particles with a higher St (>10) are concentrated near the axis while those with lower St (<1) move toward the walls. Jebakumar et al. ["Lattice Boltzmann method simulations of Stokes number effects on particle trajectories in a wall-bounded flow," Comput. Fluids 124, 208 (2016)] have carried out simulations of a particle in a laminar channel flow to investigate this behavior. In their work, they report a similar behavior where particles with low St migrate toward the wall and oscillate about a mean position near the wall while those with high St oscillate about the channel center plane. They have explained this behavior in terms of the Saffman lift, Magnus lift, and wall repulsion forces acting on the particle. The present work extends the previous work done by Jebakumar et al. and aims to study the behavior of particles at intermediate St ranging from 10 to 20. It is in this range where the equilibrium position of the particle changes from near the wall to the axis and the particle starts oscillating about the axis. The Lattice Boltzmann method is employed to carry out this study. It is shown that the change in mean equilibrium position is related to increasing oscillations of the particle with mean position near the wall which results in the particle moving past the center plane to the opposite side. The responsible mechanisms are explained in detail.

Phase-field-based lattice Boltzmann model for incompressible binary fluid systems with density and viscosity contrasts.

PubMed

Zu, Y Q; He, S

2013-04-01

A lattice Boltzmann model (LBM) is proposed based on the phase-field theory to simulate incompressible binary fluids with density and viscosity contrasts. Unlike many existing diffuse interface models which are limited to density matched binary fluids, the proposed model is capable of dealing with binary fluids with moderate density ratios. A new strategy for projecting the phase field to the viscosity field is proposed on the basis of the continuity of viscosity flux. The new LBM utilizes two lattice Boltzmann equations (LBEs): one for the interface tracking and the other for solving the hydrodynamic properties. The LBE for interface tracking can recover the Chan-Hilliard equation without any additional terms; while the LBE for hydrodynamic properties can recover the exact form of the divergence-free incompressible Navier-Stokes equations avoiding spurious interfacial forces. A series of 2D and 3D benchmark tests have been conducted for validation, which include a rigid-body rotation, stationary and moving droplets, a spinodal decomposition, a buoyancy-driven bubbly flow, a layered Poiseuille flow, and the Rayleigh-Taylor instability. It is shown that the proposed method can track the interface with high accuracy and stability and can significantly and systematically reduce the parasitic current across the interface. Comparisons with momentum-based models indicate that the newly proposed velocity-based model can better satisfy the incompressible condition in the flow fields, and eliminate or reduce the velocity fluctuations in the higher-pressure-gradient region and, therefore, achieve a better numerical stability. In addition, the test of a layered Poiseuille flow demonstrates that the proposed scheme for mixture viscosity performs significantly better than the traditional mixture viscosity methods.

Free-energy-based lattice Boltzmann model for the simulation of multiphase flows with density contrast.

PubMed

Shao, J Y; Shu, C; Huang, H B; Chew, Y T

2014-03-01

A free-energy-based phase-field lattice Boltzmann method is proposed in this work to simulate multiphase flows with density contrast. The present method is to improve the Zheng-Shu-Chew (ZSC) model [Zheng, Shu, and Chew, J. Comput. Phys. 218, 353 (2006)] for correct consideration of density contrast in the momentum equation. The original ZSC model uses the particle distribution function in the lattice Boltzmann equation (LBE) for the mean density and momentum, which cannot properly consider the effect of local density variation in the momentum equation. To correctly consider it, the particle distribution function in the LBE must be for the local density and momentum. However, when the LBE of such distribution function is solved, it will encounter a severe numerical instability. To overcome this difficulty, a transformation, which is similar to the one used in the Lee-Lin (LL) model [Lee and Lin, J. Comput. Phys. 206, 16 (2005)] is introduced in this work to change the particle distribution function for the local density and momentum into that for the mean density and momentum. As a result, the present model still uses the particle distribution function for the mean density and momentum, and in the meantime, considers the effect of local density variation in the LBE as a forcing term. Numerical examples demonstrate that both the present model and the LL model can correctly simulate multiphase flows with density contrast, and the present model has an obvious improvement over the ZSC model in terms of solution accuracy. In terms of computational time, the present model is less efficient than the ZSC model, but is much more efficient than the LL model.

Pore-scale simulation of liquid CO2 displacement of water using a two-phase lattice Boltzmann model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Haihu; Valocchi, Albert J.; Werth, Charles J.

A lattice Boltzmann color-fluid model, which was recently proposed by Liu et al. [H. Liu, A.J. Valocchi, and Q. Kang. Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations. Phys. Rev. E, 85:046309, 2012.] based on a concept of continuum surface force, is improved to simulate immiscible two-phase flows in porous media. The new improvements allow the model to account for different kinematic viscosities of both fluids and to model fluid-solid interactions. The capability and accuracy of this model is first validated by two benchmark tests: a layered two-phase flow with a viscosity ratio, and a dynamic capillary intrusion. Thismore » model is then used to simulate liquid CO2 (LCO2) displacing water in a dual-permeability pore network. The extent and behavior of LCO2 preferential flow (i.e., fingering) is found to depend on the capillary number (Ca), and three different displacement patterns observed in previous micromodel experiments are reproduced. The predicted variation of LCO2 saturation with Ca, as well as variation of specific interfacial length with LCO2 saturation, are both in good agreement with the experimental observations. To understand the effect of heterogeneity on pore-scale displacement, we also simulate LCO2 displacing water in a randomly heterogeneous pore network, which has the same size and porosity as the dual-permeability pore network. In comparison to the dual-permeability case, the transition from capillary fingering to viscous fingering occurs at a higher Ca, and LCO2 saturation is higher at low Ca but lower at high Ca. In either pore network, the LCO2-water specific interfacial length is found to obey a power-law dependence on LCO2 saturation.« less

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

NASA Technical Reports Server (NTRS)

Lallemand, Pierre; Luo, Li-Shi

2000-01-01

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Application of a flexible lattice Boltzmann method based simulation tool for modelling physico-chemical processes at different scales

NASA Astrophysics Data System (ADS)

Patel, Ravi A.; Perko, Janez; Jacques, Diederik

2017-04-01

Often, especially in the disciplines related to natural porous media, such as for example vadoze zone or aquifer hydrology or contaminant transport, the relevant spatial and temporal scales on which we need to provide information is larger than the scale where the processes actually occur. Usual techniques used to deal with these problems assume the existence of a REV. However, in order to understand the behavior on larger scales it is important to downscale the problem onto the relevant scale of the processes. Due to the limitations of resources (time, memory) the downscaling can only be made up to the certain lower scale. At this lower scale still several scales may co-exist - the scale which can be explicitly described and a scale which needs to be conceptualized by effective properties. Hence, models which are supposed to provide effective properties on relevant scales should therefor be flexible enough to represent complex pore-structure by explicit geometry on one side, and differently defined processes (e.g. by the effective properties) which emerge on lower scale. In this work we present the state-of-the-art lattice Boltzmann method based simulation tool applicable to advection-diffusion equation coupled to geochemical processes. The lattice Boltzmann transport solver can be coupled with an external geochemical solver which allows to account for a wide range of geochemical reaction networks through thermodynamic databases. The applicability to multiphase systems is ongoing. We provide several examples related to the calculation of an effective diffusion properties, permeability and effective reaction rate based on a continuum scale based on the pore scale geometry.

Lattice Boltzmann study on Kelvin-Helmholtz instability: roles of velocity and density gradients.

PubMed

Gan, Yanbiao; Xu, Aiguo; Zhang, Guangcai; Li, Yingjun

2011-05-01

A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible fluids is proposed. The fifth-order weighted essentially nonoscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions [G. A. Sod, J. Comput. Phys. 27, 1 (1978).]. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that the linear growth rate γ for the KHI decreases by increasing the width of velocity transition layer D(v) but increases by increasing the width of density transition layer D(ρ). After the initial transient period and before the vortex has been well formed, the linear growth rates γ(v) and γ(ρ), vary with D(v) and D(ρ) approximately in the following way, lnγ(v)=a-bD(v) and γ(ρ)=c+elnD(ρ)(D(ρ)D(ρ)(E) the linear growth rate γ(ρ) does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang et al., Phys. Plasma 17, 042103 (2010)]. © 2011 American Physical Society

GPU-accelerated Lattice Boltzmann method for anatomical extraction in patient-specific computational hemodynamics

NASA Astrophysics Data System (ADS)

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.

Modeling of monolayer charge-stabilized colloidal crystals with static hexagonal crystal lattice

NASA Astrophysics Data System (ADS)

Nagatkin, A. N.; Dyshlovenko, P. E.

2018-01-01

The mathematical model of monolayer colloidal crystals of charged hard spheres in liquid electrolyte is proposed. The particles in the monolayer are arranged into the two-dimensional hexagonal crystal lattice. The model enables finding elastic constants of the crystals from the stress-strain dependencies. The model is based on the nonlinear Poisson-Boltzmann differential equation. The Poisson-Boltzmann equation is solved numerically by the finite element method for any spatial configuration. The model has five geometrical and electrical parameters. The model is used to study the crystal with particles comparable in size with the Debye length of the electrolyte. The first- and second-order elastic constants are found for a broad range of densities. The model crystal turns out to be stable relative to small uniform stretching and shearing. It is also demonstrated that the Cauchy relation is not fulfilled in the crystal. This means that the pair effective interaction of any kind is not sufficient to proper model the elasticity of colloids within the one-component approach.

From Lattice Boltzmann to hydrodynamics in dissipative relativistic fluids

NASA Astrophysics Data System (ADS)

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.

Experiment and Lattice Boltzmann numerical study on nanofluids flow in a micromodel as porous medium

NASA Astrophysics Data System (ADS)

Meghdadi Isfahani, A. H.; Afrand, Masoud

2017-10-01

Al2O3 nanofluids flow has been studied in etched glass micromodel which is idealization of porous media by using a pseudo 2D Lattice Boltzmann Method (LBM). The predictions were compared with experimental results. Pressure drop / flow rate relations have been measured for pure water and Al2O3 nanofluids. Because the size of Al2O3 nanoparticles is tiny enough to permit through the pore throats of the micromodel, blockage does not occur and the permeability is independent of the nanofluid volume fraction. Therefore, the nanofluid behaves as a single phase fluid, and a single phase LBM is able to simulate the results of this experiment. Although the flow in micromodels is 3D, we showed that 2D LBM can be used provided an effective viscous drag force, representing the effect of the third dimension, is considered. Good qualitative and quantitative agreement is seen between the numerical and experimental results.

Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Boyd, Joshua; Buick, James M.; Green, Simon

2007-09-01

The lattice Boltzmann method is modified to allow the simulation of non-Newtonian shear-dependent viscosity models. Casson and Carreau-Yasuda non-Newtonian blood viscosity models are implemented and are used to compare two-dimensional Newtonian and non-Newtonian flows in the context of simple steady flow and oscillatory flow in straight and curved pipe geometries. It is found that compared to analogous Newtonian flows, both the Casson and Carreau-Yasuda flows exhibit significant differences in the steady flow situation. In the straight pipe oscillatory flows, both models exhibit differences in velocity and shear, with the largest differences occurring at low Reynolds and Womersley numbers. Larger differences occur for the Casson model. In the curved pipe Carreau-Yasuda model, moderate differences are observed in the velocities in the central regions of the geometries, and the largest shear rate differences are observed near the geometry walls. These differences may be important for the study of atherosclerotic progression.

Topology optimization of thermal fluid flows with an adjoint Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Dugast, Florian; Favennec, Yann; Josset, Christophe; Fan, Yilin; Luo, Lingai

2018-07-01

This paper presents an adjoint Lattice Boltzmann Method (LBM) coupled with the Level-Set Method (LSM) for topology optimization of thermal fluid flows. The adjoint-state formulation implies discrete velocity directions in order to take into account the LBM boundary conditions. These boundary conditions are introduced at the beginning of the adjoint-state method as the LBM residuals, so that the adjoint-state boundary conditions can appear directly during the adjoint-state equation formulation. The proposed method is tested with 3 numerical examples concerning thermal fluid flows, but with different objectives: minimization of the mean temperature in the domain, maximization of the heat evacuated by the fluid, and maximization of the heat exchange with heated solid parts. This latter example, treated in several articles, is used to validate our method. In these optimization problems, a limitation of the maximal pressure drop and of the porosity (number of fluid elements) is also applied. The obtained results demonstrate that the method is robust and effective for solving topology optimization of thermal fluid flows.

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

NASA Astrophysics Data System (ADS)

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.

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows.

PubMed

Sanjeevi, Sathish K P; Zarghami, Ahad; Padding, Johan T

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

Essentially Entropic Lattice Boltzmann Model

NASA Astrophysics Data System (ADS)

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.

Force Evaluation in the Lattice Boltzmann Method Involving Curved Geometry

NASA Technical Reports Server (NTRS)

Mei, Renwei; Yu, Dazhi; Shyy, Wei; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum- exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second order accuracy based on our recent works. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow: Two-Dimensional Case

NASA Astrophysics Data System (ADS)

Gan, Yan-Biao; Xu, Ai-Guo; Zhang, Guang-Cai; Zhang, Ping; Zhang, Lei; Li, Ying-Jun

2008-07-01

Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.

Local shear stress and its correlation with local volume fraction in concentrated non-Brownian suspensions: Lattice Boltzmann simulation

NASA Astrophysics Data System (ADS)

Lee, Young Ki; Ahn, Kyung Hyun; Lee, Seung Jong

2014-12-01

The local shear stress of non-Brownian suspensions was investigated using the lattice Boltzmann method coupled with the smoothed profile method. Previous studies have only focused on the bulk rheology of complex fluids because the local rheology of complex fluids was not accessible due to technical limitations. In this study, the local shear stress of two-dimensional solid particle suspensions in Couette flow was investigated with the method of planes to correlate non-Newtonian fluid behavior with the structural evolution of concentrated particle suspensions. Shear thickening was successfully captured for highly concentrated suspensions at high particle Reynolds number, and both the local rheology and local structure of the suspensions were analyzed. It was also found that the linear correlation between the local particle stress and local particle volume fraction was dramatically reduced during shear thickening. These results clearly show how the change in local structure of suspensions influences the local and bulk rheology of the suspensions.

Simulation of gas flow in micro-porous media with the regularized lattice Boltzmann method

DOE PAGES

Wang, Junjian; Kang, Qinjun; Wang, Yuzhu; ...

2017-06-01

One primary challenge for prediction of gas flow in the unconventional gas reservoir at the pore-scale such as shale and tight gas reservoirs is the geometric complexity of the micro-porous media. In this paper, a regularized multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is applied to analyze gas flow in 2-dimensional micro-porous medium reconstructed by quartet structure generation set (QSGS) on pore-scale. In this paper, the velocity distribution inside the porous structure is presented and analyzed, and the effects of the porosity and specific surface area on the rarefied gas flow and apparent permeability are examined and investigated. The simulation resultsmore » indicate that the gas exhibits different flow behaviours at various pressure conditions and the gas permeability is strongly related to the pressure. Finally, the increased porosity or the decreased specific surface area leads to the increase of the gas apparent permeability, and the gas flow is more sensitive to the pore morphological properties at low-pressure conditions.« less

Wetting boundary condition for the color-gradient lattice Boltzmann method: Validation with analytical and experimental data

NASA Astrophysics Data System (ADS)

Akai, Takashi; Bijeljic, Branko; Blunt, Martin J.

2018-06-01

In the color gradient lattice Boltzmann model (CG-LBM), a fictitious-density wetting boundary condition has been widely used because of its ease of implementation. However, as we show, this may lead to inaccurate results in some cases. In this paper, a new scheme for the wetting boundary condition is proposed which can handle complicated 3D geometries. The validity of our method for static problems is demonstrated by comparing the simulated results to analytical solutions in 2D and 3D geometries with curved boundaries. Then, capillary rise simulations are performed to study dynamic problems where the three-phase contact line moves. The results are compared to experimental results in the literature (Heshmati and Piri, 2014). If a constant contact angle is assumed, the simulations agree with the analytical solution based on the Lucas-Washburn equation. However, to match the experiments, we need to implement a dynamic contact angle that varies with the flow rate.

Simulation of gas flow in micro-porous media with the regularized lattice Boltzmann method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Junjian; Kang, Qinjun; Wang, Yuzhu

One primary challenge for prediction of gas flow in the unconventional gas reservoir at the pore-scale such as shale and tight gas reservoirs is the geometric complexity of the micro-porous media. In this paper, a regularized multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is applied to analyze gas flow in 2-dimensional micro-porous medium reconstructed by quartet structure generation set (QSGS) on pore-scale. In this paper, the velocity distribution inside the porous structure is presented and analyzed, and the effects of the porosity and specific surface area on the rarefied gas flow and apparent permeability are examined and investigated. The simulation resultsmore » indicate that the gas exhibits different flow behaviours at various pressure conditions and the gas permeability is strongly related to the pressure. Finally, the increased porosity or the decreased specific surface area leads to the increase of the gas apparent permeability, and the gas flow is more sensitive to the pore morphological properties at low-pressure conditions.« less

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows

NASA Astrophysics Data System (ADS)

Sanjeevi, Sathish K. P.; Zarghami, Ahad; Padding, Johan T.

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

Flow and dispersion in anisotropic porous media: A lattice-Boltzmann study

NASA Astrophysics Data System (ADS)

Maggiolo, D.; Picano, F.; Guarnieri, M.

2016-10-01

Given their capability of spreading active chemical species and collecting electricity, porous media made of carbon fibers are extensively used as diffusion layers in energy storage systems, such as redox flow batteries. In spite of this, the dispersion dynamics of species inside porous media is still not well understood and often lends itself to different interpretations. Actually, the microscopic design of efficient porous media, which can potentially and effectively improve the performances of flow batteries, is still an open challenge. The present study aims to investigate the effect of fibrous media micro-structure on dispersion, in particular the effect of fiber orientation on drag and dispersion dynamics. Several lattice-Boltzmann simulations of flows through differently oriented fibrous media coupled with Lagrangian simulations of particle tracers have been performed. Results show that orienting fibers preferentially along the streamwise direction minimizes the drag and maximizes the dispersion, which is the most desirable condition for diffusion layers in flow batteries' applications.

Influence of thermal fluctuations on ligament break-up: a fluctuating lattice Boltzmann study

NASA Astrophysics Data System (ADS)

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.

Coupling molecular dynamics with lattice Boltzmann method based on the immersed boundary method

NASA Astrophysics Data System (ADS)

Tan, Jifu; Sinno, Talid; Diamond, Scott

2017-11-01

The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable solids exposed to flow. The code was validated with the classic problem of rigid ellipsoid particle orbit in shear flow, blood cell stretching test and effective blood viscosity, and demonstrated essentially linear scaling over 16 cores. An example of the fluid-solid coupling was given for flexible filaments (drug carriers) transport in a flowing blood cell suspensions, highlighting the advantages and capabilities of the developed code. NIH 1U01HL131053-01A1.

Lattice dynamics and thermal conductivity of lithium fluoride via first-principles calculations

NASA Astrophysics Data System (ADS)

Liang, Ting; Chen, Wen-Qi; Hu, Cui-E.; Chen, Xiang-Rong; Chen, Qi-Feng

2018-04-01

The lattice thermal conductivity of lithium fluoride (LiF) is accurately computed from a first-principles approach based on an iterative solution of the Boltzmann transport equation. Real-space finite-difference supercell approach is employed to generate the second- and third-order interatomic force constants. The related physical quantities of LiF are calculated by the second- and third- order potential interactions at 30 K-1000 K. The calculated lattice thermal conductivity 13.89 W/(m K) for LiF at room temperature agrees well with the experimental value, demonstrating that the parameter-free approach can furnish precise descriptions of the lattice thermal conductivity for this material. Besides, the Born effective charges, dielectric constants and phonon spectrum of LiF accord well with the existing data. The lattice thermal conductivities for the iterative solution of BTE are also presented.

Single curved fiber sedimentation under gravity

Treesearch

Xiaoying Rong; Dewei Qi; Junyong Zhu

2005-01-01

Dynamics of single curved fiber sedimentation under the gravity are simulated by using lattice Boltzmann method. The results of migration and rotation of the curved fiber at different Reynolds numbers are reported. The results show that the rotation and migration processes are sensitive to the curvature of the fiber.

Single curved fiber sedimentation under gravity

Treesearch

Xiaoying Rong; Dewei Qi; Guowei He; Jun Yong Zhu; Tim Scott

2008-01-01

Dynamics of single curved fiber sedimentation under gravity are simulated by using the lattice Boltzmann method. The results of migration and rotation of the curved fiber at different Reynolds numbers are reported. The results show that the rotation and migration processes are sensitive to the curvature of the fiber.

Revisiting Wiedemann-Franz law through Boltzmann transport equations and ab-initio density functional theory

NASA Astrophysics Data System (ADS)

Nag, Abhinav; Kumari, Anuja; Kumar, Jagdish

2018-05-01

We have investigated structural, electronic and transport properties of the alkali metals using ab-initio density functional theory. The electron energy dispersions are found parabolic free electron like which is expected for alkali metals. The lattice constants for all the studied metals are also in good agreement within 98% with experiments. We have further computed their transport properties using semi-classical Boltzmann transport equations with special focus on electrical and thermal conductivity. Our objective was to obtain Wiedemann-Franz law and hence Lorenz number. The motivation to do these calculations is to see that how the incorporation of different interactions such as electron-lattice, electron-electron interaction affect the Wiedeman-Franz law. By solving Boltzmann transport equations, we have obtained electrical conductivity (σ/τ) and thermal conductivity (κ0 /τ) at different temperatures and then calculated Lorenz number using L = κ0 /(σT). The obtained value of Lorenz number has been found to match with value derived for free electron Fermi gas 2.44× 10-8 WΩK-2. Our results prove that the Wiedemann-Franz law as derived for free electron gas does not change much for alkali metals, even when one incorporates interaction of electrons with atomic nuclei and other electrons. However, at lower temperatures, the Lorenz number, was found to be deviating from its theoretical value.

Simulation of Sound Waves Using the Lattice Boltzmann Method for Fluid Flow: Benchmark Cases for Outdoor Sound Propagation

PubMed Central

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. PMID:26789631

Stability and stabilization of the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Brownlee, R. A.; Gorban, A. N.; Levesley, J.

2007-03-01

We revisit the classical stability versus accuracy dilemma for the lattice Boltzmann methods (LBM). Our goal is a stable method of second-order accuracy for fluid dynamics based on the lattice Bhatnager-Gross-Krook method (LBGK). The LBGK scheme can be recognized as a discrete dynamical system generated by free flight and entropic involution. In this framework the stability and accuracy analysis are more natural. We find the necessary and sufficient conditions for second-order accurate fluid dynamics modeling. In particular, it is proven that in order to guarantee second-order accuracy the distribution should belong to a distinguished surface—the invariant film (up to second order in the time step). This surface is the trajectory of the (quasi)equilibrium distribution surface under free flight. The main instability mechanisms are identified. The simplest recipes for stabilization add no artificial dissipation (up to second order) and provide second-order accuracy of the method. Two other prescriptions add some artificial dissipation locally and prevent the system from loss of positivity and local blowup. Demonstration of the proposed stable LBGK schemes are provided by the numerical simulation of a one-dimensional (1D) shock tube and the unsteady 2D flow around a square cylinder up to Reynolds number Rẽ20000 .

Simulation of Sound Waves Using the Lattice Boltzmann Method for Fluid Flow: Benchmark Cases for Outdoor Sound Propagation.

PubMed

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.

Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations

NASA Astrophysics Data System (ADS)

Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen

2015-04-01

This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive, nevertheless, the present GKUAs for kinetic model Boltzmann equations in conjunction with current available high-performance parallel computer power can provide a vital engineering tool for analyzing rarefied gas flows covering the whole range of flow regimes in aerospace engineering applications.

Basic properties of lattices of cubes, algorithms for their construction, and application capabilities in discrete optimization

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2015-01-01

The basic properties of a new type of lattices—a lattice of cubes—are described. It is shown that, with a suitable choice of union and intersection operations, the set of all subcubes of an N-cube forms a lattice, which is called a lattice of cubes. Algorithms for constructing such lattices are described, and the results produced by these algorithms in the case of lattices of various dimensions are illustrated. It is proved that a lattice of cubes is a lattice with supplements, which makes it possible to minimize and maximize supermodular functions on it. Examples of such functions are given. The possibility of applying previously developed efficient optimization algorithms to the formulation and solution of new classes of problems on lattices of cubes.

Stochastic reaction-diffusion algorithms for macromolecular crowding

NASA Astrophysics Data System (ADS)

Sturrock, Marc

2016-06-01

Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.

Efficient LBM visual simulation on face-centered cubic lattices.

PubMed

Petkov, Kaloian; Qiu, Feng; Fan, Zhe; Kaufman, Arie E; Mueller, Klaus

2009-01-01

The Lattice Boltzmann method (LBM) for visual simulation of fluid flow generally employs cubic Cartesian (CC) lattices such as the D3Q13 and D3Q19 lattices for the particle transport. However, the CC lattices lead to suboptimal representation of the simulation space. We introduce the face-centered cubic (FCC) lattice, fD3Q13, for LBM simulations. Compared to the CC lattices, the fD3Q13 lattice creates a more isotropic sampling of the simulation domain and its single lattice speed (i.e., link length) simplifies the computations and data storage. Furthermore, the fD3Q13 lattice can be decomposed into two independent interleaved lattices, one of which can be discarded, which doubles the simulation speed. The resulting LBM simulation can be efficiently mapped to the GPU, further increasing the computational performance. We show the numerical advantages of the FCC lattice on channeled flow in 2D and the flow-past-a-sphere benchmark in 3D. In both cases, the comparison is against the corresponding CC lattices using the analytical solutions for the systems as well as velocity field visualizations. We also demonstrate the performance advantages of the fD3Q13 lattice for interactive simulation and rendering of hot smoke in an urban environment using thermal LBM.

Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm

NASA Astrophysics Data System (ADS)

Backes, Werner; Wetzel, Susanne

In this paper, we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Our new, multi-threaded algorithm is the first to provide an efficient, parallel implementation of the Schorr-Euchner algorithm for today’s multi-processor, multi-core computer architectures. Experiments with sparse and dense lattice bases show a speed-up factor of about 1.8 for the 2-thread and about factor 3.2 for the 4-thread version of our new parallel lattice basis reduction algorithm in comparison to the traditional non-parallel algorithm.

Study on distributed generation algorithm of variable precision concept lattice based on ontology heterogeneous database

NASA Astrophysics Data System (ADS)

WANG, Qingrong; ZHU, Changfeng

2017-06-01

Integration of distributed heterogeneous data sources is the key issues under the big data applications. In this paper the strategy of variable precision is introduced to the concept lattice, and the one-to-one mapping mode of variable precision concept lattice and ontology concept lattice is constructed to produce the local ontology by constructing the variable precision concept lattice for each subsystem, and the distributed generation algorithm of variable precision concept lattice based on ontology heterogeneous database is proposed to draw support from the special relationship between concept lattice and ontology construction. Finally, based on the standard of main concept lattice of the existing heterogeneous database generated, a case study has been carried out in order to testify the feasibility and validity of this algorithm, and the differences between the main concept lattice and the standard concept lattice are compared. Analysis results show that this algorithm above-mentioned can automatically process the construction process of distributed concept lattice under the heterogeneous data sources.

Fast algorithms for chiral fermions in 2 dimensions

NASA Astrophysics Data System (ADS)

Hyka (Xhako), Dafina; Osmanaj (Zeqirllari), Rudina

2018-03-01

In lattice QCD simulations the formulation of the theory in lattice should be chiral in order that symmetry breaking happens dynamically from interactions. In order to guarantee this symmetry on the lattice one uses overlap and domain wall fermions. On the other hand high computational cost of lattice QCD simulations with overlap or domain wall fermions remains a major obstacle of research in the field of elementary particles. We have developed the preconditioned GMRESR algorithm as fast inverting algorithm for chiral fermions in U(1) lattice gauge theory. In this algorithm we used the geometric multigrid idea along the extra dimension.The main result of this work is that the preconditioned GMRESR is capable to accelerate the convergence 2 to 12 times faster than the other optimal algorithms (SHUMR) for different coupling constant and lattice 32x32. Also, in this paper we tested it for larger lattice size 64x64. From the results of simulations we can see that our algorithm is faster than SHUMR. This is a very promising result that this algorithm can be adapted also in 4 dimension.

Characterization and visualization of RNA secondary structure Boltzmann ensemble via information theory.

PubMed

Lin, Luan; McKerrow, Wilson H; Richards, Bryce; Phonsom, Chukiat; Lawrence, Charles E

2018-03-05

The nearest neighbor model and associated dynamic programming algorithms allow for the efficient estimation of the RNA secondary structure Boltzmann ensemble. However because a given RNA secondary structure only contains a fraction of the possible helices that could form from a given sequence, the Boltzmann ensemble is multimodal. Several methods exist for clustering structures and finding those modes. However less focus is given to exploring the underlying reasons for this multimodality: the presence of conflicting basepairs. Information theory, or more specifically mutual information, provides a method to identify those basepairs that are key to the secondary structure. To this end we find most informative basepairs and visualize the effect of these basepairs on the secondary structure. Knowing whether a most informative basepair is present tells us not only the status of the particular pair but also provides a large amount of information about which other pairs are present or not present. We find that a few basepairs account for a large amount of the structural uncertainty. The identification of these pairs indicates small changes to sequence or stability that will have a large effect on structure. We provide a novel algorithm that uses mutual information to identify the key basepairs that lead to a multimodal Boltzmann distribution. We then visualize the effect of these pairs on the overall Boltzmann ensemble.

Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Safari, Hesameddin; Rahimian, Mohammad Hassan; Krafczyk, Manfred

2014-09-01

In the present article, we extend and generalize our previous article [H. Safari, M. H. Rahimian, and M. Krafczyk, Phys. Rev. E 88, 013304 (2013), 10.1103/PhysRevE.88.013304] to include the gradient of the vapor concentration at the liquid-vapor interface as the driving force for vaporization allowing the evaporation from the phase interface to work for arbitrary temperatures. The lattice Boltzmann phase-field multiphase modeling approach with a suitable source term, accounting for the effect of the phase change on the velocity field, is used to solve the two-phase flow field. The modified convective Cahn-Hilliard equation is employed to reconstruct the dynamics of the interface topology. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius-Clapeyron correlation. Numerous validation tests including one-dimensional and two-dimensional cases are carried out to demonstrate the consistency of the presented model. Results show that the model is able to predict the flow features around and inside an evaporating droplet quantitatively in quiescent as well as convective environments.

Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method.

PubMed

Safari, Hesameddin; Rahimian, Mohammad Hassan; Krafczyk, Manfred

2014-09-01

In the present article, we extend and generalize our previous article [H. Safari, M. H. Rahimian, and M. Krafczyk, Phys. Rev. E 88, 013304 (2013)] to include the gradient of the vapor concentration at the liquid-vapor interface as the driving force for vaporization allowing the evaporation from the phase interface to work for arbitrary temperatures. The lattice Boltzmann phase-field multiphase modeling approach with a suitable source term, accounting for the effect of the phase change on the velocity field, is used to solve the two-phase flow field. The modified convective Cahn-Hilliard equation is employed to reconstruct the dynamics of the interface topology. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius-Clapeyron correlation. Numerous validation tests including one-dimensional and two-dimensional cases are carried out to demonstrate the consistency of the presented model. Results show that the model is able to predict the flow features around and inside an evaporating droplet quantitatively in quiescent as well as convective environments.

An Improved Lattice Boltzmann Model for Non-Newtonian Flows with Applications to Solid-Fluid Interactions in External Flows

NASA Astrophysics Data System (ADS)

Adam, Saad; Premnath, Kannan

2016-11-01

Fluid mechanics of non-Newtonian fluids, which arise in numerous settings, are characterized by non-linear constitutive models that pose certain unique challenges for computational methods. Here, we consider the lattice Boltzmann method (LBM), which offers some computational advantages due to its kinetic basis and its simpler stream-and-collide procedure enabling efficient simulations. However, further improvements are necessary to improve its numerical stability and accuracy for computations involving broader parameter ranges. Hence, in this study, we extend the cascaded LBM formulation by modifying its moment equilibria and relaxation parameters to handle a variety of non-Newtonian constitutive equations, including power-law and Bingham fluids, with improved stability. In addition, we include corrections to the moment equilibria to obtain an inertial frame invariant scheme without cubic-velocity defects. After preforming its validation study for various benchmark flows, we study the physics of non-Newtonian flow over pairs of circular and square cylinders in a tandem arrangement, especially the wake structure interactions and their effects on resulting forces in each cylinder, and elucidate the effect of the various characteristic parameters.

Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport

DOE PAGES

Yan, Zhifeng; Yang, Xiaofan; Li, Siliang; ...

2017-09-05

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.more » 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. Finally, 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.« less

An efficient and accurate framework for calculating lattice thermal conductivity of solids: AFLOW—AAPL Automatic Anharmonic Phonon Library

NASA Astrophysics Data System (ADS)

Plata, Jose J.; Nath, Pinku; Usanmaz, Demet; Carrete, Jesús; Toher, Cormac; de Jong, Maarten; Asta, Mark; Fornari, Marco; Nardelli, Marco Buongiorno; Curtarolo, Stefano

2017-10-01

One of the most accurate approaches for calculating lattice thermal conductivity, , is solving the Boltzmann transport equation starting from third-order anharmonic force constants. In addition to the underlying approximations of ab-initio parameterization, two main challenges are associated with this path: high computational costs and lack of automation in the frameworks using this methodology, which affect the discovery rate of novel materials with ad-hoc properties. Here, the Automatic Anharmonic Phonon Library (AAPL) is presented. It efficiently computes interatomic force constants by making effective use of crystal symmetry analysis, it solves the Boltzmann transport equation to obtain , and allows a fully integrated operation with minimum user intervention, a rational addition to the current high-throughput accelerated materials development framework AFLOW. An "experiment vs. theory" study of the approach is shown, comparing accuracy and speed with respect to other available packages, and for materials characterized by strong electron localization and correlation. Combining AAPL with the pseudo-hybrid functional ACBN0 is possible to improve accuracy without increasing computational requirements.

Effects of deformability of RBCs on their dynamics and blood flow passing through a stenosed microvessel: an immersed boundary-lattice Boltzmann approach

NASA Astrophysics Data System (ADS)

Alizadeh, As'ad; Dadvand, Abdolrahman

2018-02-01

In this paper, the motion of high deformable (healthy) and low deformable (sick) red blood cells in a microvessel with and without stenosis is simulated using a combined lattice Boltzmann-immersed boundary method. The RBC is considered as neo-Hookean elastic membrane with bending resistance. The motion and deformation of the RBC under different values of the Reynolds number are evaluated. In addition, the variations of blood flow resistance and time-averaged pressure due to the motion and deformation of the RBC are assessed. It was found that a healthy RBC moves faster than a sick one. The apparent viscosity and blood flow resistance are greater for the case involving the sick RBC. Blood pressure at the presence of stenosis and low deformable RBC increases, which is thought of as the reason of many serious diseases including cardiovascular diseases. As the Re number increases, the RBC deforms further and moves easier and faster through the stenosis. The results of this study were compared to the available experimental and numerical results, and good agreements were observed.

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

NASA Astrophysics Data System (ADS)

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.

LBM-EP: Lattice-Boltzmann method for fast cardiac electrophysiology simulation from 3D images.

PubMed

Rapaka, S; Mansi, T; Georgescu, B; Pop, M; Wright, G A; Kamen, A; Comaniciu, Dorin

2012-01-01

Current treatments of heart rhythm troubles require careful planning and guidance for optimal outcomes. Computational models of cardiac electrophysiology are being proposed for therapy planning but current approaches are either too simplified or too computationally intensive for patient-specific simulations in clinical practice. This paper presents a novel approach, LBM-EP, to solve any type of mono-domain cardiac electrophysiology models at near real-time that is especially tailored for patient-specific simulations. The domain is discretized on a Cartesian grid with a level-set representation of patient's heart geometry, previously estimated from images automatically. The cell model is calculated node-wise, while the transmembrane potential is diffused using Lattice-Boltzmann method within the domain defined by the level-set. Experiments on synthetic cases, on a data set from CESC'10 and on one patient with myocardium scar showed that LBM-EP provides results comparable to an FEM implementation, while being 10 - 45 times faster. Fast, accurate, scalable and requiring no specific meshing, LBM-EP paves the way to efficient and detailed models of cardiac electrophysiology for therapy planning.

Axisymmetric Lattice Boltzmann Model of Droplet Impact on Solid Surfaces

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem

PubMed Central

Abas, Aizat; Mokhtar, N. Hafizah; Ishak, M. H. H.; Abdullah, M. Z.; Ho Tian, Ang

2016-01-01

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. PMID:27239221

A direct force model for Galilean invariant lattice Boltzmann simulation of fluid-particle flows

NASA Astrophysics Data System (ADS)

Tao, Shi; He, Qing; Chen, Baiman; Yang, Xiaoping; Huang, Simin

The lattice Boltzmann method (LBM) has been widely used in the simulation of particulate flows involving complex moving boundaries. Due to the kinetic background of LBM, the bounce-back (BB) rule and the momentum exchange (ME) method can be easily applied to the solid boundary treatment and the evaluation of fluid-solid interaction force, respectively. However, recently it has been found that both the BB and ME schemes may violate the principle of Galilean invariance (GI). Some modified BB and ME methods have been proposed to reduce the GI error. But these remedies have been recognized subsequently to be inconsistent with Newton’s Third Law. Therefore, contrary to those corrections based on the BB and ME methods, a unified iterative approach is adopted to handle the solid boundary in the present study. Furthermore, a direct force (DF) scheme is proposed to evaluate the fluid-particle interaction force. The methods preserve the efficiency of the BB and ME schemes, and the performance on the accuracy and GI is verified and validated in the test cases of particulate flows with freely moving particles.

Lattice Boltzmann Simulation Optimization on Leading Multicore Platforms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Samuel; Carter, Jonathan; Oliker, Leonid

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 LBMHDmore » 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.« less

Lattice Boltzmann simulation optimization on leading multicore platforms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, S.; Carter, J.; Oliker, L.

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 LBMHDmore » 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.« less

Flow and Sedimentation of particulate suspensions in Fractures

NASA Astrophysics Data System (ADS)

Lo, Tak Shing; Koplik, Joel

2011-03-01

Suspended particles are commonly found in reservoir fluids. They alter the rheology of the flowing liquids and may obstruct transport by narrowing flow channels due to gravitational sedimentation. An understanding of the dynamics of particle transport and deposition is, therefore, important to many geological, enviromental and industrial processes. Realistic geological fractures usually have irregular surfaces with self-affine structures, and the surface roughness plays a crucial role in the flow and sedimentation processes. Recently, we have used the lattice Boltzmann method to study the combined effects of sedimentation and transport of particles suspended in a Newtonian fluid in a pressure-driven flow in self-affine channels, which is especially relevant to clogging phenomena where sediments may block fluid flows in narrow constrictions of the channels. The lattice Boltzmann method is flexible and particularly suitable for handling irregular geometry. Our work covers a broad range in Reynolds and buoyancy numbers, and in particle concentrations. In this talk, we focus on the transitions between the ``jammed'' and the ``flow'' states in fractures, and on the effects of nonuniform particle size distributions. Work supported by DOE and NERSC.

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

NASA Astrophysics Data System (ADS)

Zhuo, Congshan; Zhong, Chengwen

2016-11-01

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB-LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Reτ of 180. The turbulence statistics computed from the present FMLB-LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB-D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.

Extension of lattice Boltzmann flux solver for simulation of compressible multi-component flows

NASA Astrophysics Data System (ADS)

Yang, Li-Ming; Shu, Chang; Yang, Wen-Ming; Wang, Yan

2018-05-01

The lattice Boltzmann flux solver (LBFS), which was presented by Shu and his coworkers for solving compressible fluid flow problems, is extended to simulate compressible multi-component flows in this work. To solve the two-phase gas-liquid problems, the model equations with stiffened gas equation of state are adopted. In this model, two additional non-conservative equations are introduced to represent the material interfaces, apart from the classical Euler equations. We first convert the interface equations into the full conservative form by applying the mass equation. After that, we calculate the numerical fluxes of the classical Euler equations by the existing LBFS and the numerical fluxes of the interface equations by the passive scalar approach. Once all the numerical fluxes at the cell interface are obtained, the conservative variables at cell centers can be updated by marching the equations in time and the material interfaces can be identified via the distributions of the additional variables. The numerical accuracy and stability of present scheme are validated by its application to several compressible multi-component fluid flow problems.

Two-Relaxation-Time Lattice Boltzmann Method and its Application to Advective-Diffusive-Reactive Transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Zhifeng; Yang, Xiaofan; Li, Siliang

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.more » 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. Finally, 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.« less

Acoustic equations of state for simple lattice Boltzmann velocity sets.

PubMed

Viggen, Erlend Magnus

2014-07-01

The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξ(iα)∈(-1,0,1) for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.

Consistent lattice Boltzmann methods for incompressible axisymmetric flows

NASA Astrophysics Data System (ADS)

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei

2016-08-01

In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.

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

NASA Astrophysics Data System (ADS)

Zheng, Lin; Zheng, Song; Zhai, Qinglan

2016-02-01

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.

Stable lattice Boltzmann model for Maxwell equations in media

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann heat transfer model for permeable voxels

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann Simulation of Shale Gas Transport in Organic Nano-Pores

PubMed Central

Zhang, Xiaoling; Xiao, Lizhi; Shan, Xiaowen; Guo, Long

2014-01-01

Permeability is a key parameter for investigating the flow ability of sedimentary rocks. The conventional model for calculating permeability is derived from Darcy's law, which is valid only for continuum flow in porous rocks. We discussed the feasibility of simulating methane transport characteristics in the organic nano-pores of shale through the Lattice Boltzmann method (LBM). As a first attempt, the effects of high Knudsen number and the associated slip flow are considered, whereas the effect of adsorption in the capillary tube is left for future work. Simulation results show that at small Knudsen number, LBM results agree well with Poiseuille's law, and flow rate (flow capacity) is proportional to the square of the pore scale. At higher Knudsen numbers, the relaxation time needs to be corrected. In addition, velocity increases as the slip effect causes non negligible velocities on the pore wall, thereby enhancing the flow rate inside the pore, i.e., the permeability. Therefore, the LBM simulation of gas flow characteristics in organic nano-pores provides an effective way of evaluating the permeability of gas-bearing shale. PMID:24784022

Multiple-relaxation-time lattice Boltzmann study of the magnetic field effects on natural convection of non-Newtonian fluids

NASA Astrophysics Data System (ADS)

Yang, Xuguang; Wang, Lei

In this paper, the magnetic field effects on natural convection of power-law non-Newtonian fluids in rectangular enclosures are numerically studied by the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). To maintain the locality of the LBM, a local computing scheme for shear rate is used. Thus, all simulations can be easily performed on the Graphics Processing Unit (GPU) using NVIDIA’s CUDA, and high computational efficiency can be achieved. The numerical simulations presented here span a wide range of thermal Rayleigh number (104≤Ra≤106), Hartmann number (0≤Ha≤20), power-law index (0.5≤n≤1.5) and aspect ratio (0.25≤AR≤4.0) to identify the different flow patterns and temperature distributions. The results show that the heat transfer rate is increased with the increase of thermal Rayleigh number, while it is decreased with the increase of Hartmann number, and the average Nusselt number is found to decrease with an increase in the power-law index. Moreover, the effects of aspect ratio have also investigated in detail.

Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring

NASA Astrophysics Data System (ADS)

Zhang, Rui; Roberts, Tyler; Aranson, Igor S.; de Pablo, Juan J.

2016-02-01

Liquid crystals (LCs) display many of the flow characteristics of liquids but exhibit long range orientational order. In the nematic phase, the coupling of structure and flow leads to complex hydrodynamic effects that remain to be fully elucidated. Here, we consider the hydrodynamics of a nematic LC in a hybrid cell, where opposite walls have conflicting anchoring boundary conditions, and we employ a 3D lattice Boltzmann method to simulate the time-dependent flow patterns that can arise. Due to the symmetry breaking of the director field within the hybrid cell, we observe that at low to moderate shear rates, the volumetric flow rate under Couette and Poiseuille flows is different for opposite flow directions. At high shear rates, the director field may undergo a topological transition which leads to symmetric flows. By applying an oscillatory pressure gradient to the channel, a net volumetric flow rate is found to depend on the magnitude and frequency of the oscillation, as well as the anchoring strength. Taken together, our findings suggest several intriguing new applications for LCs in microfluidic devices.

Dynamics of an acoustically levitated particle using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Barrios, G.; Rechtman, R.

When the acoustic force inside a cavity balances the gravitational force on a particle the result is known as acoustic levitation. Using the lattice Boltzmann equation method we find the acoustic force acting on a rounded particle for two different single-axis acoustic levitators in two dimensions, the first with plane waves, the second with a rounded reflector that enhances the acoustic force. With no gravitational force, a particle oscillates around a pressure node; in the presence of gravity the oscillation is shifted a small vertical distance below the pressure node. This distance increases linearly as the density ratio between the solid particle and fluid grows. For both cavities, the particle oscillates with the frequency of the sound source and its harmonics and in some cases there is a much smaller second dominant frequency. When the momentum of the acoustic source changes, the oscillation around the average vertical position can have both frequencies mentioned above. However, if this quantity is large enough, the oscillations of the particle are aperiodic in the cavity with a rounded reflector.

Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains.

PubMed

Nash, Rupert W; Carver, Hywel B; Bernabeu, Miguel O; Hetherington, James; Groen, Derek; Krüger, Timm; Coveney, Peter V

2014-02-01

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002); Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001); Junk and Yang, Phys. Rev. E 72, 066701 (2005)] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices

NASA Astrophysics Data System (ADS)

Janse van Rensburg, E. J.; Rechnitzer, A.

2011-04-01

In this paper, the elementary moves of the BFACF-algorithm (Aragão de Carvalho and Caracciolo 1983 Phys. Rev. B 27 1635-45, Aragão de Carvalho and Caracciolo 1983 Nucl. Phys. B 215 209-48, Berg and Foester 1981 Phys. Lett. B 106 323-6) for lattice polygons are generalized to elementary moves of BFACF-style algorithms for lattice polygons in the body-centered (BCC) and face-centered (FCC) cubic lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC lattices and so expand a similar result for the cubic lattice (see Janse van Rensburg and Whittington (1991 J. Phys. A: Math. Gen. 24 5553-67)). Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC lattices.

Effects of surface roughness and electrokinetic heterogeneity on electroosmotic flow in microchannel

NASA Astrophysics Data System (ADS)

Masilamani, Kannan; Ganguly, Suvankar; Feichtinger, Christian; Bartuschat, Dominik; Rüde, Ulrich

2015-06-01

In this paper, a hybrid lattice-Boltzmann and finite-difference (LB-FD) model is applied to simulate the effects of three-dimensional surface roughness and electrokinetic heterogeneity on electroosmotic flow (EOF) in a microchannel. The lattice-Boltzmann (LB) method has been employed to obtain the flow field and a finite-difference (FD) method is used to solve the Poisson-Boltzmann (PB) equation for the electrostatic potential distribution. Numerical simulation of flow through a square cross-section microchannel with designed roughness is conducted and the results are critically analysed. The effects of surface heterogeneity on the electroosmotic transport are investigated for different roughness height, width, roughness interval spacing, and roughness surface potential. Numerical simulations reveal that the presence of surface roughness changes the nature of electroosmotic transport through the microchannel. It is found that the electroosmotic velocity decreases with the increase in roughness height and the velocity profile becomes asymmetric. For the same height of the roughness elements, the EOF velocity rises with the increase in roughness width. For the heterogeneously charged rough channel, the velocity profile shows a distinct deviation from the conventional plug-like flow pattern. The simulation results also indicate locally induced flow vortices which can be utilized to enhance the flow and mixing within the microchannel. The present study has important implications towards electrokinetic flow control in the microchannel, and can provide an efficient way to design a microfluidic system of practical interest.

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

NASA Astrophysics Data System (ADS)

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 Boltzmann method framework. Simulations can be run in single or double precision using one or more GPUs. Restrictions: The lattice Boltzmann method works for low Mach number flows only. Unusual features: The actual numerical calculations run exclusively on GPUs. The numerical code is built dynamically at run-time in CUDA C or OpenCL, using templates and symbolic formulas. The high-level control of the simulation is maintained by a Python process. Additional comments: !!!!! The distribution file for this program is over 45 Mbytes and therefore is not delivered directly when Download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. !!!!! Running time: Problem-dependent, typically minutes (for small cases or short simulations) to hours (large cases or long simulations).

GPUs in a computational physics course

NASA Astrophysics Data System (ADS)

Adler, Joan; Nissim, Gal; Kiswani, Ahmad

2017-10-01

In an introductory computational physics class of the type that many of us give, time constraints lead to hard choices on topics. Everyone likes to include their own research in such a class but an overview of many areas is paramount. Parallel programming algorithms using MPI is one important topic. Both the principle and the need to break the “fear barrier” of using a large machine with a queuing system via ssh must be sucessfully passed on. Due to the plateau in chip development and to power considerations future HPC hardware choices will include heavy use of GPUs. Thus the need to introduce these at the level of an introductory course has arisen. Just as for parallel coding, explanation of the benefits and simple examples to guide the hesitant first time user should be selected. Several student projects using GPUs that include how-to pages were proposed at the Technion. Two of the more successful ones were lattice Boltzmann and a finite element code, and we present these in detail.

Conjugate heat and mass transfer in the lattice Boltzmann equation method.

PubMed

Li, Like; Chen, Chen; Mei, Renwei; Klausner, James F

2014-04-01

An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer in porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved interfaces, the present treatment yields second-order accurate interior and interfacial temperatures (concentrations) and first-order accurate interfacial heat (mass) flux. An increase of order of convergence by one degree is obtained for each of these three quantities compared with the half-lattice division scheme. The surface-averaged Sherwood numbers computed in test (iv) agree well with published results.

Conjugate heat and mass transfer in the lattice Boltzmann equation method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, LK; Chen, C; Mei, RW

2014-04-22

An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer inmore » porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved interfaces, the present treatment yields second-order accurate interior and interfacial temperatures (concentrations) and first-order accurate interfacial heat (mass) flux. An increase of order of convergence by one degree is obtained for each of these three quantities compared with the half-lattice division scheme. The surface-averaged Sherwood numbers computed in test (iv) agree well with published results.« less

Learning algorithm in restricted Boltzmann machines using Kullback-Leibler importance estimation procedure

NASA Astrophysics Data System (ADS)

Yasuda, Muneki; Sakurai, Tetsuharu; Tanaka, Kazuyuki

Restricted Boltzmann machines (RBMs) are bipartite structured statistical neural networks and consist of two layers. One of them is a layer of visible units and the other one is a layer of hidden units. In each layer, any units do not connect to each other. RBMs have high flexibility and rich structure and have been expected to applied to various applications, for example, image and pattern recognitions, face detections and so on. However, most of computational models in RBMs are intractable and often belong to the class of NP-hard problem. In this paper, in order to construct a practical learning algorithm for them, we employ the Kullback-Leibler Importance Estimation Procedure (KLIEP) to RBMs, and give a new scheme of practical approximate learning algorithm for RBMs based on the KLIEP.

Lattice gas models for particle systems in an underdamped hopping regime

NASA Astrophysics Data System (ADS)

Gobron, Thierry

A model in which the state of the particle is described by a multicomponent vector, each possible kinetic state for the particle being associated with one of the components is presented. A master equation describes the evolution of the probability distribution in an independent particle model. From the master equation and with the help of the symmetry group that leaves the state transition operator invariant, physical quantities such as the diffusion constant are explicitly calculated for several lattices in one, two, and three dimensions. A Boltzmann equation is established and compared to the Rice and Roth proposal.

Density waves in granular flow

NASA Astrophysics Data System (ADS)

Herrmann, H. J.; Flekkøy, E.; Nagel, K.; Peng, G.; Ristow, G.

Ample experimental evidence has shown the existence of spontaneous density waves in granular material flowing through pipes or hoppers. Using Molecular Dynamics Simulations we show that several types of waves exist and find that these density fluctuations follow a 1/f spectrum. We compare this behaviour to deterministic one-dimensional traffic models. If positions and velocities are continuous variables the model shows self-organized criticality driven by the slowest car. We also present Lattice Gas and Boltzmann Lattice Models which reproduce the experimentally observed effects. Density waves are spontaneously generated when the viscosity has a nonlinear dependence on density which characterizes granular flow.

The power of neural nets

NASA Technical Reports Server (NTRS)

Ryan, J. P.; Shah, B. H.

1987-01-01

Implementation of the Hopfield net which is used in the image processing type of applications where only partial information about the image may be available is discussed. The image classification type of algorithm of Hopfield and other learning algorithms, such as the Boltzmann machine and the back-propagation training algorithm, have many vital applications in space.

Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains

NASA Astrophysics Data System (ADS)

Nash, Rupert W.; Carver, Hywel B.; Bernabeu, Miguel O.; Hetherington, James; Groen, Derek; Krüger, Timm; Coveney, Peter V.

2014-02-01

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002), 10.1063/1.1471914; Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001), 10.1063/1.1399290; Junk and Yang, Phys. Rev. E 72, 066701 (2005), 10.1103/PhysRevE.72.066701] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

Low lattice thermal conductivity of stanene

NASA Astrophysics Data System (ADS)

Peng, Bo; Zhang, Hao; Shao, Hezhu; Xu, Yuchen; Zhang, Xiangchao; Zhu, Heyuan

2016-02-01

A fundamental understanding of phonon transport in stanene is crucial to predict the thermal performance in potential stanene-based devices. By combining first-principle calculation and phonon Boltzmann transport equation, we obtain the lattice thermal conductivity of stanene. A much lower thermal conductivity (11.6 W/mK) is observed in stanene, which indicates higher thermoelectric efficiency over other 2D materials. The contributions of acoustic and optical phonons to the lattice thermal conductivity are evaluated. Detailed analysis of phase space for three-phonon processes shows that phonon scattering channels LA + LA/TA/ZA ↔ TA/ZA are restricted, leading to the dominant contributions of high-group-velocity LA phonons to the thermal conductivity. The size dependence of thermal conductivity is investigated as well for the purpose of the design of thermoelectric nanostructures.

Using Mathematics to Make Computing on Encrypted Data Secure and Practical

DTIC Science & Technology

2015-12-01

LLL) lattice basis reduction algorithm, G-Lattice, Cryptography , Security, Gentry-Szydlo Algorithm, Ring-LWE 16. SECURITY CLASSIFICATION OF: 17...with symmetry be further developed, in order to quantify the security of lattice-based cryptography , including especially the security of homomorphic...the Gentry-Szydlo algorithm, and the ideas should be applicable to a range of questions in cryptography . The new algorithm of Lenstra and Silverberg

GPU accelerated edge-region based level set evolution constrained by 2D gray-scale histogram.

PubMed

Balla-Arabé, Souleymane; Gao, Xinbo; Wang, Bin

2013-07-01

Due to its intrinsic nature which allows to easily handle complex shapes and topological changes, the level set method (LSM) has been widely used in image segmentation. Nevertheless, LSM is computationally expensive, which limits its applications in real-time systems. For this purpose, we propose a new level set algorithm, which uses simultaneously edge, region, and 2D histogram information in order to efficiently segment objects of interest in a given scene. The computational complexity of the proposed LSM is greatly reduced by using the highly parallelizable lattice Boltzmann method (LBM) with a body force to solve the level set equation (LSE). The body force is the link with image data and is defined from the proposed LSE. The proposed LSM is then implemented using an NVIDIA graphics processing units to fully take advantage of the LBM local nature. The new algorithm is effective, robust against noise, independent to the initial contour, fast, and highly parallelizable. The edge and region information enable to detect objects with and without edges, and the 2D histogram information enable the effectiveness of the method in a noisy environment. Experimental results on synthetic and real images demonstrate subjectively and objectively the performance of the proposed method.

Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Zhihui; Ma, Qiang; Wu, Junlin

2014-12-09

Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinatemore » points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.« less

Simulation of blood flow using extended Boltzmann kinetic approach

NASA Astrophysics Data System (ADS)

Chen, Caixia; Chen, Hudong; Freed, David; Shock, Richard; Staroselsky, Ilya; Zhang, Raoyang; Ümit Coşkun, A.; Stone, Peter H.; Feldman, Charles L.

2006-03-01

Lattice Boltzmann (LB) simulations are conducted to obtain the detailed hydrodynamics in a variety of blood vessel setups, including a prototype stented channel and four human coronary artery geometries based on the images obtained from real patients. For a model of stented flow involving an S-shape stent, a pulsatile flow rate is applied as the inlet boundary condition, and the time- and space-dependent flow field is computed. The LB simulation is found to reproduce the analytical solutions for the velocity profiles and wall shear stress distributions for the pulsatile channel flow. For the coronary arteries, the distributions of wall shear stress, which is important for clinical diagnostic purposes, are in good agreement with the conventional CFD predictions.

Kinetic solvers with adaptive mesh in phase space

NASA Astrophysics Data System (ADS)

Arslanbekov, Robert R.; Kolobov, Vladimir I.; Frolova, Anna A.

2013-12-01

An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a “tree of trees” (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.

Kinetic solvers with adaptive mesh in phase space.

PubMed

Arslanbekov, Robert R; Kolobov, Vladimir I; Frolova, Anna A

2013-12-01

An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a "tree of trees" (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.

Emergent dynamic structures and statistical law in spherical lattice gas automata.

PubMed

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

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann modeling to explain volcano acoustic source.

PubMed

Brogi, Federico; Ripepe, Maurizio; Bonadonna, Costanza

2018-06-22

Acoustic pressure is largely used to monitor explosive activity at volcanoes and has become one of the most promising technique to monitor volcanoes also at large scale. However, no clear relation between the fluid dynamics of explosive eruptions and the associated acoustic signals has yet been defined. Linear acoustic has been applied to derive source parameters in the case of strong explosive eruptions which are well-known to be driven by large overpressure of the magmatic fluids. Asymmetric acoustic waveforms are generally considered as the evidence for supersonic explosive dynamics also for small explosive regimes. We have used Lattice-Boltzmann modeling of the eruptive fluid dynamics to analyse the acoustic wavefield produced by different flow regimes. We demonstrate that acoustic waveform well reproduces the flow dynamics of a subsonic fluid injection related to discrete explosive events. Different volumetric flow rate, at low-Mach regimes, can explain both the observed symmetric and asymmetric waveform. Hence, asymmetric waveforms are not necessarily related to the shock/supersonic fluid dynamics of the source. As a result, we highlight an ambiguity in the general interpretation of volcano acoustic signals for the retrieval of key eruption source parameters, necessary for a reliable volcanic hazard assessment.

Dynamic behaviors of liquid droplets on a gas diffusion layer surface: Hybrid lattice Boltzmann investigation

NASA Astrophysics Data System (ADS)

Wu, Jie; Huang, Jun-Jie

2015-07-01

Water management is one of the key issues in proton exchange membrane fuel cells. Fundamentally, it is related to dynamic behaviors of droplets on a gas diffusion layer (GDL) surface, and consequently they are investigated in this work. A two-dimensional hybrid method is employed to implement numerical simulations, in which the flow field is solved by using the lattice Boltzmann method and the interface between droplet and gas is captured by solving the Cahn-Hilliard equation directly. One or two liquid droplets are initially placed on the GDL surface of a gas channel, which is driven by the fully developed Poiseuille flow. At a fixed channel size, the effects of viscosity ratio of droplet to gas ( μ ∗ ), Capillary number (Ca, ratio of gas viscosity to surface tension), and droplet interaction on the dynamic behaviors of droplets are systematically studied. By decreasing viscosity ratio or increasing Capillary number, the single droplet can detach from the GDL surface easily. On the other hand, when two identical droplets stay close to each other or a larger droplet is placed in front of a smaller droplet, the removal of two droplets is promoted.

Hovering and targeting flight simulations of a dragonfly-like flapping wing-body model by the immersed boundary-lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Hirohashi, Kensuke; Inamuro, Takaji

2017-08-01

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.

Modeling mass transfer and reaction of dilute solutes in a ternary phase system by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Fu, Yu-Hang; Bai, Lin; Luo, Kai-Hong; Jin, Yong; Cheng, Yi

2017-04-01

In this work, we propose a general approach for modeling mass transfer and reaction of dilute solute(s) in incompressible three-phase flows by introducing a collision operator in lattice Boltzmann (LB) method. An LB equation was used to simulate the solute dynamics among three different fluids, in which the newly expanded collision operator was used to depict the interface behavior of dilute solute(s). The multiscale analysis showed that the presented model can recover the macroscopic transport equations derived from the Maxwell-Stefan equation for dilute solutes in three-phase systems. Compared with the analytical equation of state of solute and dynamic behavior, these results are proven to constitute a generalized framework to simulate solute distributions in three-phase flows, including compound soluble in one phase, compound adsorbed on single-interface, compound in two phases, and solute soluble in three phases. Moreover, numerical simulations of benchmark cases, such as phase decomposition, multilayered planar interfaces, and liquid lens, were performed to test the stability and efficiency of the model. Finally, the multiphase mass transfer and reaction in Janus droplet transport in a straight microchannel were well reproduced.

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

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann accelerated direct simulation Monte Carlo for dilute gas flow simulations.

PubMed

Di Staso, G; Clercx, H J H; Succi, S; Toschi, F

2016-11-13

Hybrid particle-continuum computational frameworks permit the simulation of gas flows by locally adjusting the resolution to the degree of non-equilibrium displayed by the flow in different regions of space and time. In this work, we present a new scheme that couples the direct simulation Monte Carlo (DSMC) with the lattice Boltzmann (LB) method in the limit of isothermal flows. The former handles strong non-equilibrium effects, as they typically occur in the vicinity of solid boundaries, whereas the latter is in charge of the bulk flow, where non-equilibrium can be dealt with perturbatively, i.e. according to Navier-Stokes hydrodynamics. The proposed concurrent multiscale method is applied to the dilute gas Couette flow, showing major computational gains when compared with the full DSMC scenarios. In addition, it is shown that the coupling with LB in the bulk flow can speed up the DSMC treatment of the Knudsen layer with respect to the full DSMC case. In other words, LB acts as a DSMC accelerator.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'. © 2016 The Author(s).

Optimization of a Lattice Boltzmann Computation on State-of-the-Art Multicore Platforms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Samuel; Carter, Jonathan; Oliker, Leonid

2009-04-10

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 Xeon E5345 (Clovertown), AMD Opteron 2214 (Santa Rosa), AMD Opteron 2356 (Barcelona), Sun T5140 T2+ (Victoria Falls), as well asmore » a QS20 IBM Cell Blade. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us to 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 15x improvement compared with the original code at a given concurrency. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.« less

A lattice Boltzmann simulation of coalescence-induced droplet jumping on superhydrophobic surfaces with randomly distributed structures

NASA Astrophysics Data System (ADS)

Zhang, Li-Zhi; Yuan, Wu-Zhi

2018-04-01

The motion of coalescence-induced condensate droplets on superhydrophobic surface (SHS) has attracted increasing attention in energy-related applications. Previous researches were focused on regularly rough surfaces. Here a new approach, a mesoscale lattice Boltzmann method (LBM), is proposed and used to model the dynamic behavior of coalescence-induced droplet jumping on SHS with randomly distributed rough structures. A Fast Fourier Transformation (FFT) method is used to generate non-Gaussian randomly distributed rough surfaces with the skewness (Sk), kurtosis (K) and root mean square (Rq) obtained from real surfaces. Three typical spreading states of coalesced droplets are observed through LBM modeling on various rough surfaces, which are found to significantly influence the jumping ability of coalesced droplet. The coalesced droplets spreading in Cassie state or in composite state will jump off the rough surfaces, while the ones spreading in Wenzel state would eventually remain on the rough surfaces. It is demonstrated that the rough surfaces with smaller Sks, larger Rqs and a K at 3.0 are beneficial to coalescence-induced droplet jumping. The new approach gives more detailed insights into the design of SHS.

Simulations of reactive transport and precipitation with smoothed particle hydrodynamics

NASA Astrophysics Data System (ADS)

Tartakovsky, Alexandre M.; Meakin, Paul; Scheibe, Timothy D.; Eichler West, Rogene M.

2007-03-01

A numerical model based on smoothed particle hydrodynamics (SPH) was developed for reactive transport and mineral precipitation in fractured and porous materials. Because of its Lagrangian particle nature, SPH has several advantages for modeling Navier-Stokes flow and reactive transport including: (1) in a Lagrangian framework there is no non-linear term in the momentum conservation equation, so that accurate solutions can be obtained for momentum dominated flows and; (2) complicated physical and chemical processes such as surface growth due to precipitation/dissolution and chemical reactions are easy to implement. In addition, SPH simulations explicitly conserve mass and linear momentum. The SPH solution of the diffusion equation with fixed and moving reactive solid-fluid boundaries was compared with analytical solutions, Lattice Boltzmann [Q. Kang, D. Zhang, P. Lichtner, I. Tsimpanogiannis, Lattice Boltzmann model for crystal growth from supersaturated solution, Geophysical Research Letters, 31 (2004) L21604] simulations and diffusion limited aggregation (DLA) [P. Meakin, Fractals, scaling and far from equilibrium. Cambridge University Press, Cambridge, UK, 1998] model simulations. To illustrate the capabilities of the model, coupled three-dimensional flow, reactive transport and precipitation in a fracture aperture with a complex geometry were simulated.

Pore-scale water dynamics during drying and the impacts of structure and surface wettability

NASA Astrophysics Data System (ADS)

Cruz, Brian C.; Furrer, Jessica M.; Guo, Yi-Syuan; Dougherty, Daniel; Hinestroza, Hector F.; Hernandez, Jhoan S.; Gage, Daniel J.; Cho, Yong Ku; Shor, Leslie M.

2017-07-01

Plants and microbes secrete mucilage into soil during dry conditions, which can alter soil structure and increase contact angle. Structured soils exhibit a broad pore size distribution with many small and many large pores, and strong capillary forces in narrow pores can retain moisture in soil aggregates. Meanwhile, contact angle determines the water repellency of soils, which can result in suppressed evaporation rates. Although they are often studied independently, both structure and contact angle influence water movement, distribution, and retention in soils. Here drying experiments were conducted using soil micromodels patterned to emulate different aggregation states of a sandy loam soil. Micromodels were treated to exhibit contact angles representative of those in bulk soil (8.4° ± 1.9°) and the rhizosphere (65° ± 9.2°). Drying was simulated using a lattice Boltzmann single-component, multiphase model. In our experiments, micromodels with higher contact angle surfaces took 4 times longer to completely dry versus micromodels with lower contact angle surfaces. Microstructure influenced drying rate as a function of saturation and controlled the spatial distribution of moisture within micromodels. Lattice Boltzmann simulations accurately predicted pore-scale moisture retention patterns within micromodels with different structures and contact angles.

Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows.

PubMed

Liang, H; Shi, B C; Guo, Z L; Chai, Z H

2014-05-01

In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is proposed for incompressible multiphase flow systems. In this model, one distribution function is used to solve the Chan-Hilliard equation and the other is adopted to solve the Navier-Stokes equations. Unlike previous phase-field-based LB models, a proper source term is incorporated in the interfacial evolution equation such that the Chan-Hilliard equation can be derived exactly and also a pressure distribution is designed to recover the correct hydrodynamic equations. Furthermore, the pressure and velocity fields can be calculated explicitly. A series of numerical tests, including Zalesak's disk rotation, a single vortex, a deformation field, and a static droplet, have been performed to test the accuracy and stability of the present model. The results show that, compared with the previous models, the present model is more stable and achieves an overall improvement in the accuracy of the capturing interface. In addition, compared to the single-relaxation-time LB model, the present model can effectively reduce the spurious velocity and fluctuation of the kinetic energy. Finally, as an application, the Rayleigh-Taylor instability at high Reynolds numbers is investigated.

High-order regularization in lattice-Boltzmann equations

NASA Astrophysics Data System (ADS)

Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.

2017-04-01

A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS: Highly Efficient Lattice Boltzmann Model for Compressible Fluids: Two-Dimensional Case

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Ai-Guo; Zhang, Guang-Cai; Gan, Yan-Biao; Cheng, Tao; Li, Ying-Jun

2009-10-01

We present a highly efficient lattice Boltzmann model for simulating compressible flows. This model is based on the combination of an appropriate finite difference scheme, a 16-discrete-velocity model [Kataoka and Tsutahara, Phys. Rev. E 69 (2004) 035701(R)] and reasonable dispersion and dissipation terms. The dispersion term effectively reduces the oscillation at the discontinuity and enhances numerical precision. The dissipation term makes the new model more easily meet with the von Neumann stability condition. This model works for both high-speed and low-speed flows with arbitrary specific-heat-ratio. With the new model simulation results for the well-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include (i) Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, (ii) Regular and Mach shock reflections, and (iii) Shock wave reaction on cylindrical bubble problems. With a more realistic equation of state or free-energy functional, the new model has the potential tostudy the complex procedure of shock wave reaction on porous materials.

Nonequilibrium scheme for computing the flux of the convection-diffusion equation in the framework of the lattice Boltzmann method.

PubMed

Chai, Zhenhua; Zhao, T S

2014-07-01

In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.

X-Ray Micro-CT Observations of Hydrate Pore Habit and Lattice Boltzmann Simulations on Permeability Evolution in Hydrate Bearing Sediments (HBS)

NASA Astrophysics Data System (ADS)

Chen, X.; Espinoza, N.; Verma, R.; Prodanovic, M.

2017-12-01

We use X-ray micro-computed tomography (μCT) to observe xenon hydrate growth. During xenon hydrate formation in a single pore and a sandpack, we observe heterogeneous (patchy) hydrate distribution at both pore (10 μm) and core scales (10 cm). These results present similarities with earlier observations on naturally occurring and synthetic hydrate-bearing sediment (HBS). Based on image analyses of xenon hydrate in the single pore, we find that, under the quasi-isothermal condition, the xenon volumetric growth rate versus overpressurization curve fits an Arrhenius type equation. Using the μCT images of HBS, we are able to calculate the permeability of HBS using a lattice Boltzmann method. We find the reduced permeability versus hydrate saturation curve fits a simple Corey-type model as suggested by earlier studies. However, patchy distribution of hydrate does not permit a straightforward interpretation of the saturation exponent. This work provides fundamental observations of hydrate growth and pore habit in sediments and how hydrate habit affects the hydraulic conductivity of HBS. Further implications can be extended to the strength, seismic velocities and electrical properties of HBS.

Investigation of GDL compression effects on the performance of a PEM fuel cell cathode by lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Molaeimanesh, G. R.; Nazemian, M.

2017-08-01

Proton exchange membrane (PEM) fuel cells with a great potential for application in vehicle propulsion systems will have a promising future. However, to overcome the exiting challenges against their wider commercialization further fundamental research is inevitable. The effects of gas diffusion layer (GDL) compression on the performance of a PEM fuel cell is not well-recognized; especially, via pore-scale simulation technique capturing the fibrous microstructure of the GDL. In the current investigation, a stochastic microstructure reconstruction method is proposed which can capture GDL microstructure changes by compression. Afterwards, lattice Boltzmann pore-scale simulation technique is adopted to simulate the reactive gas flow through 10 different cathode electrodes with dissimilar carbon paper GDLs produced from five different compression levels and two different carbon fiber diameters. The distributions of oxygen mole fraction, water vapor mole fraction and current density for the simulated cases are presented and analyzed. The results of simulations demonstrate that when the fiber diameter is 9 μm adding compression leads to lower average current density while when the fiber diameter is 7 μm the compression effect is not monotonic.

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Galilean-invariant preconditioned central-moment lattice Boltzmann method without cubic velocity errors for efficient steady flow simulations

NASA Astrophysics Data System (ADS)

Hajabdollahi, Farzaneh; Premnath, Kannan N.

2018-05-01

Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean-invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third-order diagonal moments on the first-order moments for standard lattices, and strategies have recently been introduced to restore Galilean invariance without such errors using a modified collision operator involving corrections to either the relaxation times or the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that can be used to tune the effective sound speed, and thereby alleviating the numerical stiffness. In the present paper, we present a GI formulation of the preconditioned cascaded central-moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice, for steady flows. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Such parameter dependent corrections eliminate the remaining truncation errors arising from the degeneracy of the diagonal third-order moments and fully restore Galilean invariance without cubic defects for the preconditioned LB scheme on a standard lattice. Several conclusions are drawn from the analysis of the structure of the non-GI errors and the associated corrections, with particular emphasis on their dependence on the preconditioning parameter. The GI preconditioned central-moment LB method is validated for a number of complex flow benchmark problems and its effectiveness to achieve convergence acceleration and improvement in accuracy is demonstrated.

A Lagrangian model for the age of tracer in surface water

NASA Astrophysics Data System (ADS)

Ding, Yu; Liu, Haifei; Yi, Yujun

The age of tracer is a spatio-temporal scale, indicating the transition time of solute particles, which is helpful to monitor and manage the pollutant leakage accidents. In this study, an effective Lagrangian model for the age of tracer is developed based on the lattice Boltzmann method in D2Q5 lattices. A tracer age problem in an asymmetrical circular reservoir is then employed as a benchmark test to verify this method. Then it is applied to computing the age of tracers under two different reservoir operation schemes in the Danjiangkou Reservoir, the drinking water source for the Middle Route of South-to-North Water Transfer Project.

Calculating lattice thermal conductivity: a synopsis

NASA Astrophysics Data System (ADS)

Fugallo, Giorgia; Colombo, Luciano

2018-04-01

We provide a tutorial introduction to the modern theoretical and computational schemes available to calculate the lattice thermal conductivity in a crystalline dielectric material. While some important topics in thermal transport will not be covered (including thermal boundary resistance, electronic thermal conduction, and thermal rectification), we aim at: (i) framing the calculation of thermal conductivity within the general non-equilibrium thermodynamics theory of transport coefficients, (ii) presenting the microscopic theory of thermal conduction based on the phonon picture and the Boltzmann transport equation, and (iii) outlining the molecular dynamics schemes to calculate heat transport. A comparative and critical addressing of the merits and drawbacks of each approach will be discussed as well.

Determination of the Lowest-Energy States for the Model Distribution of Trained Restricted Boltzmann Machines Using a 1000 Qubit D-Wave 2X Quantum Computer.

PubMed

Koshka, Yaroslav; Perera, Dilina; Hall, Spencer; Novotny, M A

2017-07-01

The possibility of using a quantum computer D-Wave 2X with more than 1000 qubits to determine the global minimum of the energy landscape of trained restricted Boltzmann machines is investigated. In order to overcome the problem of limited interconnectivity in the D-Wave architecture, the proposed RBM embedding combines multiple qubits to represent a particular RBM unit. The results for the lowest-energy (the ground state) and some of the higher-energy states found by the D-Wave 2X were compared with those of the classical simulated annealing (SA) algorithm. In many cases, the D-Wave machine successfully found the same RBM lowest-energy state as that found by SA. In some examples, the D-Wave machine returned a state corresponding to one of the higher-energy local minima found by SA. The inherently nonperfect embedding of the RBM into the Chimera lattice explored in this work (i.e., multiple qubits combined into a single RBM unit were found not to be guaranteed to be all aligned) and the existence of small, persistent biases in the D-Wave hardware may cause a discrepancy between the D-Wave and the SA results. In some of the investigated cases, introduction of a small bias field into the energy function or optimization of the chain-strength parameter in the D-Wave embedding successfully addressed difficulties of the particular RBM embedding. With further development of the D-Wave hardware, the approach will be suitable for much larger numbers of RBM units.

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

NASA Astrophysics Data System (ADS)

Oganesov, Armen; Vahala, George; Vahala, Linda; Soe, Min

2018-04-01

All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.

A high data rate universal lattice decoder on FPGA

NASA Astrophysics Data System (ADS)

Ma, Jing; Huang, Xinming; Kura, Swapna

2005-06-01

This paper presents the architecture design of a high data rate universal lattice decoder for MIMO channels on FPGA platform. A phost strategy based lattice decoding algorithm is modified in this paper to reduce the complexity of the closest lattice point search. The data dependency of the improved algorithm is examined and a parallel and pipeline architecture is developed with the iterative decoding function on FPGA and the division intensive channel matrix preprocessing on DSP. Simulation results demonstrate that the improved lattice decoding algorithm provides better bit error rate and less iteration number compared with the original algorithm. The system prototype of the decoder shows that it supports data rate up to 7Mbit/s on a Virtex2-1000 FPGA, which is about 8 times faster than the original algorithm on FPGA platform and two-orders of magnitude better than its implementation on a DSP platform.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

Low lattice thermal conductivity of stanene

PubMed Central

Peng, Bo; Zhang, Hao; Shao, Hezhu; Xu, Yuchen; Zhang, Xiangchao; Zhu, Heyuan

2016-01-01

A fundamental understanding of phonon transport in stanene is crucial to predict the thermal performance in potential stanene-based devices. By combining first-principle calculation and phonon Boltzmann transport equation, we obtain the lattice thermal conductivity of stanene. A much lower thermal conductivity (11.6 W/mK) is observed in stanene, which indicates higher thermoelectric efficiency over other 2D materials. The contributions of acoustic and optical phonons to the lattice thermal conductivity are evaluated. Detailed analysis of phase space for three-phonon processes shows that phonon scattering channels LA + LA/TA/ZA ↔ TA/ZA are restricted, leading to the dominant contributions of high-group-velocity LA phonons to the thermal conductivity. The size dependence of thermal conductivity is investigated as well for the purpose of the design of thermoelectric nanostructures. PMID:26838731

First-principles analysis of anharmonic nuclear motion and thermal transport in thermoelectric materials

NASA Astrophysics Data System (ADS)

Tadano, Terumasa; Tsuneyuki, Shinji

2015-12-01

We show a first-principles approach for analyzing anharmonic properties of lattice vibrations in solids. We firstly extract harmonic and anharmonic force constants from accurate first-principles calculations based on the density functional theory. Using the many-body perturbation theory of phonons, we then estimate the phonon scattering probability due to anharmonic phonon-phonon interactions. We show the validity of the approach by computing the lattice thermal conductivity of Si, a typical covalent semiconductor, and selected thermoelectric materials PbTe and Bi2Te3 based on the Boltzmann transport equation. We also show that the phonon lifetime and the lattice thermal conductivity of the high-temperature phase of SrTiO3 can be estimated by employing the perturbation theory on top of the solution of the self-consistent phonon equation.

Lateral Migration and Rotational Motion of Elliptic Particles in Planar Poiseuille Flow

NASA Technical Reports Server (NTRS)

Qi, Dewei; Luo, Li-Shi; Aravamuthan, Raja; Strieder, William; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

Simulations of elliptic particulate suspensions in the planar Poiseuille flow are performed by using the lattice Boltzmann equation. Effects of the multi-particle on the lateral migration and rotational motion of both neutrally and non-neutrally buoyant elliptic particles are investigated. Low and intermediate total particle volume fraction f(sub a) = 13%, 15%, and 40% are considered in this work.

Comment on "Heat transfer and fluid flow in microchannels and nanochannels at high Knudsen number using thermal lattice-Boltzmann method".

PubMed

Luo, Li-Shi

2011-10-01

In this Comment we reveal the falsehood of the claim that the lattice Bhatnagar-Gross-Krook (BGK) model "is capable of modeling shear-driven, pressure-driven, and mixed shear-pressure-driven rarified [sic] flows and heat transfer up to Kn=1 in the transitional regime" made in a recent paper [Ghazanfarian and Abbassi, Phys. Rev. E 82, 026307 (2010)]. In particular, we demonstrate that the so-called "Knudsen effects" described are merely numerical artifacts of the lattice BGK model and they are unphysical. Specifically, we show that the erroneous results for the pressure-driven flow in a microchannel imply the false and unphysical condition that 6σKn<-1, where Kn is the Knudsen number σ=(2-σ(v))/σ(v) and σ(v)∈(0,1] is the tangential momentum accommodation coefficient. We also show explicitly that the defects of the lattice BGK model can be completely removed by using the multiple-relaxation-time collision model.

A Lattice-Boltzmann model to simulate diffractive nonlinear ultrasound beam propagation in a dissipative fluid medium

NASA Astrophysics Data System (ADS)

Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan

2012-12-01

Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.

Lattice Boltzmann for Simulation of Gases Mixture in Fruit Storage Chambers

NASA Astrophysics Data System (ADS)

Fabero, J. C.; Barreiro, P.; Casasús, L.

2003-04-01

Fluid Dynamics can be modelled through the Navier-Stokes equations. This description corresponds to a macroscopic definition of the fluid motion phenomena. During the past 20 year new simulation procedures are emerging from Statistical Physics and Computer Science domains. One of them is the Lattice Gas Cellular Automata (LGCA) method. This approach, which is considered to be a microscopic description of the world, in spite of its intuitiveness and numerical efficiency, fails to simulate the real Navier-Stokes equations. Another classical simulation procedure for the fluid motion phenomena is the so called Lattice Boltzmann method [1]. This corresponds to a meso-scale description of the world [2]. Simulation of laminar and turbulent motions of fluids, specially when considering several gas species is still an ongoing research [3]. Nowadays, the use of Low Oxygen and Ultra Low Oxygen Controlled Atmospheres has been recognized as a reliable method to extend the storage life of fruits an vegetables. However, small spatial gradients in gas concentration during storage may generate internal disorders in the commodities. In this work, four different gases will be considered: oxygen, carbon dioxide, water vapor and ethylene. Physiological effects such as transpiration, which affects the level of water vapor, respiration, which modifies both oxygen and carbon dioxide concentrations, and ethylene emission, must be taken into account in the hole model. The numerical model, based on that proposed by Shan and Chen, is implemented, being able to consider the behavior of multiple mixable gas species. Forced air motion, needed to obtain a correct ventilation of the chamber, has also been modelled.

Simulatng Sawtooth Mixers For Biofouling Mitigation

NASA Astrophysics Data System (ADS)

Waters, James; Balazs, Anna

2017-11-01

We demonstrate how a ridged surface can be used to generate vortices that will break up clusters of cells as they form. This offers an appealing avenue for fouling mitigation, as it relies on a physical mechanism without unintended environmental consequences. By adjusting the shape of these ridges, we can increase the effectiveness of the surface across a range of shear values. We represent such a system computationally using a hybrid of bulk fluid simulated via the lattice Boltzmann method, and deformable vesicles, representing cells, simulated via that lattice spring method. This simulation methodology allows us to rapidly implement and test different surface patterns, and explore how their parameters can most effectively deter the accumulation of biofilms.

Spontaneous density fluctuations in granular flow and traffic

NASA Astrophysics Data System (ADS)

Herrmann, Hans J.

It is known that spontaneous density waves appear in granular material flowing through pipes or hoppers. A similar phenomenon is known from traffic jams on highways. Using numerical simulations we show that several types of waves exist and find that the density fluctuations follow a power law spectrum. We also investigate one-dimensional traffic models. If positions and velocities are continuous variables the model shows self-organized criticality driven by the slowest car. Lattice gas and lattice Boltzmann models reproduce the experimentally observed effects. Density waves are spontaneously generated when the viscosity has a non-linear dependence on density or shear rate as it is the case in traffic or granular flow.

Grain-Size-Dependent Thermoelectric Properties of SrTiO3 3D Superlattice Ceramics

NASA Astrophysics Data System (ADS)

Zhang, Rui-zhi; Koumoto, Kunihito

2013-07-01

The thermoelectric (TE) performance of SrTiO3 (STO) 3D superlattice ceramics with 2D electron gas grain boundaries (GBs) was theoretically investigated. The grain size dependence of the power factor, lattice thermal conductivity, and ZT value were calculated by using Boltzmann transport equations. It was found that nanostructured STO ceramics with smaller grain size have larger ZT value. This is because the quantum confinement effect, energy filtering effect, and interfacial phonon scattering at GBs all become stronger with decreasing grain size, resulting in higher power factor and lower lattice thermal conductivity. These findings will aid the design of nanostructured oxide ceramics with high TE performance.

An application of the discrete-time Toda lattice to the progressive algorithm by Lanczos and related problems

NASA Astrophysics Data System (ADS)

Nakamura, Yoshimasa; Sekido, Hiroto

2018-04-01

The finite or the semi-infinite discrete-time Toda lattice has many applications to various areas in applied mathematics. The purpose of this paper is to review how the Toda lattice appears in the Lanczos algorithm through the quotient-difference algorithm and its progressive form (pqd). Then a multistep progressive algorithm (MPA) for solving linear systems is presented. The extended Lanczos parameters can be given not by computing inner products of the extended Lanczos vectors but by using the pqd algorithm with highly relative accuracy in a lower cost. The asymptotic behavior of the pqd algorithm brings us some applications of MPA related to eigenvectors.

An Improved Neutron Transport Algorithm for Space Radiation

NASA Technical Reports Server (NTRS)

Heinbockel, John H.; Clowdsley, Martha S.; Wilson, John W.

2000-01-01

A low-energy neutron transport algorithm for use in space radiation protection is developed. The algorithm is based upon a multigroup analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. This analysis is accomplished by solving a realistic but simplified neutron transport test problem. The test problem is analyzed by using numerical and analytical procedures to obtain an accurate solution within specified error bounds. Results from the test problem are then used for determining mean values associated with rescattering terms that are associated with a multigroup solution of the straight-ahead Boltzmann equation. The algorithm is then coupled to the Langley HZETRN code through the evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for a water and an aluminum-water shield-target configuration is then compared with LAHET and MCNPX Monte Carlo code calculations for the same shield-target configuration. The algorithm developed showed a great improvement in results over the unmodified HZETRN solution. In addition, a two-directional solution of the evaporation source showed even further improvement of the fluence near the front of the water target where diffusion from the front surface is important.

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene.

PubMed

Oettinger, D; Mendoza, M; Herrmann, H J

2013-07-01

We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.

Magnon Polarons in the Spin Seebeck Effect.

PubMed

Kikkawa, Takashi; Shen, Ka; Flebus, Benedetta; Duine, Rembert A; Uchida, Ken-Ichi; Qiu, Zhiyong; Bauer, Gerrit E W; Saitoh, Eiji

2016-11-11

Sharp structures in the magnetic field-dependent spin Seebeck effect (SSE) voltages of Pt/Y_{3}Fe_{5}O_{12} at low temperatures are attributed to the magnon-phonon interaction. Experimental results are well reproduced by a Boltzmann theory that includes magnetoelastic coupling. The SSE anomalies coincide with magnetic fields tuned to the threshold of magnon-polaron formation. The effect gives insight into the relative quality of the lattice and magnetization dynamics.

Revised Chapman-Enskog analysis for a class of forcing schemes in the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Li, Q.; Zhou, P.; Yan, H. J.

2016-10-01

In the lattice Boltzmann (LB) method, the forcing scheme, which is used to incorporate an external or internal force into the LB equation, plays an important role. It determines whether the force of the system is correctly implemented in an LB model and affects the numerical accuracy. In this paper we aim to clarify a critical issue about the Chapman-Enskog analysis for a class of forcing schemes in the LB method in which the velocity in the equilibrium density distribution function is given by u =∑αeαfα / ρ , while the actual fluid velocity is defined as u ̂=u +δtF / (2 ρ ) . It is shown that the usual Chapman-Enskog analysis for this class of forcing schemes should be revised so as to derive the actual macroscopic equations recovered from these forcing schemes. Three forcing schemes belonging to the above class are analyzed, among which Wagner's forcing scheme [A. J. Wagner, Phys. Rev. E 74, 056703 (2006), 10.1103/PhysRevE.74.056703] is shown to be capable of reproducing the correct macroscopic equations. The theoretical analyses are examined and demonstrated with two numerical tests, including the simulation of Womersley flow and the modeling of flat and circular interfaces by the pseudopotential multiphase LB model.

Lattice Boltzmann simulations of the bead-spring microswimmer with a responsive stroke—from an individual to swarms

NASA Astrophysics Data System (ADS)

Pickl, Kristina; Pande, Jayant; Köstler, Harald; Rüde, Ulrich; Smith, Ana-Sunčana

2017-03-01

Propulsion at low Reynolds numbers is often studied by defining artificial microswimmers which exhibit a particular stroke. The disadvantage of such an approach is that the stroke does not adjust to the environment, in particular the fluid flow, which can diminish the effect of hydrodynamic interactions. To overcome this limitation, we simulate a microswimmer consisting of three beads connected by springs and dampers, using the self-developed waLBerla and pe framework based on the lattice Boltzmann method and the discrete element method. In our approach, the swimming stroke of a swimmer emerges as a balance of the drag, the driving and the elastic internal forces. We validate the simulations by comparing the obtained swimming velocity to the velocity found analytically using a perturbative method where the bead oscillations are taken to be small. Including higher-order terms in the hydrodynamic interactions between the beads improves the agreement to the simulations in parts of the parameter space. Encouraged by the agreement between the theory and the simulations and aided by the massively parallel capabilities of the waLBerla-pe framework, we simulate more than ten thousand such swimmers together, thus presenting the first fully resolved simulations of large swarms with active responsive components.

A multiphase three-dimensional multi-relaxation time (MRT) lattice Boltzmann model with surface tension adjustment

NASA Astrophysics Data System (ADS)

Ammar, Sami; Pernaudat, Guillaume; Trépanier, Jean-Yves

2017-08-01

The interdependence of surface tension and density ratio is a weakness of pseudo-potential based lattice Boltzmann models (LB). In this paper, we propose a 3D multi-relaxation time (MRT) model for multiphase flows at large density ratios. The proposed model is capable of adjusting the surface tension independently of the density ratio. We also present the 3D macroscopic equations recovered by the proposed forcing scheme. A high order of isotropy for the interaction force is used to reduce the amplitude of spurious currents. The proposed 3D-MRT model is validated by verifying Laplace's law and by analyzing its thermodynamic consistency and the oscillation period of a deformed droplet. The model is then applied to the simulation of the impact of a droplet on a dry surface. Impact dynamics are determined and the maximum spread factor calculated for different Reynolds and Weber numbers. The numerical results are in agreement with data published in the literature. The influence of surface wettability on the spread factor is also investigated. Finally, our 3D-MRT model is applied to the simulation of the impact of a droplet on a wet surface. The propagation of transverse waves is observed on the liquid surface.

An Incompressible, Depth-Averaged Lattice Boltzmann Method for Liquid Flow in Microfluidic Devices with Variable Aperture

DOE PAGES

Laleian, Artin; Valocchi, Albert J.; Werth, Charles J.

2015-11-24

Two-dimensional (2D) pore-scale models have successfully simulated microfluidic experiments of aqueous-phase flow with mixing-controlled reactions in devices with small aperture. A standard 2D model is not generally appropriate when the presence of mineral precipitate or biomass creates complex and irregular three-dimensional (3D) pore geometries. We modify the 2D lattice Boltzmann method (LBM) to incorporate viscous drag from the top and bottom microfluidic device (micromodel) surfaces, typically excluded in a 2D model. Viscous drag from these surfaces can be approximated by uniformly scaling a steady-state 2D velocity field at low Reynolds number. We demonstrate increased accuracy by approximating the viscous dragmore » with an analytically-derived body force which assumes a local parabolic velocity profile across the micromodel depth. Accuracy of the generated 2D velocity field and simulation permeability have not been evaluated in geometries with variable aperture. We obtain permeabilities within approximately 10% error and accurate streamlines from the proposed 2D method relative to results obtained from 3D simulations. Additionally, the proposed method requires a CPU run time approximately 40 times less than a standard 3D method, representing a significant computational benefit for permeability calculations.« less

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

PubMed Central

Gan, Z. L.; Ishak, M. H. H.; Abdullah, M. Z.; Khor, Soon Fuat

2016-01-01

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. PMID:27454872

IB-LBM simulation on blood cell sorting with a micro-fence structure.

PubMed

Wei, Qiang; Xu, Yuan-Qing; Tian, Fang-bao; Gao, Tian-xin; Tang, Xiao-ying; Zu, Wen-Hong

2014-01-01

A size-based blood cell sorting model with a micro-fence structure is proposed in the frame of immersed boundary and lattice Boltzmann method (IB-LBM). The fluid dynamics is obtained by solving the discrete lattice Boltzmann equation, and the cells motion and deformation are handled by the immersed boundary method. A micro-fence consists of two parallel slope post rows which are adopted to separate red blood cells (RBCs) from white blood cells (WBCs), in which the cells to be separated are transported one after another by the flow into the passageway between the two post rows. Effected by the cross flow, RBCs are schemed to get through the pores of the nether post row since they are smaller and more deformable compared with WBCs. WBCs are required to move along the nether post row till they get out the micro-fence. Simulation results indicate that for a fix width of pores, the slope angle of the post row plays an important role in cell sorting. The cells mixture can not be separated properly in a small slope angle, while obvious blockages by WBCs will take place to disturb the continuous cell sorting in a big slope angle. As an optimal result, an adaptive slope angle is found to sort RBCs form WBCs correctly and continuously.

Modelling and investigation of partial wetting surfaces for drop dynamics using lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Pravinraj, T.; Patrikar, Rajendra

2017-07-01

Partial wetting surfaces and its influence on the droplet movement of micro and nano scale being contemplated for many useful applications. The dynamics of the droplet usually analyzed with a multiphase lattice Boltzmann method (LBM). In this paper, the influence of partial wetting surface on the dynamics of droplet is systematically analyzed for various cases. Splitting of droplets due to chemical gradient of the surface is studied and analyses of splitting time for various widths of the strips for different Weber numbers are computed. With the proposed model one can tune the splitting volume and time by carefully choosing a strip width and droplet position. The droplet spreading on chemically heterogeneous surfaces shows that the spreading can be controlled not only by parameters of Weber number but also by tuning strip width ratio. The transportation of the droplet from hydrophobic surface to hydrophilic surface due to chemical gradient is simulated and analyzed using our hybrid thermodynamic-image processing technique. The results prove that with the progress of time the surface free energy decreases with increase in spreading area. Finally, the transportation of a droplet on microstructure gradient is demonstrated. The model explains the temporal behaviour of droplet during the spreading, recoiling and translation along with tracking of contact angle hysteresis phenomenon.

Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations.

PubMed

Asinari, Pietro

2009-11-01

A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.

Lattice Boltzmann study of slip flow over structured surface with transverse slots

NASA Astrophysics Data System (ADS)

Chen, Wei; Wang, Kai; Wang, Lei; Hou, Guoxiang; Leng, Wenjun

2018-04-01

Slip flow over structured superhydrophobic surface with transverse slots is investigated by the lattice Boltzmann method. The Shan-Chen multiphase model is employed to simulate the flow over gas bubbles in the slots. The Carnahan-Starling equation of state is applied to obtain large density ratio. The interface thickness of the multiphase model is discussed. We find that the Cahn number Cn should be smaller than 0.02 when the temperature T = 0.5T c to restrict the influence of interface thickness on slip length. Influences of slot fraction on slip length is then studied, and the result is compared with single LB simulation of which the interface is treated as free-slip boundary. The slip length obtained by the multiphase model is a little smaller. After that, the shape of the liquid-gas interface is considered, and simulations with different initial protrusion angles and capillary numbers are performed. Effective slip length as a function of initial protrusion angle is obtained. The result is in qualitative agreement with a previous study and main features are reproduced. Furthermore, the influence of Capillary number Ca is studied. Larger Ca causes larger interface deformation and smaller slip length. But when the interface is concaving into the slot, this influence is less obvious.

Simulation of the spreading of a gas-propelled micro-droplet upon impact on a dry surface using a lattice-Boltzmann approach

NASA Astrophysics Data System (ADS)

Ebrahim, Mahsa; Ortega, Alfonso; Delbosc, Nicolas; Wilson, Mark C. T.; Summers, Jonathan L.

2017-07-01

Spray cooling is one of the most promising methods of cooling high heat flux electronics. Depending on the type of the nozzle, spray cooling can be categorized as single-phase or two-phase. In the latter, which is known to be more effective, a secondary gas is used to further pressurize the liquid and form smaller droplets at higher velocities. The gas is also assumed to assist the spreading phase by imposing normal and tangential forces on the droplet free surface which adds to the complicated hydrodynamics of the droplet impact. Moreover, the order of magnitude of droplet size in spray cooling is 10-6 m, thereby introducing a low Weber and Reynolds numbers' impact regime which heretofore has not been well understood. A 3D lattice Boltzmann method was implemented to simulate the impact of a single micro-droplet on a dry surface both in ambient air and under a stagnation gas flow. Two cases were closely compared and correlations were proposed for the instantaneous spreading diameter. Contrary to recent findings at higher impact Weber and Reynolds numbers, it was found that a stagnation flow only significantly affects the spreading phase for Ca* ≥ 0.35 but has little influence on the receding physics.

Lattice Boltzmann modeling of boiling heat transfer: The boiling curve and the effects of wettability

DOE PAGES

Li, Q.; Kang, Q. J.; Francois, M. M.; ...

2015-03-03

A hybrid thermal lattice Boltzmann (LB) model is presented to simulate thermal multiphase flows with phase change based on an improved pseudopotential LB approach (Li et al., 2013). The present model does not suffer from the spurious term caused by the forcing-term effect, which was encountered in some previous thermal LB models for liquid–vapor phase change. Using the model, the liquid–vapor boiling process is simulated. The boiling curve together with the three boiling stages (nucleate boiling, transition boiling, and film boiling) is numerically reproduced in the LB community for the first time. The numerical results show that the basic featuresmore » and the fundamental characteristics of boiling heat transfer are well captured, such as the severe fluctuation of transient heat flux in the transition boiling and the feature that the maximum heat transfer coefficient lies at a lower wall superheat than that of the maximum heat flux. Moreover, the effects of the heating surface wettability on boiling heat transfer are investigated. It is found that an increase in contact angle promotes the onset of boiling but reduces the critical heat flux, and makes the boiling process enter into the film boiling regime at a lower wall superheat, which is consistent with the findings from experimental studies.« less

Lattice Boltzmann modeling of self-propelled Leidenfrost droplets on ratchet surfaces

DOE PAGES

Li, Qing; Kang, Qinjun J.; Francois, Marianne M.; ...

2016-10-09

Here in this paper, the self-propelled motion of Leidenfrost droplets on ratchet surfaces is numerically investigated with a thermal multiphase lattice Boltzmann model with liquid-vapor phase change. The capability of the model for simulating evaporation is validated via the D 2 law. Using the model, we first study the performances of Leidenfrost droplets on horizontal ratchet surfaces. It is numerically shown that the motion of self-propelled Leidenfrost droplets on ratchet surfaces is owing to the asymmetry of the ratchets and the vapor flows beneath the droplets. It is found that the Leidenfrost droplets move in the direction toward the slowlymore » inclined side from the ratchet peaks, which agrees with the direction of droplet motion in experiments [Linke et al., Phys. Rev. Lett., 2006, 96, 154502]. Moreover, the influences of the ratchet aspect ratio are investigated. For the considered ratchet surfaces, a critical value of the ratchet aspect ratio is approximately found, which corresponds to the maximum droplet moving velocity. Furthermore, the processes that the Leidenfrost droplets climb uphill on inclined ratchet surfaces are also studied. Lastly, numerical results show that the maximum inclination angle at which a Leidenfrost droplet can still climb uphill successfully is affected by the initial radius of the droplet.« less

Numerical simulation the pollutants transport in the Lake base on remote sensing image with Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Qiao, Y.

2013-12-01

As China's economic development, water pollution incidents happened frequently. For example, the cyanobacterial bloom events repeatedly occur in Taihu Lake. In this research, we investigate the pollutants solute transport start at different points, such as the eutrophication substances Nitrogen and Phosphorus et al, with the Lattice Boltzmann Method (LBM) performed on real pore geometries. The LBM has emerged as a powerful tool for simulating the behaviour of multi-component fluid systems in complex pore networks. We will build a quick response simulation system, which is base on the high resolution GIS figure, using the LBM numerical method.When the start two deferent points at the Meiliang Bay nearby the Wuxi City, it is shown that the pollutants solute can't transport out of the bay to influence the Taihu Lake and the diffusion areas are similar. On the other hand, when the start point at central region of the Taihu Lake, it is found that the pollutants solute covered the almost whole area of the lake and the cyanobacterial bloom with good condition. In the same way, if the cyanobacterial bloom transport in the central area, then it will pollute the whole Taihu Lake. Therefore, when we monitor and deal with the eutrophication substances, we need to focus on the central area of lake.

Airframe Noise Prediction of a Full Aircraft in Model and Full Scale Using a Lattice Boltzmann Approach

NASA Technical Reports Server (NTRS)

Fares, Ehab; Duda, Benjamin; Khorrami, Mehdi R.

2016-01-01

Unsteady flow computations are presented for a Gulfstream aircraft model in landing configuration, i.e., flap deflected 39deg and main landing gear deployed. The simulations employ the lattice Boltzmann solver PowerFLOW(Trademark) to simultaneously capture the flow physics and acoustics in the near field. Sound propagation to the far field is obtained using a Ffowcs Williams and Hawkings acoustic analogy approach. Two geometry representations of the same aircraft are analyzed: an 18% scale, high-fidelity, semi-span model at wind tunnel Reynolds number and a full-scale, full-span model at half-flight Reynolds number. Previously published and newly generated model-scale results are presented; all full-scale data are disclosed here for the first time. Reynolds number and geometrical fidelity effects are carefully examined to discern aerodynamic and aeroacoustic trends with a special focus on the scaling of surface pressure fluctuations and farfield noise. An additional study of the effects of geometrical detail on farfield noise is also documented. The present investigation reveals that, overall, the model-scale and full-scale aeroacoustic results compare rather well. Nevertheless, the study also highlights that finer geometrical details that are typically not captured at model scales can have a non-negligible contribution to the farfield noise signature.

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

NASA Astrophysics Data System (ADS)

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.

Harmonic oscillations of laminae in non-Newtonian fluids: A lattice Boltzmann-Immersed Boundary approach

NASA Astrophysics Data System (ADS)

De Rosis, Alessandro

2014-11-01

In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.

Effect of initial densities in the lattice Boltzmann model for non-ideal fluid with curved interface

NASA Astrophysics Data System (ADS)

Gong, Jiaming; Oshima, Nobuyuki

2017-06-01

The effect of initial densities in a free energy based two-phase-flow lattice Boltzmann method for non-ideal fluids with a curved interface was investigated in the present work. To investigate this effect, the initial densities in the liquid and gas phases coming from the saturation points and the equilibrium state were adopted in the simulation of a static droplet in an open and a closed system. For the purpose of simplicity and easier comparison, the closed system is fabricated by the implementation of the periodic boundary condition at the inlet and outlet of a gas channel, and the open system is fabricated by the implementation of a constant flux boundary condition at the inlet and a free-out boundary condition at the outlet of the same gas channel. By comparing the simulation results from the two types of initial densities in the open and closed systems, it is proven that the commonly used saturation initial densities setting is the reason for droplet mass and volume variation which occurred in the simulation, particularly in the open system with a constant flux boundary condition. Such problems are believed to come from the curvature effect of the surface tension and can be greatly reduced by adopting the initial densities in the two phases from equilibrium state.

Evaluation of Airframe Noise Reduction Concepts via Simulations Using a Lattice Boltzmann Approach

NASA Technical Reports Server (NTRS)

Fares, Ehab; Casalino, Damiano; Khorrami, Mehdi R.

2015-01-01

Unsteady computations are presented for a high-fidelity, 18% scale, semi-span Gulfstream aircraft model in landing configuration, i.e. flap deflected at 39 degree and main landing gear deployed. The simulations employ the lattice Boltzmann solver PowerFLOW® to simultaneously capture the flow physics and acoustics in the near field. Sound propagation to the far field is obtained using a Ffowcs Williams and Hawkings acoustic analogy approach. In addition to the baseline geometry, which was presented previously, various noise reduction concepts for the flap and main landing gear are simulated. In particular, care is taken to fully resolve the complex geometrical details associated with these concepts in order to capture the resulting intricate local flow field thus enabling accurate prediction of their acoustic behavior. To determine aeroacoustic performance, the farfield noise predicted with the concepts applied is compared to high-fidelity simulations of the untreated baseline configurations. To assess the accuracy of the computed results, the aerodynamic and aeroacoustic impact of the noise reduction concepts is evaluated numerically and compared to experimental results for the same model. The trends and effectiveness of the simulated noise reduction concepts compare well with measured values and demonstrate that the computational approach is capable of capturing the primary effects of the acoustic treatment on a full aircraft model.

Lattice Boltzmann modeling of self-propelled Leidenfrost droplets on ratchet surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Qing; Kang, Qinjun J.; Francois, Marianne M.

Here in this paper, the self-propelled motion of Leidenfrost droplets on ratchet surfaces is numerically investigated with a thermal multiphase lattice Boltzmann model with liquid-vapor phase change. The capability of the model for simulating evaporation is validated via the D 2 law. Using the model, we first study the performances of Leidenfrost droplets on horizontal ratchet surfaces. It is numerically shown that the motion of self-propelled Leidenfrost droplets on ratchet surfaces is owing to the asymmetry of the ratchets and the vapor flows beneath the droplets. It is found that the Leidenfrost droplets move in the direction toward the slowlymore » inclined side from the ratchet peaks, which agrees with the direction of droplet motion in experiments [Linke et al., Phys. Rev. Lett., 2006, 96, 154502]. Moreover, the influences of the ratchet aspect ratio are investigated. For the considered ratchet surfaces, a critical value of the ratchet aspect ratio is approximately found, which corresponds to the maximum droplet moving velocity. Furthermore, the processes that the Leidenfrost droplets climb uphill on inclined ratchet surfaces are also studied. Lastly, numerical results show that the maximum inclination angle at which a Leidenfrost droplet can still climb uphill successfully is affected by the initial radius of the droplet.« less

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: Permeability and diffusivity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Li; Zhang, Lei; Kang, Qinjun

Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsicmore » permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.« less

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

NASA Astrophysics Data System (ADS)

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.

LBflow: An extensible lattice Boltzmann framework for the simulation of geophysical flows. Part II: usage and validation

NASA Astrophysics Data System (ADS)

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.

Lattice Boltzmann Simulation of Seismic Mobilization of Residual Oil in Sandstone

NASA Astrophysics Data System (ADS)

Guo, R.; Jiang, F.; Deng, W.

2017-12-01

Seismic stimulation is a promising technology for enhanced oil recovery. However, current mechanism studies are mainly in the single constricted tubes or idealized porous media, and no study has been conducted in real reservoir porous media. We have developed a numerical simulation which uses the lattice Boltzmann method to directly calculate the characteristics of residual oil clusters to quantify seismic mobilization of residual oil in real Berea sandstone in a scale of 400μm x 400μm x 400μm. The residual oil clusters will be firstly obtained by applying the water flooding scheme to the oil-saturated sandstone. Then, we will apply the seismic stimulation to the sandstone by converting the seismic effect to oscillatory inertial force and add to the pore fluids. This oscillatory inertial force causes the mobilization of residual oil by overcoming the capillary force. The response of water and oil to the seismic stimulation will be observed in our simulations. Two seismic oil mobilization mechanisms will be investigated: (1) the passive response of residual oil clusters to the seismic stimulation, and (2) the resonance of oil clusters subject to low frequency seismic stimulation. We will then discuss which mechanism should be the dominant mechanism for the seismic stimulation oil recovery for practical applications.

Noise prediction of a subsonic turbulent round jet using the lattice-Boltzmann method

PubMed Central

Lew, Phoi-Tack; Mongeau, Luc; Lyrintzis, Anastasios

2010-01-01

The lattice-Boltzmann method (LBM) was used to study the far-field noise generated from a Mach, Mj=0.4, unheated turbulent axisymmetric jet. A commercial code based on the LBM kernel was used to simulate the turbulent flow exhausting from a pipe which is 10 jet radii in length. Near-field flow results such as jet centerline velocity decay rates and turbulence intensities were in agreement with experimental results and results from comparable LES studies. The predicted far field sound pressure levels were within 2 dB from published experimental results. Weak unphysical tones were present at high frequency in the computed radiated sound pressure spectra. These tones are believed to be due to spurious sound wave reflections at boundaries between regions of varying voxel resolution. These “VR tones” did not appear to bias the underlying broadband noise spectrum, and they did not affect the overall levels significantly. The LBM appears to be a viable approach, comparable in accuracy to large eddy simulations, for the problem considered. The main advantages of this approach over Navier–Stokes based finite difference schemes may be a reduced computational cost, ease of including the nozzle in the computational domain, and ease of investigating nozzles with complex shapes. PMID:20815448

Development of an Efficient Meso- scale Multi-phase Flow Solver in Nuclear Applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Taehun

2015-10-20

The proposed research aims at formulating a predictive high-order Lattice Boltzmann Equation for multi-phase flows relevant to nuclear energy related application - namely, saturated and sub-cooled boiling in reactors, and liquid- liquid mixing and extraction for fuel cycle separation. An efficient flow solver will be developed based on the Finite Element based Lattice Boltzmann Method (FE- LBM), accounting for phase-change heat transfer and capable of treating multiple phases over length scales from the submicron to the meter. A thermal LBM will be developed in order to handle adjustable Prandtl number, arbitrary specific heat ratio, a wide range of temperature variations,more » better numerical stability during liquid-vapor phase change, and full thermo-hydrodynamic consistency. Two-phase FE-LBM will be extended to liquid–liquid–gas multi-phase flows for application to high-fidelity simulations building up from the meso-scale up to the equipment sub-component scale. While several relevant applications exist, the initial applications for demonstration of the efficient methods to be developed as part of this project include numerical investigations of Critical Heat Flux (CHF) phenomena in nuclear reactor fuel bundles, and liquid-liquid mixing and interfacial area generation for liquid-liquid separations. In addition, targeted experiments will be conducted for validation of this advanced multi-phase model.« less

Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mishra, Subhash C.; Roy, Hillol K.

2007-04-10

The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The finite volume method (FVM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the FVM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 1-D planar and 2-D rectangular geometries were considered. In order to establish the suitability of the LBM, the energy equations of the two problems were also solved using the FVM of the computational fluid dynamics. The FVM used in the radiative heatmore » transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FVM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the FVM for the radiative information, results were analyzed for the effects of various parameters such as the scattering albedo, the conduction-radiation parameter and the boundary emissivity. The results of the LBM-FVM combination were found to be in excellent agreement with the FVM-FVM combination. The number of iterations and CPU times in both the combinations were found comparable.« less

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: Permeability and diffusivity

DOE PAGES

Chen, Li; Zhang, Lei; Kang, Qinjun; ...

2015-01-28

Here, porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsicmore » permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. We find that for the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.« less

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity

PubMed Central

Chen, Li; Zhang, Lei; Kang, Qinjun; Viswanathan, Hari S.; Yao, Jun; Tao, Wenquan

2015-01-01

Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed. PMID:25627247

Study of Gas Flow Characteristics in Tight Porous Media with a Microscale Lattice Boltzmann Model

PubMed Central

Zhao, Jianlin; Yao, Jun; Zhang, Min; Zhang, Lei; Yang, Yongfei; Sun, Hai; An, Senyou; Li, Aifen

2016-01-01

To investigate the gas flow characteristics in tight porous media, a microscale lattice Boltzmann (LB) model with the regularization procedure is firstly adopted to simulate gas flow in three-dimensional (3D) digital rocks. A shale digital rock and a sandstone digital rock are reconstructed to study the effects of pressure, temperature and pore size on microscale gas flow. The simulation results show that because of the microscale effect in tight porous media, the apparent permeability is always higher than the intrinsic permeability, and with the decrease of pressure or pore size, or with the increase of temperature, the difference between apparent permeability and intrinsic permeability increases. In addition, the Knudsen numbers under different conditions are calculated and the results show that gas flow characteristics in the digital rocks under different Knudsen numbers are quite different. With the increase of Knudsen number, gas flow in the digital rocks becomes more uniform and the effect of heterogeneity of the porous media on gas flow decreases. Finally, two commonly used apparent permeability calculation models are evaluated by the simulation results and the Klinkenberg model shows better accuracy. In addition, a better proportionality factor in Klinkenberg model is proposed according to the simulation results. PMID:27587293

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vahala, G.; Tracy, E.

During the past year, the authors have concentrated on (1) divertor physics, (2) thermo-lattice Boltzmann (TLBE) approach to turbulence, and (3) phase space techniques in gyro-resonance problems in collaboration with Dieter Sigmar (MIT), Sergei Krasheninnikov (MIT), Linda Vahala (ODU), Joseph Morrison (AS and M/NASA-Langley), Pavol Pavlo and Josef Preinhaelter (institute of Plasma Physics, Czech Academy of Sciences) and Allan Kaufman (LBL/U.C.Berkeley). Using a 2-equation compressible closure model with a 2D mean flow, the authors are investigating the effects of 3D neutral turbulence on reducing the heat load to the divertor plate by various toroidal cavity geometries. These studies are beingmore » extended to examine 3D mean flows. Thermal Lattice Boltzmann (TLBE) methods are being investigated to handle 3D turbulent flows in nontrivial geometries. It is planned to couple the TLBE collisional regime to the weakly collisional regime and so be able to tackle divertor physics. In the application of phase space techniques to minority-ion RF heating, resonance heating is treated as a multi-stage process. A generalization of the Case-van Kampen analysis is presented for multi-dimensional non-uniform plasmas. Effects such as particle trapping and the ray propagation dynamics in tokamak geometry can now be handled using Weyl calculus.« less

In situ contact angle measurements of liquid CO 2, brine, and Mount Simon sandstone core using micro X-ray CT imaging, sessile drop, and Lattice Boltzmann modeling

DOE PAGES

Tudek, John; Crandall, Dustin; Fuchs, Samantha; ...

2017-01-30

Three techniques to measure and understand the contact angle, θ, of a CO 2/brine/rock system relevant to geologic carbon storage were performed with Mount Simon sandstone. Traditional sessile drop measurements of CO 2/brine on the sample were conducted and a water-wet system was observed, as is expected. A novel series of measurements inside of a Mount Simon core, using a micro X-ray computed tomography imaging system with the ability to scan samples at elevated pressures, was used to examine the θ of residual bubbles of CO 2. Within the sandstone core the matrix appeared to be neutrally wetting, with anmore » average θ around 90°. A large standard deviation of θ (20.8°) within the core was also observed. To resolve this discrepancy between experimental measurements, a series of Lattice Boltzmann model simulations were performed with differing intrinsic θ values. The model results with a θ = 80° were shown to match the core measurements closely, in both magnitude and variation. The small volume and complex geometry of the pore spaces that CO 2 was trapped in is the most likely explanation of this discrepancy between measured values, though further work is warranted.« less

A lattice Boltzmann model for substrates with regularly structured surface roughness

NASA Astrophysics Data System (ADS)

Yagub, A.; Farhat, H.; Kondaraju, S.; Singh, T.

2015-11-01

Superhydrophobic surface characteristics are important in many industrial applications, ranging from the textile to the military. It was observed that surfaces fabricated with nano/micro roughness can manipulate the droplet contact angle, thus providing an opportunity to control the droplet wetting characteristics. The Shan and Chen (SC) lattice Boltzmann model (LBM) is a good numerical tool, which holds strong potentials to qualify for simulating droplets wettability. This is due to its realistic nature of droplet contact angle (CA) prediction on flat smooth surfaces. But SC-LBM was not able to replicate the CA on rough surfaces because it lacks a real representation of the physics at work under these conditions. By using a correction factor to influence the interfacial tension within the asperities, the physical forces acting on the droplet at its contact lines were mimicked. This approach allowed the model to replicate some experimentally confirmed Wenzel and Cassie wetting cases. Regular roughness structures with different spacing were used to validate the study using the classical Wenzel and Cassie equations. The present work highlights the strength and weakness of the SC model and attempts to qualitatively conform it to the fundamental physics, which causes a change in the droplet apparent contact angle, when placed on nano/micro structured surfaces.

Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

PubMed

Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

2008-12-19

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

A realistic 3+1D Viscous Hydro Algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romatschke, Paul

2015-05-31

DoE funds were used as bridge funds for the faculty position for the PI at the University of Colorado. The total funds for the Years 3-5 of the JET Topical Collaboration amounted to about 50 percent of the academic year salary of the PI.The PI contributed to the JET Topical Collaboration by developing, testing and applying algorithms for a realistic simulation of the bulk medium created in relativistic ion collisions.Specifically, two approaches were studied, one based on a new Lattice-Boltzmann (LB) framework, and one on a more traditional viscous hydro-dynamics framework. Both approaches were found to be viable in principle,more » with the LB approach being more elegant but needing still more time to develop.The traditional approach led to the super-hybrid model of ion collisions dubbed 'superSONIC', and has been successfully used for phenomenology of relativistic heavy-ion and light-on-heavy-ion collisions.In the time-frame of the JET Topical Collaboration, the Colorado group has published 15 articles in peer-reviewed journals, three of which were published in Physical Review Letters. The group graduated one Master student during this time-frame and two more PhD students are expected to graduate in the next few years. The PI has given more than 28 talks and presentations during this period.« less

Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study

NASA Astrophysics Data System (ADS)

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 recent ‘extended’ scaling theory of Kendon (in which R2 is self-limiting but Re[phi] not). Obtaining our results has required careful steering of several numerical control parameters so as to maintain adequate algorithmic stability, efficiency and isotropy, while eliminating unwanted residual diffusion. (We argue that the latter affects some studies in the literature which report l [similar] t2/3 for t [less, similar] 104.) We analyse the various sources of error and find them just within acceptable levels (a few percent each) in most of our datasets. To bring these under significantly better control, or to go much further into the inertial regime, would require much larger computational resources and/or a breakthrough in algorithm design.

Quantum search algorithms on a regular lattice

NASA Astrophysics Data System (ADS)

Hein, Birgit; Tanner, Gregor

2010-07-01

Quantum algorithms for searching for one or more marked items on a d-dimensional lattice provide an extension of Grover’s search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.

Graphical Representations and Cluster Algorithms for Ice Rule Vertex Models.

NASA Astrophysics Data System (ADS)

Shtengel, Kirill; Chayes, L.

2002-03-01

We introduce a new class of polymer models which is closely related to loop models, recently a topic of intensive studies. These particular models arise as graphical representations for ice-rule vertex models. The associated cluster algorithms provide a unification and generalisation of most of the existing algorithms. For many lattices, percolation in the polymer models evidently indicates first order phase transitions in the vertex models. Critical phases can be understood as being susceptible to colour symmetry breaking in the polymer models. The analysis includes, but is certainly not limited to the square lattice six-vertex model. In particular, analytic criteria can be found for low temperature phases in other even coordinated 2D lattices such as the triangular lattice, or higher dimensional lattices such as the hyper-cubic lattices of arbitrary dimensionality. Finally, our approach can be generalised to the vertex models that do not obey the ice rule, such as the eight-vertex model.

Multiphase flow in geometrically simple fracture intersections

USGS Publications Warehouse

Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,

2006-01-01

A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.

Modeling Flue Pipes: Subsonic Flow, Lattice Boltzmann, and Parallel Distributed Computers.

DTIC Science & Technology

1995-01-01

Abstract The problem of simulating the hydrodynamics and the acoustic waves inside wind musical instruments such as the recorder, the organ, and the ute...inside wind musical instruments such as the recorder, the organ, and the ute is considered. The problem is attacked by developing suitable local...applications such as the simulation of uid dynamics inside wind musical instruments. In the past, he has also worked on numerical methods for ordinary di

Diffuse sorption modeling.

PubMed

Pivovarov, Sergey

2009-04-01

This work presents a simple solution for the diffuse double layer model, applicable to calculation of surface speciation as well as to simulation of ionic adsorption within the diffuse layer of solution in arbitrary salt media. Based on Poisson-Boltzmann equation, the Gaines-Thomas selectivity coefficient for uni-bivalent exchange on clay, K(GT)(Me(2+)/M(+))=(Q(Me)(0.5)/Q(M)){M(+)}/{Me(2+)}(0.5), (Q is the equivalent fraction of cation in the exchange capacity, and {M(+)} and {Me(2+)} are the ionic activities in solution) may be calculated as [surface charge, mueq/m(2)]/0.61. The obtained solution of the Poisson-Boltzmann equation was applied to calculation of ionic exchange on clays and to simulation of the surface charge of ferrihydrite in 0.01-6 M NaCl solutions. In addition, a new model of acid-base properties was developed. This model is based on assumption that the net proton charge is not located on the mathematical surface plane but diffusely distributed within the subsurface layer of the lattice. It is shown that the obtained solution of the Poisson-Boltzmann equation makes such calculations possible, and that this approach is more efficient than the original diffuse double layer model.

Ising antiferromagnet on the Archimedean lattices.

PubMed

Yu, Unjong

2015-06-01

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.

Ising antiferromagnet on the Archimedean lattices

NASA Astrophysics Data System (ADS)

Yu, Unjong

2015-06-01

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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 domainmore » 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.« less

Invariant patterns in crystal lattices: Implications for protein folding algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

HART,WILLIAM E.; ISTRAIL,SORIN

2000-06-01

Crystal lattices are infinite periodic graphs that occur naturally in a variety of geometries and which are of fundamental importance in polymer science. Discrete models of protein folding use crystal lattices to define the space of protein conformations. Because various crystal lattices provide discretizations of the same physical phenomenon, it is reasonable to expect that there will exist invariants across lattices related to fundamental properties of the protein folding process. This paper considers whether performance-guaranteed approximability is such an invariant for HP lattice models. The authors define a master approximation algorithm that has provable performance guarantees provided that a specificmore » sublattice exists within a given lattice. They describe a broad class of crystal lattices that are approximable, which further suggests that approximability is a general property of HP lattice models.« less

Lattice surgery on the Raussendorf lattice

NASA Astrophysics Data System (ADS)

Herr, Daniel; Paler, Alexandru; Devitt, Simon J.; Nori, Franco

2018-07-01

Lattice surgery is a method to perform quantum computation fault-tolerantly by using operations on boundary qubits between different patches of the planar code. This technique allows for universal planar code computation without eliminating the intrinsic two-dimensional nearest-neighbor properties of the surface code that eases physical hardware implementations. Lattice surgery approaches to algorithmic compilation and optimization have been demonstrated to be more resource efficient for resource-intensive components of a fault-tolerant algorithm, and consequently may be preferable over braid-based logic. Lattice surgery can be extended to the Raussendorf lattice, providing a measurement-based approach to the surface code. In this paper we describe how lattice surgery can be performed on the Raussendorf lattice and therefore give a viable alternative to computation using braiding in measurement-based implementations of topological codes.

Multitarget Tracking Studies.

DTIC Science & Technology

1981-07-01

ie "n.: r c:.t. ’ur wn Le r":2- ence Indistes :nac pole a n :arc loca- 40 ":Lors !AVe a sinificant effect n convergence raes.- .ahdn te poles and...LATTICE ALGORITHMS ( LADO ) 1. The Normalized AR Lattice (ARN) This algorithm implements the normalized algorithm described in [23]. The AR coefficients are

A Boltzmann machine for the organization of intelligent machines

NASA Technical Reports Server (NTRS)

Moed, Michael C.; Saridis, George N.

1990-01-01

A three-tier structure consisting of organization, coordination, and execution levels forms the architecture of an intelligent machine using the principle of increasing precision with decreasing intelligence from a hierarchically intelligent control. This system has been formulated as a probabilistic model, where uncertainty and imprecision can be expressed in terms of entropies. The optimal strategy for decision planning and task execution can be found by minimizing the total entropy in the system. The focus is on the design of the organization level as a Boltzmann machine. Since this level is responsible for planning the actions of the machine, the Boltzmann machine is reformulated to use entropy as the cost function to be minimized. Simulated annealing, expanding subinterval random search, and the genetic algorithm are presented as search techniques to efficiently find the desired action sequence and illustrated with numerical examples.

Erosion of cohesive soil layers above underground conduits

NASA Astrophysics Data System (ADS)

Luu, Li-Hua; Philippe, Pierre; Noury, Gildas; Perrin, Jérôme; Brivois, Olivier

2017-06-01

Using a recently developed 2D numerical modelling that combines Discrete Element (DEM) and Lattice Boltzmann methods (LBM), we simulate the destabilisation by an hydraulic gradient of a cohesive granular soil clogging the top of an underground conduit. We aim to perform a multi-scale study that relates the grain scale behavior to the macroscopic erosion process. In particular, we study the influence of the flow conditions and the inter-particle contact forces intensity on the erosion kinetic.

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

NASA Astrophysics Data System (ADS)

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.

Minimized Capillary End Effect During CO2 Displacement in 2-D Micromodel by Manipulating Capillary Pressure at the Outlet Boundary in Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Kang, Dong Hun; Yun, Tae Sup

2018-02-01

We propose a new outflow boundary condition to minimize the capillary end effect for a pore-scale CO2 displacement simulation. The Rothman-Keller lattice Boltzmann method with multi-relaxation time is implemented to manipulate a nonflat wall and inflow-outflow boundaries with physically acceptable fluid properties in 2-D microfluidic chip domain. Introducing a mean capillary pressure acting at CO2-water interface to the nonwetting fluid at the outlet effectively prevents CO2 injection pressure from suddenly dropping upon CO2 breakthrough such that the continuous CO2 invasion and the increase of CO2 saturation are allowed. This phenomenon becomes most pronounced at capillary number of logCa = -5.5, while capillary fingering and massive displacement of CO2 prevail at low and high capillary numbers, respectively. Simulations with different domain length in homogeneous and heterogeneous domains reveal that capillary pressure and CO2 saturation near the inlet are reproducible compared with those with a proposed boundary condition. The residual CO2 saturation uniquely follows the increasing tendency with increasing capillary number, corroborated by experimental evidences. The determination of the mean capillary pressure and its sensitivity are also discussed. The proposed boundary condition is commonly applicable to other pore-scale simulations to accurately capture the spatial distribution of nonwetting fluid and corresponding displacement ratio.

Numerical Simulation of Natural Convection of a Nanofluid in an Inclined Heated Enclosure Using Two-Phase Lattice Boltzmann Method: Accurate Effects of Thermophoresis and Brownian Forces.

PubMed

Ahmed, Mahmoud; Eslamian, Morteza

2015-12-01

Laminar natural convection in differentially heated (β = 0°, where β is the inclination angle), inclined (β = 30° and 60°), and bottom-heated (β = 90°) square enclosures filled with a nanofluid is investigated, using a two-phase lattice Boltzmann simulation approach. The effects of the inclination angle on Nu number and convection heat transfer coefficient are studied. The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation. The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors. Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect. Here we show that thermophoresis has a considerable effect on heat transfer augmentation in laminar natural convection. Our non-homogenous modeling approach shows that heat transfer in nanofluids is a function of the inclination angle and Ra number. It also reveals some details of flow behavior which cannot be captured by single-phase models. The minimum heat transfer rate is associated with β = 90° (bottom-heated) and the maximum heat transfer rate occurs in an inclination angle which varies with the Ra number.

Effect of the forcing term in the pseudopotential lattice Boltzmann modeling of thermal flows

NASA Astrophysics Data System (ADS)

Li, Qing; Luo, K. H.

2014-05-01

The pseudopotential lattice Boltzmann (LB) model is a popular model in the LB community for simulating multiphase flows. Recently, several thermal LB models, which are based on the pseudopotential LB model and constructed within the framework of the double-distribution-function LB method, were proposed to simulate thermal multiphase flows [G. Házi and A. Márkus, Phys. Rev. E 77, 026305 (2008), 10.1103/PhysRevE.77.026305; L. Biferale, P. Perlekar, M. Sbragaglia, and F. Toschi, Phys. Rev. Lett. 108, 104502 (2012), 10.1103/PhysRevLett.108.104502; S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012), 10.1016/j.ijheatmasstransfer.2012.04.037; M. R. Kamali et al., Phys. Rev. E 88, 033302 (2013), 10.1103/PhysRevE.88.033302]. The objective of the present paper is to show that the effect of the forcing term on the temperature equation must be eliminated in the pseudopotential LB modeling of thermal flows. First, the effect of the forcing term on the temperature equation is shown via the Chapman-Enskog analysis. For comparison, alternative treatments that are free from the forcing-term effect are provided. Subsequently, numerical investigations are performed for two benchmark tests. The numerical results clearly show that the existence of the forcing-term effect will lead to significant numerical errors in the pseudopotential LB modeling of thermal flows.

Numerical simulation of convection and heat transfer in Czochralski crystal growth by multiple-relaxation-time LBM

NASA Astrophysics Data System (ADS)

Liu, Ding; Huang, Weichao; Zhang, Ni

2017-07-01

A two-dimensional axisymmetric swirling model based on the lattice Boltzmann method (LBM) in a pseudo Cartesian coordinate system is posited to simulate Czochralski (Cz) crystal growth in this paper. Specifically, the multiple-relaxation-time LBM (MRT-LBM) combined with the finite difference method (FDM) is used to analyze the melt convection and heat transfer in the process of Cz crystal growth. An incompressible axisymmetric swirling MRT-LB D2Q9 model is applied to solve for the axial and radial velocities by inserting thermal buoyancy and rotational inertial force into the two-dimensional lattice Boltzmann equation. In addition, the melt temperature and the azimuthal velocity are solved by MRT-LB D2Q5 models, and the crystal temperature is solved by FDM. The comparison results of stream functions values of different methods demonstrate that our hybrid model can be used to simulate the fluid-thermal coupling in the axisymmetric swirling model correctly and effectively. Furthermore, numerical simulations of melt convection and heat transfer are conducted under the conditions of high Grashof (Gr) numbers, within the range of 105 ˜ 107, and different high Reynolds (Re) numbers. The experimental results show our hybrid model can obtain the exact solution of complex crystal-growth models and analyze the fluid-thermal coupling effectively under the combined action of natural convection and forced convection.

Large Eddy Simulation of Wall-Bounded Turbulent Flows with the Lattice Boltzmann Method: Effect of Collision Model, SGS Model and Grid Resolution

NASA Astrophysics Data System (ADS)

Pradhan, Aniruddhe; Akhavan, Rayhaneh

2017-11-01

Effect of collision model, subgrid-scale model and grid resolution in Large Eddy Simulation (LES) of wall-bounded turbulent flows with the Lattice Boltzmann Method (LBM) is investigated in turbulent channel flow. The Single Relaxation Time (SRT) collision model is found to be more accurate than Multi-Relaxation Time (MRT) collision model in well-resolved LES. Accurate LES requires grid resolutions of Δ+ <= 4 in the near-wall region, which is comparable to Δ+ <= 2 required in DNS. At larger grid resolutions SRT becomes unstable, while MRT remains stable but gives unacceptably large errors. LES with no model gave errors comparable to the Dynamic Smagorinsky Model (DSM) and the Wall Adapting Local Eddy-viscosity (WALE) model. The resulting errors in the prediction of the friction coefficient in turbulent channel flow at a bulk Reynolds Number of 7860 (Reτ 442) with Δ+ = 4 and no-model, DSM and WALE were 1.7%, 2.6%, 3.1% with SRT, and 8.3% 7.5% 8.7% with MRT, respectively. These results suggest that LES of wall-bounded turbulent flows with LBM requires either grid-embedding in the near-wall region, with grid resolutions comparable to DNS, or a wall model. Results of LES with grid-embedding and wall models will be discussed.

a Lattice Boltzmann Study of the 2d Boundary Layer Created by AN Oscillating Plate

NASA Astrophysics Data System (ADS)

Cappietti, L.; Chopard, B.

We study the applicability of the Lattice Boltzmann Method (LBM) to simulate the 2D laminar boundary layer induced by an oscillating flat plate. We also investigate the transition to the disturbed laminar regime that occurs with a rough oscillating plate. The simulations were performed in two cases: first with a fluid otherwise at rest and second in presence of superimposed current. The generation of coherent vortex structures and their evolution are commented. The accuracy of the method was checked by comparisons with the exact analytical solution of the Navier-Stokes equations for the so-called Stokes' Second Problem. The comparisons show that LBM reproduces this time varying flow with first order accuracy. In the case of the wavy-plate, the results show that a mechanism of vortex-jet formations, low speed-streak and shear instability sustain a systems of stationary vortices outside the boundary layer. The vortex-jet takes place at the end of the decelerating phase whereas the boundary layer turns out to be laminar when the plate accelerates. In the presence of the superimposed current, the vortex-jet mechanism is still effective but the vortices outside the boundary layer are only present during part of the oscillating period. During the remaining part, the flow turns out to be laminar although a wave perturbation in the velocity field is present.

Multi-relaxation-time lattice Boltzmann modeling of the acoustic field generated by focused transducer

NASA Astrophysics Data System (ADS)

Shan, Feng; Guo, Xiasheng; Tu, Juan; Cheng, Jianchun; Zhang, Dong

The high-intensity focused ultrasound (HIFU) has become an attractive therapeutic tool for the noninvasive tumor treatment. The ultrasonic transducer is the key component in HIFU treatment to generate the HIFU energy. The dimension of focal region generated by the transducer is closely relevant to the safety of HIFU treatment. Therefore, it is essential to numerically investigate the focal region of the transducer. Although the conventional acoustic wave equations have been used successfully to describe the acoustic field, there still exist some inherent drawbacks. In this work, we presented an axisymmetric isothermal multi-relaxation-time lattice Boltzmann method (MRT-LBM) model with the Bouzidi-Firdaouss-Lallemand (BFL) boundary condition in cylindrical coordinate system. With this model, some preliminary simulations were firstly conducted to determine a reasonable value of the relaxation parameter. Then, the validity of the model was examined by comparing the results obtained with the LBM results with the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Spheroidal beam equation (SBE) for the focused transducers with different aperture angles, respectively. In addition, the influences of the aperture angle on the focal region were investigated. The proposed model in this work will provide significant references for the parameter optimization of the focused transducer for applications in the HIFU treatment or other fields, and provide new insights into the conventional acoustic numerical simulations.

Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers.

PubMed

Rosén, T; Einarsson, J; Nordmark, A; Aidun, C K; Lundell, F; Mehlig, B

2015-12-01

We numerically analyze the rotation of a neutrally buoyant spheroid in a shear flow at small shear Reynolds number. Using direct numerical stability analysis of the coupled nonlinear particle-flow problem, we compute the linear stability of the log-rolling orbit at small shear Reynolds number Re(a). As Re(a)→0 and as the box size of the system tends to infinity, we find good agreement between the numerical results and earlier analytical predictions valid to linear order in Re(a) for the case of an unbounded shear. The numerical stability analysis indicates that there are substantial finite-size corrections to the analytical results obtained for the unbounded system. We also compare the analytical results to results of lattice Boltzmann simulations to analyze the stability of the tumbling orbit at shear Reynolds numbers of order unity. Theory for an unbounded system at infinitesimal shear Reynolds number predicts a bifurcation of the tumbling orbit at aspect ratio λ(c)≈0.137 below which tumbling is stable (as well as log rolling). The simulation results show a bifurcation line in the λ-Re(a) plane that reaches λ≈0.1275 at the smallest shear Reynolds number (Re(a)=1) at which we could simulate with the lattice Boltzmann code, in qualitative agreement with the analytical results.

Three-dimensional lattice Boltzmann simulations of microdroplets including contact angle hysteresis on topologically structured surfaces

DOE PAGES

Ba, Yan; Kang, Qinjun; Liu, Haihu; ...

2016-04-14

In this study, the dynamical behavior of a droplet on topologically structured surface is investigated by using a three-dimensional color-gradient lattice Boltzmann model. A wetting boundary condition is proposed to model fluid-surface interactions, which is advantageous to improve the accuracy of the simulation and suppress spurious velocities at the contact line. The model is validated by the droplet partial wetting test and reproduction of the Cassie and Wenzel states. A series of simulations are conducted to investigate the behavior of a droplet when subjected to a shear flow. It is found that in Cassie state, the droplet undergoes a transitionmore » from stationary, to slipping and finally to detachment states as the capillary number increases, while in Wenzel state, the last state changes to the breakup state. The critical capillary number, above which the droplet slipping occurs, is small for the Cassie droplet, but is significantly enhanced for the Wenzel droplet due to the increased contact angle hysteresis. In Cassie state, the receding contact angle nearly equals the prediction by the Cassie relation, and the advancing contact angle is close to 180°, leading to a small contact angle hysteresis. In Wenzel state, however, the contact angle hysteresis is extremely large (around 100°). Finally, high droplet mobility can be easily achieved for Cassie droplets, whereas in Wenzel state, extremely low droplet mobility is identified.« less

Generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect

NASA Astrophysics Data System (ADS)

Chen, Li; Fang, Wenzhen; Kang, Qinjun; De'Haven Hyman, Jeffrey; Viswanathan, Hari S.; Tao, Wen-Quan

2015-03-01

Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. [Phys. Rev. E 65, 046308 (2002), 10.1103/PhysRevE.65.046308]. The second-order Beskok and Karniadakis-Civan's correlation [A. Beskok and G. Karniadakis, Microscale Thermophys. Eng. 3, 43 (1999), 10.1080/108939599199864 and F. Civan, Transp. Porous Med. 82, 375 (2010), 10.1007/s11242-009-9432-z] is adopted to calculate the apparent permeability based on intrinsic permeability and the Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate the model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicate that Klinkenberg's effect plays a significant role on fluid flow in low-permeability porous media, and it is more pronounced as the Knudsen number increases. Fluid flow in a shale matrix with and without fractures is also studied, and it is found that the fractures greatly enhance the fluid flow and Klinkenberg's effect leads to higher global permeability of the shale matrix.

Lattice Boltzmann simulations of supercritical CO2-water drainage displacement in porous media: CO2 saturation and displacement mechanism.

PubMed

Yamabe, Hirotatsu; Tsuji, Takeshi; Liang, Yunfeng; Matsuoka, Toshifumi

2015-01-06

CO2 geosequestration in deep aquifers requires the displacement of water (wetting phase) from the porous media by supercritical CO2 (nonwetting phase). However, the interfacial instabilities, such as viscous and capillary fingerings, develop during the drainage displacement. Moreover, the burstlike Haines jump often occurs under conditions of low capillary number. To study these interfacial instabilities, we performed lattice Boltzmann simulations of CO2-water drainage displacement in a 3D synthetic granular rock model at a fixed viscosity ratio and at various capillary numbers. The capillary numbers are varied by changing injection pressure, which induces changes in flow velocity. It was observed that the viscous fingering was dominant at high injection pressures, whereas the crossover of viscous and capillary fingerings was observed, accompanied by Haines jumps, at low injection pressures. The Haines jumps flowing forward caused a significant drop of CO2 saturation, whereas Haines jumps flowing backward caused an increase of CO2 saturation (per injection depth). We demonstrated that the pore-scale Haines jumps remarkably influenced the flow path and therefore equilibrium CO2 saturation in crossover domain, which is in turn related to the storage efficiency in the field-scale geosequestration. The results can improve our understandings of the storage efficiency by the effects of pore-scale displacement phenomena.

Observation of Bright Ring Phenomenon for Red Blood Cells by Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Kim, Young Woo; Moon, Ji Young; Lee, Joon Sang

2017-11-01

RBC (Red Blood Cell) aggregation is one of interests for various biomechanical fields such as cell chip or visualization. The unique phenomenon called ``bright ring'' is due to RBC aggregation in pulsatile flow of blood. Shear rate and flow acceleration on RBC causes them to repeat aggregating and scattering from center of the channel. The reason that this phenomenon is called bright ring is because that when observed by ultrasound imaging, the bright ring occurs periodically. Many studies tried to observe this bright ring phenomenon experimentally. However, there are yet not many studies trying to make use of this phenomenon for practical purposes. Bright ring phenomenon has high potential when used for cell separation or other microchip devices. In this paper, the Lattice Boltzmann method is used to control this bright ring phenomenon. The purpose of this paper is to find conditions when bright ring phenomenon occurs, and to control the aggregating-scattering frequency and degree. Deformability of RBC is calculated following the work of Moon JY et al. (2016). The result of this paper could be further extended to the optimization of cell-separating microchips. This work was also supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (No. 2015R1A5A1037668) and Brain Korea 21 Plus.

The effects of gas diffusion layers structure on water transportation using X-ray computed tomography based Lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Jinuntuya, Fontip; Whiteley, Michael; Chen, Rui; Fly, Ashley

2018-02-01

The Gas Diffusion Layer (GDL) of a Polymer Electrolyte Membrane Fuel Cell (PEMFC) plays a crucial role in overall cell performance. It is responsible for the dissemination of reactant gasses from the gas supply channels to the reactant sites at the Catalyst Layer (CL), and the adequate removal of product water from reactant sites back to the gas channels. Existing research into water transport in GDLs has been simplified to 2D estimations of GDL structures or use virtual stochastic models. This work uses X-ray computed tomography (XCT) to reconstruct three types of GDL in a model. These models are then analysed via Lattice Boltzmann methods to understand the water transport behaviours under differing contact angles and pressure differences. In this study, the three GDL samples were tested over the contact angles of 60°, 80°, 90°, 100°, 120° and 140° under applied pressure differences of 5 kPa, 10 kPa and 15 kPa. By varying the contact angle and pressure difference, it was found that the transition between stable displacement and capillary fingering is not a gradual process. Hydrophilic contact angles in the region of 60°<θ < 90° showed stable displacement properties, whereas contact angles in the region of 100°<θ < 140° displayed capillary fingering characteristics.

Extended lattice Boltzmann scheme for droplet combustion.

PubMed

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.

Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles

NASA Astrophysics Data System (ADS)

Zhang, Pei; Galindo-Torres, S. A.; Tang, Hongwu; Jin, Guangqiu; Scheuermann, A.; Li, Ling

2016-06-01

We investigated the settling dynamics of irregularly shaped particles in a still fluid under a wide range of conditions with Reynolds numbers Re varying between 1 and 2000, sphericity ϕ and circularity c both greater than 0.5, and Corey shape factor (CSF) less than 1. To simulate the particle settling process, a modified lattice Boltzmann model combined with a turbulence module was adopted. This model was first validated using experimental data for particles of spherical and cubic shapes. For irregularly shaped particles, two different types of settling behaviors were observed prior to particles reaching a steady state: accelerating and accelerating-decelerating, which could be distinguished by a critical CSF value of approximately 0.7. The settling dynamics were analyzed with a focus on the projected areas and angular velocities of particles. It was found that a minor change in the starting projected area, an indicator of the initial particle orientation, would not strongly affect the settling velocity for low Re. Periodic oscillations developed for all simulated particles when Re>100 . The amplitude of these oscillations increased with Re. However, the periods were not sensitive to Re. The critical Re that defined the transition between the steady and periodically oscillating behaviors depended on the inertia tensor. In particular, the maximum eigenvalue of the inertia tensor played a major role in signaling this transition in comparison to the intermediate and minimum eigenvalues.

Investigation of heat transfer in cereal-based foam from a micro-scale perspective using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Mack, Simone; Hussein, Mohamed A.; Becker, Thomas

2011-12-01

Foam materials are multicomponent and multiphase systems, where under the influence of heat several temperature-dependent processes occur. In cereal-based foams these processes include protein denaturation, starch gelatinization, phase changes such as water evaporation, and structural changes covering bubble expansion and coalescence. This research focuses on modeling heat transfer processes in cereal foams under thermal treatment from a microstructural point of view. The complex thermo-fluidic processes inside the foam are considered for the solid and the gaseous phase, respectively. Additionally, the microstructural foam characteristics are modified to establish their effect on the overall heat transfer rate, and the micro-scale dynamics are introduced by means of lattice Boltzmann methods (LBM). The objective of this study is to deliver sophisticated insight into the impact of structural properties, due to the fact that optimized parameters would help to improve the bakery industry by means of reduction in baking time, energy, and costs. The results show that altering the porosity and/or the interconnectivity of gas pores in bread crumb influences the overall heat transfer. In comparison to foams having a porosity of 55% and discrete pores, the impact of coalescence exhibits a reduction of baking time of about 2 min. Increasing the porosity about 20% results in reducing the baking time about 7 min.

Multiple-relaxation-time color-gradient lattice Boltzmann model for simulating two-phase flows with high density ratio

NASA Astrophysics Data System (ADS)

Ba, Yan; Liu, Haihu; Li, Qing; Kang, Qinjun; Sun, Jinju

2016-08-01

In this paper we propose a color-gradient lattice Boltzmann (LB) model for simulating two-phase flows with high density ratio and high Reynolds number. The model applies a multirelaxation-time (MRT) collision operator to enhance the stability of the simulation. A source term, which is derived by the Chapman-Enskog analysis, is added into the MRT LB equation so that the Navier-Stokes equations can be exactly recovered. Also, a form of the equilibrium density distribution function is used to simplify the source term. To validate the proposed model, steady flows of a static droplet and the layered channel flow are first simulated with density ratios up to 1000. Small values of spurious velocities and interfacial tension errors are found in the static droplet test, and improved profiles of velocity are obtained by the present model in simulating channel flows. Then, two cases of unsteady flows, Rayleigh-Taylor instability and droplet splashing on a thin film, are simulated. In the former case, the density ratio of 3 and Reynolds numbers of 256 and 2048 are considered. The interface shapes and spike and bubble positions are in good agreement with the results of previous studies. In the latter case, the droplet spreading radius is found to obey the power law proposed in previous studies for the density ratio of 100 and Reynolds number up to 500.

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

NASA Astrophysics Data System (ADS)

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.

Study on C-S and P-R EOS in pseudo-potential lattice Boltzmann model for two-phase flows

NASA Astrophysics Data System (ADS)

Peng, Yong; Mao, Yun Fei; Wang, Bo; Xie, Bo

Equations of State (EOS) is crucial in simulating multiphase flows by the pseudo-potential lattice Boltzmann method (LBM). In the present study, the Peng and Robinson (P-R) and Carnahan and Starling (C-S) EOS in the pseudo-potential LBM with Exact Difference Method (EDM) scheme for two-phase flows have been compared. Both of P-R and C-S EOS have been used to study the two-phase separation, surface tension, the maximum two-phase density ratio and spurious currents. The study shows that both of P-R and C-S EOS agree with the analytical solutions although P-R EOS may perform better. The prediction of liquid phase by P-R EOS is more accurate than that of air phase and the contrary is true for C-S EOS. Predictions by both of EOS conform with the Laplace’s law. Besides, adjustment of surface tension is achieved by adjusting T. The P-R EOS can achieve larger maximum density ratio than C-S EOS under the same τ. Besides, no matter the C-S EOS or the P-R EOS, if τ tends to 0.5, the computation is prone to numerical instability. The maximum spurious current for P-R is larger than that of C-S. The multiple-relaxation-time LBM still can improve obviously the numerical stability and can achieve larger maximum density ratio.

Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios

NASA Astrophysics Data System (ADS)

Fakhari, Abbas; Mitchell, Travis; Leonardi, Christopher; Bolster, Diogo

2017-11-01

Based on phase-field theory, we introduce a robust lattice-Boltzmann equation for modeling immiscible multiphase flows at large density and viscosity contrasts. Our approach is built by modifying the method proposed by Zu and He [Phys. Rev. E 87, 043301 (2013), 10.1103/PhysRevE.87.043301] in such a way as to improve efficiency and numerical stability. In particular, we employ a different interface-tracking equation based on the so-called conservative phase-field model, a simplified equilibrium distribution that decouples pressure and velocity calculations, and a local scheme based on the hydrodynamic distribution functions for calculation of the stress tensor. In addition to two distribution functions for interface tracking and recovery of hydrodynamic properties, the only nonlocal variable in the proposed model is the phase field. Moreover, within our framework there is no need to use biased or mixed difference stencils for numerical stability and accuracy at high density ratios. This not only simplifies the implementation and efficiency of the model, but also leads to a model that is better suited to parallel implementation on distributed-memory machines. Several benchmark cases are considered to assess the efficacy of the proposed model, including the layered Poiseuille flow in a rectangular channel, Rayleigh-Taylor instability, and the rise of a Taylor bubble in a duct. The numerical results are in good agreement with available numerical and experimental data.

Pore-Scale Determination of Gas Relative Permeability in Hydrate-Bearing Sediments Using X-Ray Computed Micro-Tomography and Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Chen, Xiongyu; Verma, Rahul; Espinoza, D. Nicolas; Prodanović, Maša.

2018-01-01

This work uses X-ray computed micro-tomography (μCT) to monitor xenon hydrate growth in a sandpack under the excess gas condition. The μCT images give pore-scale hydrate distribution and pore habit in space and time. We use the lattice Boltzmann method to calculate gas relative permeability (krg) as a function of hydrate saturation (Shyd) in the pore structure of the experimental hydrate-bearing sand retrieved from μCT data. The results suggest the krg - Shyd data fit well a new model krg = (1-Shyd)·exp(-4.95·Shyd) rather than the simple Corey model. In addition, we calculate krg-Shyd curves using digital models of hydrate-bearing sand based on idealized grain-attaching, coarse pore-filling, and dispersed pore-filling hydrate habits. Our pore-scale measurements and modeling show that the krg-Shyd curves are similar regardless of whether hydrate crystals develop grain-attaching or coarse pore-filling habits. The dispersed pore filling habit exhibits much lower gas relative permeability than the other two, but it is not observed in the experiment and not compatible with Ostwald ripening mechanisms. We find that a single grain-shape factor can be used in the Carman-Kozeny equation to calculate krg-Shyd data with known porosity and average grain diameter, suggesting it is a useful model for hydrate-bearing sand.

Large scale simulation of liquid water transport in a gas diffusion layer of polymer electrolyte membrane fuel cells using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Sakaida, Satoshi; Tabe, Yutaka; Chikahisa, Takemi

2017-09-01

A method for the large-scale simulation with the lattice Boltzmann method (LBM) is proposed for liquid water movement in a gas diffusion layer (GDL) of polymer electrolyte membrane fuel cells. The LBM is able to analyze two-phase flows in complex structures, however the simulation domain is limited due to heavy computational loads. This study investigates a variety means to reduce computational loads and increase the simulation areas. One is applying an LBM treating two-phases as having the same density, together with keeping numerical stability with large time steps. The applicability of this approach is confirmed by comparing the results with rigorous simulations using actual density. The second is establishing the maximum limit of the Capillary number that maintains flow patterns similar to the precise simulation; this is attempted as the computational load is inversely proportional to the Capillary number. The results show that the Capillary number can be increased to 3.0 × 10-3, where the actual operation corresponds to Ca = 10-5∼10-8. The limit is also investigated experimentally using an enlarged scale model satisfying similarity conditions for the flow. Finally, a demonstration is made of the effects of pore uniformity in GDL as an example of a large-scale simulation covering a channel.

Investigation of the Effect of the Tortuous Pore Structure on Water Diffusion through a Polymer Film Using Lattice Boltzmann Simulations.

PubMed

Gebäck, Tobias; Marucci, Mariagrazia; Boissier, Catherine; Arnehed, Johan; Heintz, Alexei

2015-04-23

Understanding how the pore structure influences the mass transport through a porous material is important in several applications, not the least in the design of polymer film coatings intended to control drug release. In this study, a polymer film made of ethyl cellulose and hydroxypropyl cellulose was investigated. The 3D structure of the films was first experimentally characterized using confocal laser scanning microscopy data and then mathematically reconstructed for the whole film thickness. Lattice Boltzmann simulations were performed to compute the effective diffusion coefficient of water in the film and the results were compared to experimental data. The local porosities and pore sizes were also analyzed to determine how the properties of the internal film structure affect the water effective diffusion coefficient. The results show that the top part of the film has lower porosity, lower pore size, and lower connectivity, which results in a much lower effective diffusion coefficient in this part, largely determining the diffusion rate through the entire film. Furthermore, the local effective diffusion coefficients were not proportional to the local film porosity, indicating that the results cannot be explained by a single tortuosity factor. In summary, the proposed methodology of combining microscopy data, mass transport simulations, and pore space analysis can give valuable insights on how the film structure affects the mass transport through the film.

Multiphase Simulated Annealing Based on Boltzmann and Bose-Einstein Distribution Applied to Protein Folding Problem.

PubMed

Frausto-Solis, Juan; Liñán-García, Ernesto; Sánchez-Hernández, Juan Paulo; González-Barbosa, J Javier; González-Flores, Carlos; Castilla-Valdez, Guadalupe

2016-01-01

A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the final temperature of the fourth phase, which can be seen as a second Bose-Einstein phase. MQP is a search process that ranges from extremely high to high temperatures, applying a very fast cooling process, and is not very restrictive to accept new solutions. However, BAP and BEAP range from high to low and from low to very low temperatures, respectively. They are more restrictive for accepting new solutions. DEP uses a particular heuristic to detect the stochastic equilibrium by applying a least squares method during its execution. MPSABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of problem instances. MPSABBE was tested with several instances of PFP, showing that the use of both distributions is better than using only the Boltzmann distribution on the classical SA.

Dual representation of lattice QCD with worldlines and worldsheets of Abelian color fluxes

NASA Astrophysics Data System (ADS)

Marchis, Carlotta; Gattringer, Christof

2018-02-01

We present a new dual representation for lattice QCD in terms of wordlines and worldsheets. The exact reformulation is carried out using the recently developed Abelian color flux method where the action is decomposed into commuting minimal terms that connect different colors on neighboring sites. Expanding the Boltzmann factors for these commuting terms allows one to reorganize the gauge field contributions according to links such that the gauge fields can be integrated out in closed form. The emerging constraints give the dual variables the structure of worldlines for the fermions and worldsheets for the gauge degrees of freedom. The partition sum has the form of a strong coupling expansion, and with the Abelian color flux approach discussed here all coefficients of the expansion are known in closed form. We present the dual form for three cases: pure SU(3) lattice gauge theory, strong coupling QCD and full QCD, and discuss in detail the constraints for the color fluxes and their physical interpretation.

Active semi-supervised learning method with hybrid deep belief networks.

PubMed

Zhou, Shusen; Chen, Qingcai; Wang, Xiaolong

2014-01-01

In this paper, we develop a novel semi-supervised learning algorithm called active hybrid deep belief networks (AHD), to address the semi-supervised sentiment classification problem with deep learning. First, we construct the previous several hidden layers using restricted Boltzmann machines (RBM), which can reduce the dimension and abstract the information of the reviews quickly. Second, we construct the following hidden layers using convolutional restricted Boltzmann machines (CRBM), which can abstract the information of reviews effectively. Third, the constructed deep architecture is fine-tuned by gradient-descent based supervised learning with an exponential loss function. Finally, active learning method is combined based on the proposed deep architecture. We did several experiments on five sentiment classification datasets, and show that AHD is competitive with previous semi-supervised learning algorithm. Experiments are also conducted to verify the effectiveness of our proposed method with different number of labeled reviews and unlabeled reviews respectively.

Role of hydrodynamic interactions in dynamics of semi-flexible polyelectrolytes

NASA Astrophysics Data System (ADS)

Kekre, Rahul

Experiments have shown that DNA molecules in capillary electrophoresis migrate across field lines if a pressure gradient is applied simultaneously. We suggest that this migration results from an electrically driven flow field around the polyelectrolyte, which generates additional contributions to the center-of-mass velocity if the overall polymer conformation is asymmetric. Numerical simulations and experiments have demonstrated that confined polymers migrate towards the center of the channel in response to both external forces and uniaxial flows. Yet, migration towards the walls has been observed with combinations of external force and flow. In this work, the kinetic theory for an elastic dumbbell developed by Ma and Graham [Phys. Fluids 17, 083103 (2005)] has been extended to account for the effects of an external body force. Further modifications account for counterion screening within a Debye-Huckel approximation for the specific case of applied electric field. The theory qualitatively reproduces results of both experiments for the migration of neutral polymers and polyelectrolytes. The favorable comparison supports the contention [Long et al., Phys. Rev. Lett. 76, 3858 (1996)] that the hydrodynamic interactions in polyelectrolytes decay algebraically, as 1/r 3, rather than exponentially. A coarse-grained polymer model, without explicit charges, is developed and integrated using Brownian-dynamics simulations in analogy with the kinetic theory. The novel feature of the simulations is the inclusion of hydrodynamic interactions induced by the electric field. This model quantitatively captures experimental observations [Zheng and Yeung, Anal. Chem. 75, 3675 (2003)] of DNA migration under combined electric and pressure-driven flow fields in absence of any adjusted parameters. In addition the model predicts dependence of electrophoretic velocity on the instantaneous length of the polyelectrolyte which has been verified by experiments of Lee et. al. [Electrophoresis 31, 2813 (2010)]. The model also predicts phenomenons that are yet to be verified experimentally. These include decrease in diffusivity and increase in radius of gyration of the polyelectrolyte in high electric fields due to internal dispersion. The resulting change in orientation distribution at high electric fields decreases the extent of migration. Preliminary results from microfluidic experiments are presented in this dissertation demonstrating the saturation of migration. This dissertation also includes comparison of results from lattice-Boltzmann and Brownian dynamics simulations of a linear bead-spring model of DNA for two cases; infinite dilution and confinement. We have systematically varied the parameters that may affect the accuracy of the lattice-Boltzmann simulations, including grid resolution, temperature, polymer mass, periodic boundary size and fluid viscosity. For the case of a single chain Lattice-Boltzmann results for the diffusion coefficient and Rouse mode relaxation times were within 1--2% from those obtained from Brownian-dynamics. Results from both methods are also compared for polymer migration in confined flows driven by a uniform shear or pressure gradient. Center-of-mass distribution obtained from Lattice-Boltzmann simulations agrees quantitatively with Brownian-dynamics results, contradicting previously published results. The mobility matrix for a confined polymer was derived by applying Faxen's correction to the flow-field generated by a point force bounded by two parallel plates. This formulation of the mobility matrix is symmetric and positive-definite for all physically accessible configurations of the polymer.

Towards Direct Numerical Simulation of mass and energy fluxes at the soil-atmospheric interface with advanced Lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

Wang, Ying; Krafczyk, Manfred; Geier, Martin; Schönherr, Martin

2014-05-01

The quantification of soil evaporation and of soil water content dynamics near the soil surface are critical in the physics of land-surface processes on many scales and are dominated by multi-component and multi-phase mass and energy fluxes between the ground and the atmosphere. Although it is widely recognized that both liquid and gaseous water movement are fundamental factors in the quantification of soil heat flux and surface evaporation, their computation has only started to be taken into account using simplified macroscopic models. As the flow field over the soil can be safely considered as turbulent, it would be natural to study the detailed transient flow dynamics by means of Large Eddy Simulation (LES [1]) where the three-dimensional flow field is resolved down to the laminar sub-layer. Yet this requires very fine resolved meshes allowing a grid resolution of at least one order of magnitude below the typical grain diameter of the soil under consideration. In order to gain reliable turbulence statistics, up to several hundred eddy turnover times have to be simulated which adds up to several seconds of real time. Yet, the time scale of the receding saturated water front dynamics in the soil is on the order of hours. Thus we are faced with the task of solving a transient turbulent flow problem including the advection-diffusion of water vapour over the soil-atmospheric interface represented by a realistic tomographic reconstruction of a real porous medium taken from laboratory probes. Our flow solver is based on the Lattice Boltzmann method (LBM) [2] which has been extended by a Cumulant approach similar to the one described in [3,4] to minimize the spurious coupling between the degrees of freedom in previous LBM approaches and can be used as an implicit LES turbulence model due to its low numerical dissipation and increased stability at high Reynolds numbers. The kernel has been integrated into the research code Virtualfluids [5] and delivers up to 30% of the peak performance of modern General Purpose Graphics Processing Units (GPGPU, [6]) allowing the simulation of several minutes real-time for an LES LBM model. In our contribution we will present detailed profiles of the velocity distribution for different surface roughnesses, describe our multi-scale approach for the advection diffusion and estimate water vapour fluxes from transient simulations of the coupled problem. REFERENCES [1] J. Fröhlich and D. von Terzi. Hybrid LES/RANS methods for the simulation of turbulent flows. Progress in Aerospace Sciences, 44(5):349 - 377, 2008. [2] S. Chen and G. D. Doolen, Annual Review, of Fluid Mechanics 30, 329, 1998, [3] S. Seeger and K. H. Hoffmann, The cumulant method for computational kinetic theory, Continuum Mech. Thermodyn., 12:403-421, 2000. [4] S. Seeger and K. H. Hoffmann, The cumulant method applied to a mixture of Maxwell gases, Continuum Mech. Thermodyn., 14:321-335, 2002. [5] S. Freudiger, J. Hegewald and M. Krafczyk. A parallelisation concept for a mult-physics Lattice Boltzmann prototype based on hierarchical grids. Progress in Computational Fluid Dynamics, 8(1):168-178, 2008. [6] M. Schönherr, K. Kucher, M. Geier, M. Stiebler, S. Freudiger and M. Krafczyk, Multi- thread implementations of the Lattice Boltzmann method on non-uniform grids for CPUs and GPUs. Computers & Mathematics with Applications, 61(12):3730-3743, 2011.

Charge Relaxation Dynamics of an Electrolytic Nanocapacitor

PubMed Central

2015-01-01

Understanding ion relaxation dynamics in overlapping electric double layers (EDLs) is critical for the development of efficient nanotechnology-based electrochemical energy storage, electrochemomechanical energy conversion, and bioelectrochemical sensing devices as well as the controlled synthesis of nanostructured materials. Here, a lattice Boltzmann (LB) method is employed to simulate an electrolytic nanocapacitor subjected to a step potential at t = 0 for various degrees of EDL overlap, solvent viscosities, ratios of cation-to-anion diffusivity, and electrode separations. The use of a novel continuously varying and Galilean-invariant molecular-speed-dependent relaxation time (MSDRT) with the LB equation recovers a correct microscopic description of the molecular-collision phenomena and enhances the stability of the LB algorithm. Results for large EDL overlaps indicated oscillatory behavior for the ionic current density, in contrast to monotonic relaxation to equilibrium for low EDL overlaps. Further, at low solvent viscosities and large EDL overlaps, anomalous plasmalike spatial oscillations of the electric field were observed that appeared to be purely an effect of nanoscale confinement. Employing MSDRT in our simulations enabled modeling of the fundamental physics of the transient charge relaxation dynamics in electrochemical systems operating away from equilibrium wherein Nernst–Einstein relation is known to be violated. PMID:25678941

Development and parallelization of a direct numerical simulation to study the formation and transport of nanoparticle clusters in a viscous fluid

NASA Astrophysics Data System (ADS)

Sloan, Gregory James

The direct numerical simulation (DNS) offers the most accurate approach to modeling the behavior of a physical system, but carries an enormous computation cost. There exists a need for an accurate DNS to model the coupled solid-fluid system seen in targeted drug delivery (TDD), nanofluid thermal energy storage (TES), as well as other fields where experiments are necessary, but experiment design may be costly. A parallel DNS can greatly reduce the large computation times required, while providing the same results and functionality of the serial counterpart. A D2Q9 lattice Boltzmann method approach was implemented to solve the fluid phase. The use of domain decomposition with message passing interface (MPI) parallelism resulted in an algorithm that exhibits super-linear scaling in testing, which may be attributed to the caching effect. Decreased performance on a per-node basis for a fixed number of processes confirms this observation. A multiscale approach was implemented to model the behavior of nanoparticles submerged in a viscous fluid, and used to examine the mechanisms that promote or inhibit clustering. Parallelization of this model using a masterworker algorithm with MPI gives less-than-linear speedup for a fixed number of particles and varying number of processes. This is due to the inherent inefficiency of the master-worker approach. Lastly, these separate simulations are combined, and two-way coupling is implemented between the solid and fluid.

Anisotropic lattice thermal conductivity in three-fold degeneracy topological semimetal MoP: a first-principles study

NASA Astrophysics Data System (ADS)

Guo, San-Dong

2017-11-01

Recently, three-component new fermions in topological semimetal MoP are experimentally observed (2017 Nature 546 627), which may have potential applications like topological qubits, low-power electronics and spintronics. These are closely related to thermal transport properties of MoP. In this work, the phonon transport of MoP is investigated by solving the linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA). The calculated room-temperature lattice thermal conductivity is 18.41 W m-1 K^{-1} and 34.71 W m-1 K^{-1} along the in- and cross-plane directions, exhibiting very strong anisotropy. The isotope and size effects on the lattice thermal conductivity are also considered. It is found that isotope scattering produces little effect, and phonon has little contribution to the lattice thermal conductivity, when phonon mean free path (MFP) is larger than 0.15 μ m at 300 K. It is noted that average room-temperature lattice thermal conductivity of MoP is lower than that of representative Weyl semimetal TaAs, which is due to smaller group velocities and larger Grüneisen parameters. Our works provide valuable informations for the thermal management of MoP-based nano-electronics devices, and motivate further experimental works to study thermal transport of MoP.

First-principles investigations on elastic, thermodynamic and lattice thermal conductivity of topological insulator LaAs

NASA Astrophysics Data System (ADS)

Zhou, Yu; Cheng, Yan; Chen, Xiang-Rong; Hu, Cui-E.; Chen, Qi-Feng

2018-07-01

Topological insulators are always a hot topic owing to their various peculiar physical effects, which are useful in spintronics and quantum information processing. Herein, we systematically investigate the elastic, thermodynamic and lattice thermal conductivity of a new typical topological insulator LaAs by combining the first-principles approach and an iterative solution of the Boltzmann transport equation. The obtained elastic constants and other lattice structural parameters of LaAs are well consistent with the experimental and other theoretical results. For the first time, the lattice thermal conductivity (5.46 W/(m•K)) and mean free path (14.4 nm) of LaAs are obtained, which manifests that the LaAs is more likely to be a desirable thermoelectric material. It is noted that the obtained mode-averaged Grüneisen parameters by different ab initio simulation packages are very similar, suggesting that our results are rather responsible. From the phonon scattering rates of LaAs, we speculate that the reduction of acoustic-optical gap and the larger phonon scattering may jointly result in reduction of thermal conductivity for LaAs. Meanwhile, the temperature dependence curves of the lattice thermal conductivity, heat capacity and phonon mean free path are also presented. We expect our work can provide more information for further experimental studies.

Privacy-preserving restricted boltzmann machine.

PubMed

Li, Yu; Zhang, Yuan; Ji, Yue

2014-01-01

With the arrival of the big data era, it is predicted that distributed data mining will lead to an information technology revolution. To motivate different institutes to collaborate with each other, the crucial issue is to eliminate their concerns regarding data privacy. In this paper, we propose a privacy-preserving method for training a restricted boltzmann machine (RBM). The RBM can be got without revealing their private data to each other when using our privacy-preserving method. We provide a correctness and efficiency analysis of our algorithms. The comparative experiment shows that the accuracy is very close to the original RBM model.

Privacy-Preserving Restricted Boltzmann Machine

PubMed Central

Li, Yu

2014-01-01

With the arrival of the big data era, it is predicted that distributed data mining will lead to an information technology revolution. To motivate different institutes to collaborate with each other, the crucial issue is to eliminate their concerns regarding data privacy. In this paper, we propose a privacy-preserving method for training a restricted boltzmann machine (RBM). The RBM can be got without revealing their private data to each other when using our privacy-preserving method. We provide a correctness and efficiency analysis of our algorithms. The comparative experiment shows that the accuracy is very close to the original RBM model. PMID:25101139

Multiscale modelling of Flow-Induced Blood Cell Damage

NASA Astrophysics Data System (ADS)

Liu, Yaling; Sohrabi, Salman

2017-11-01

We study red blood cell (RBC) damage and hemolysis at cellular level. Under high shear rates, pores form on RBC membranes through which hemoglobin (Hb) leaks out and increases free Hb content of plasma leading to hemolysis. By coupling lattice Boltzmann and spring connected network models through immersed boundary method, we estimate hemolysis of a single RBC under various shear rates. The developed cellular damage model can be used as a predictive tool for hydrodynamic and hematologic design optimization of blood-wetting medical devices.

Numerical Simulation of Particle Motion in a Curved Channel

NASA Astrophysics Data System (ADS)

Liu, Yi; Nie, Deming

2018-01-01

In this work the lattice Boltzmann method (LBM) is used to numerically study the motion of a circular particle in a curved channel at intermediate Reynolds numbers (Re). The effects of the Reynolds number and the initial particle position are taken into account. Numerical results include the streamlines, particle trajectories and final equilibrium positions. It has been found that the particle is likely to migrate to a similar equilibrium position irrespective of its initial position when Re is large.

Comparison/Validation Study of Lattice Boltzmann and Navier Stokes for Various Benchmark Applications: Report 1 in Discrete Nano-Scale Mechanics and Simulations Series

DTIC Science & Technology

2014-09-15

solver, OpenFOAM version 2.1.‡ In particular, the incompressible laminar flow equations (Eq. 6-8) were solved in conjunction with the pressure im- plicit...central differencing and upwinding schemes, respectively. Since the OpenFOAM code is inherently transient, steady-state conditions were ob- tained...collaborative effort between Kitware and Los Alamos National Laboratory. ‡ OpenFOAM is a free, open-source computational fluid dynamics software developed

A pedagogical approach to the Boltzmann factor through experiments and simulations

NASA Astrophysics Data System (ADS)

Battaglia, O. R.; Bonura, A.; Sperandeo-Mineo, R. M.

2009-09-01

The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment that, besides having a user-friendly interface, allows an easy interaction with the algorithm. The approach supplies pedagogical support for the introduction of the Boltzmann factor at the undergraduate level to students without a background in statistical mechanics.

A new splitting scheme to the discrete Boltzmann equation for non-ideal gases on non-uniform meshes

NASA Astrophysics Data System (ADS)

Patel, Saumil; Lee, Taehun

2016-12-01

We present a novel numerical procedure for solving the discrete Boltzmann equations (DBE) on non-uniform meshes. Our scheme is based on the Strang splitting method where we seek to investigate two-phase flow applications. In this note, we investigate the onset of parasitic currents which arise in many computational two-phase algorithms. To the best of our knowledge, the results presented in this work show, for the first time, a spectral element discontinuous Galerkin (SEDG) discretization of a discrete Boltzmann equation which successfully eliminates parasitic currents on non-uniform meshes. With the hope that this technique can be used for applications in complex geometries, calculations are performed on non-uniform mesh distributions by using high-order (spectral), body-fitting quadrilateral elements. Validation and verification of our work is carried out by comparing results against the classical 2D Young-Laplace law problem for a static drop.

Defect-free atomic array formation using the Hungarian matching algorithm

NASA Astrophysics Data System (ADS)

Lee, Woojun; Kim, Hyosub; Ahn, Jaewook

2017-05-01

Deterministic loading of single atoms onto arbitrary two-dimensional lattice points has recently been demonstrated, where by dynamically controlling the optical-dipole potential, atoms from a probabilistically loaded lattice were relocated to target lattice points to form a zero-entropy atomic lattice. In this atom rearrangement, how to pair atoms with the target sites is a combinatorial optimization problem: brute-force methods search all possible combinations so the process is slow, while heuristic methods are time efficient but optimal solutions are not guaranteed. Here, we use the Hungarian matching algorithm as a fast and rigorous alternative to this problem of defect-free atomic lattice formation. Our approach utilizes an optimization cost function that restricts collision-free guiding paths so that atom loss due to collision is minimized during rearrangement. Experiments were performed with cold rubidium atoms that were trapped and guided with holographically controlled optical-dipole traps. The result of atom relocation from a partially filled 7 ×7 lattice to a 3 ×3 target lattice strongly agrees with the theoretical analysis: using the Hungarian algorithm minimizes the collisional and trespassing paths and results in improved performance, with over 50% higher success probability than the heuristic shortest-move method.

Theory of the Lattice Thermal Conductivity of Nanowires

NASA Astrophysics Data System (ADS)

Broido, D. A.; Mingo, N.

2004-03-01

Thermal transport in semiconductor nanowires is of considerable scientific interest, and its understanding is important as well for potential applications[1]. We present a theory of the lattice thermal conductivity along semiconductor nanowires which includes anharmonic phonon-phonon scattering as well as defect and boundary scattering. These latter two scattering mechanisms are treated in relaxation time approximations. Our theory provides an iterative solution [2] of the phonon Boltzmann equation in which the full nanowire phonon dispersions and modes obtained from lattice dynamics calculations are included consistently in treating the anharmonic three-phonon scattering. We calculate the lattice thermal conductivity of Si nanowires as a function of temperature and wire thickness, and we compare our results with recent measurements [3], and with previous calculations in the relaxation time approximation [4].-------- [1] D. Cahill, W. ford, K. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin and S. Phillpot, J. Appl. Phys. 93, 793 (2003). [2] M. Omini and A. Sparavigna, Nuovo Cimento, D 19, 1537 (1997). [3] D. Li, Y. Wu, P. Kim, L. Shi, P. Yang and A. Majumdar, Appl. Phys. Lett. 83, 2934 (2003). [4] N. Mingo, Phys. Rev. B 68, 113308 (2003).

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

NASA Astrophysics Data System (ADS)

Leclaire, Sébastien; Parmigiani, Andrea; Malaspinas, Orestis; Chopard, Bastien; Latt, Jonas

2017-03-01

This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.

Multiple-relaxation-time color-gradient lattice Boltzmann model for simulating two-phase flows with high density ratio

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ba, Yan; Liu, Haihu; Li, Qing

2016-08-15

In this paper, we propose a color-gradient lattice Boltzmann (LB) model for simulating two-phase flows with high density ratio and high Reynolds number. The model applies a multi-relaxation-time (MRT) collision operator to enhance the stability of the simulation. A source term, which is derived by the Chapman-Enskog analysis, is added into the MRT LB equation so that the Navier-Stokes equations can be exactly recovered. Also, a new form of the equilibrium density distribution function is used to simplify the source term. To validate the proposed model, steady flows of a static droplet and the layered channel flow are first simulatedmore » with density ratios up to 1000. Small values of spurious velocities and interfacial tension errors are found in the static droplet test, and improved profiles of velocity are obtained by the present model in simulating channel flows. Then, two cases of unsteady flows, Rayleigh-Taylor instability and droplet splashing on a thin film, are simulated. In the former case, the density ratio of 3 and Reynolds numbers of 256 and 2048 are considered. The interface shapes and spike/bubble positions are in good agreement with the results of previous studies. In the latter case, the droplet spreading radius is found to obey the power law proposed in previous studies for the density ratio of 100 and Reynolds number up to 500.« less

Flow visualisation of downhill skiers using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Asai, Takeshi; Hong, Sungchan; Ijuin, Koichi

2017-03-01

In downhill alpine skiing, skiers often exceed speeds of 120 km h-1, with air resistance substantially affecting the overall race times. To date, studies on air resistance in alpine skiing have used wind tunnels and actual skiers to examine the relationship between the gliding posture and magnitude of drag and for the design of skiing equipment. However, these studies have not revealed the flow velocity distribution and vortex structure around the skier. In the present study, computational fluid dynamics are employed with the lattice Boltzmann method to derive the relationship between total drag and the flow velocity around a downhill skier in the full-tuck position. Furthermore, the flow around the downhill skier is visualised, and its vortex structure is examined. The results show that the total drag force in the downhill skier model is 27.0 N at a flow velocity of 15 m s-1, increasing to 185.8 N at 40 m s-1. From analysis of the drag distribution and the flow profile, the head, upper arms, lower legs, and thighs (including buttocks) are identified as the major sources of drag on a downhill skier. Based on these results, the design of suits and equipment for reducing the drag from each location should be the focus of research and development in ski equipment. This paper describes a pilot study that introduces undergraduate students of physics or engineering into this research field. The results of this study are easy to understand for undergraduate students.

Numerical and experimental investigation of a beveled trailing-edge flow field and noise emission

NASA Astrophysics Data System (ADS)

van der Velden, W. C. P.; Pröbsting, S.; van Zuijlen, A. H.; de Jong, A. T.; Guan, Y.; Morris, S. C.

2016-12-01

Efficient tools and methodology for the prediction of trailing-edge noise experience substantial interest within the wind turbine industry. In recent years, the Lattice Boltzmann Method has received increased attention for providing such an efficient alternative for the numerical solution of complex flow problems. Based on the fully explicit, transient, compressible solution of the Lattice Boltzmann Equation in combination with a Ffowcs-Williams and Hawking aeroacoustic analogy, an estimation of the acoustic radiation in the far field is obtained. To validate this methodology for the prediction of trailing-edge noise, the flow around a flat plate with an asymmetric 25° beveled trailing edge and obtuse corner in a low Mach number flow is analyzed. Flow field dynamics are compared to data obtained experimentally from Particle Image Velocimetry and Hot Wire Anemometry, and compare favorably in terms of mean velocity field and turbulent fluctuations. Moreover, the characteristics of the unsteady surface pressure, which are closely related to the acoustic emission, show good agreement between simulation and experiment. Finally, the prediction of the radiated sound is compared to the results obtained from acoustic phased array measurements in combination with a beamforming methodology. Vortex shedding results in a strong narrowband component centered at a constant Strouhal number in the acoustic spectrum. At higher frequency, a good agreement between simulation and experiment for the broadband noise component is obtained and a typical cardioid-like directivity is recovered.

Simulation of regimes of convection and plume dynamics by the thermal Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Mora, Peter; Yuen, David A.

2018-02-01

We present 2D simulations using the Lattice Boltzmann Method (LBM) of a fluid in a rectangular box being heated from below, and cooled from above. We observe plumes, hot narrow upwellings from the base, and down-going cold chutes from the top. We have varied both the Rayleigh numbers and the Prandtl numbers respectively from Ra = 1000 to Ra =1010 , and Pr = 1 through Pr = 5 ×104 , leading to Rayleigh-Bénard convection cells at low Rayleigh numbers through to vigorous convection and unstable plumes with pronounced vortices and eddies at high Rayleigh numbers. We conduct simulations with high Prandtl numbers up to Pr = 50, 000 to simulate in the inertial regime. We find for cases when Pr ⩾ 100 that we obtain a series of narrow plumes of upwelling fluid with mushroom heads and chutes of downwelling fluid. We also present simulations at a Prandtl number of 0.7 for Rayleigh numbers varying from Ra =104 through Ra =107.5 . We demonstrate that the Nusselt number follows power law scaling of form Nu ∼Raγ where γ = 0.279 ± 0.002 , which is consistent with published results of γ = 0.281 in the literature. These results show that the LBM is capable of reproducing results obtained with classical macroscopic methods such as spectral methods, and demonstrate the great potential of the LBM for studying thermal convection and plume dynamics relevant to geodynamics.

Lattice Boltzmann study of chemically-driven self-propelled droplets.

PubMed

Fadda, F; Gonnella, G; Lamura, A; Tiribocchi, A

2017-12-19

We numerically study the behavior of self-propelled liquid droplets whose motion is triggered by a Marangoni-like flow. This latter is generated by variations of surfactant concentration which affect the droplet surface tension promoting its motion. In the present paper a model for droplets with a third amphiphilic component is adopted. The dynamics is described by Navier-Stokes and convection-diffusion equations, solved by the lattice Boltzmann method coupled with finite-difference schemes. We focus on two cases. First, the study of self-propulsion of an isolated droplet is carried on and, then, the interaction of two self-propelled droplets is investigated. In both cases, when the surfactant migrates towards the interface, a quadrupolar vortex of the velocity field forms inside the droplet and causes the motion. A weaker dipolar field emerges instead when the surfactant is mainly diluted in the bulk. The dynamics of two interacting droplets is more complex and strongly depends on their reciprocal distance. If, in a head-on collision, droplets are close enough, the velocity field initially attracts them until a motionless steady state is achieved. If the droplets are vertically shifted, the hydrodynamic field leads to an initial reciprocal attraction followed by a scattering along opposite directions. This hydrodynamic interaction acts on a separation of some droplet radii otherwise it becomes negligible and droplets motion is only driven by the Marangoni effect. Finally, if one of the droplets is passive, this latter is generally advected by the fluid flow generated by the active one.

Simulation of condensation and liquid break-up on a micro-object with upper and lower movable walls using Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

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 model for high-order nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann simulation of the gas-solid adsorption process in reconstructed random porous media.

PubMed

Zhou, L; Qu, Z G; Ding, T; Miao, J Y

2016-04-01

The gas-solid adsorption process in reconstructed random porous media is numerically studied with the lattice Boltzmann (LB) method at the pore scale with consideration of interparticle, interfacial, and intraparticle mass transfer performances. Adsorbent structures are reconstructed in two dimensions by employing the quartet structure generation set approach. To implement boundary conditions accurately, all the porous interfacial nodes are recognized and classified into 14 types using a proposed universal program called the boundary recognition and classification program. The multiple-relaxation-time LB model and single-relaxation-time LB model are adopted to simulate flow and mass transport, respectively. The interparticle, interfacial, and intraparticle mass transfer capacities are evaluated with the permeability factor and interparticle transfer coefficient, Langmuir adsorption kinetics, and the solid diffusion model, respectively. Adsorption processes are performed in two groups of adsorbent media with different porosities and particle sizes. External and internal mass transfer resistances govern the adsorption system. A large porosity leads to an early time for adsorption equilibrium because of the controlling factor of external resistance. External and internal resistances are dominant at small and large particle sizes, respectively. Particle size, under which the total resistance is minimum, ranges from 3 to 7 μm with the preset parameters. Pore-scale simulation clearly explains the effect of both external and internal mass transfer resistances. The present paper provides both theoretical and practical guidance for the design and optimization of adsorption systems.

Lattice Boltzmann simulation of the gas-solid adsorption process in reconstructed random porous media

NASA Astrophysics Data System (ADS)

Zhou, L.; Qu, Z. G.; Ding, T.; Miao, J. Y.

2016-04-01

The gas-solid adsorption process in reconstructed random porous media is numerically studied with the lattice Boltzmann (LB) method at the pore scale with consideration of interparticle, interfacial, and intraparticle mass transfer performances. Adsorbent structures are reconstructed in two dimensions by employing the quartet structure generation set approach. To implement boundary conditions accurately, all the porous interfacial nodes are recognized and classified into 14 types using a proposed universal program called the boundary recognition and classification program. The multiple-relaxation-time LB model and single-relaxation-time LB model are adopted to simulate flow and mass transport, respectively. The interparticle, interfacial, and intraparticle mass transfer capacities are evaluated with the permeability factor and interparticle transfer coefficient, Langmuir adsorption kinetics, and the solid diffusion model, respectively. Adsorption processes are performed in two groups of adsorbent media with different porosities and particle sizes. External and internal mass transfer resistances govern the adsorption system. A large porosity leads to an early time for adsorption equilibrium because of the controlling factor of external resistance. External and internal resistances are dominant at small and large particle sizes, respectively. Particle size, under which the total resistance is minimum, ranges from 3 to 7 μm with the preset parameters. Pore-scale simulation clearly explains the effect of both external and internal mass transfer resistances. The present paper provides both theoretical and practical guidance for the design and optimization of adsorption systems.

Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change

NASA Astrophysics Data System (ADS)

Li, Qing; Zhou, P.; Yan, H. J.

2017-12-01

In this paper, an improved thermal lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change, which is aimed at improving an existing thermal LB model for liquid-vapor phase change [S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012), 10.1016/j.ijheatmasstransfer.2012.04.037]. First, we emphasize that the replacement of ∇ .(λ ∇ T ) /∇.(λ ∇ T ) ρ cV ρ cV with ∇ .(χ ∇ T ) is an inappropriate treatment for diffuse interface modeling of liquid-vapor phase change. Furthermore, the error terms ∂t 0(T v ) +∇ .(T vv ) , which exist in the macroscopic temperature equation recovered from the previous model, are eliminated in the present model through a way that is consistent with the philosophy of the LB method. Moreover, the discrete effect of the source term is also eliminated in the present model. Numerical simulations are performed for droplet evaporation and bubble nucleation to validate the capability of the model for simulating liquid-vapor phase change. It is shown that the numerical results of the improved model agree well with those of a finite-difference scheme. Meanwhile, it is found that the replacement of ∇ .(λ ∇ T ) /∇ .(λ ∇ T ) ρ cV ρ cV with ∇ .(χ ∇ T ) leads to significant numerical errors and the error terms in the recovered macroscopic temperature equation also result in considerable errors.

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

NASA Astrophysics Data System (ADS)

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.

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

DOE PAGES

Zhao, Jianlin; Kang, Qinjun; Yao, Jun; ...

2018-02-27

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. In this study, 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 themore » 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. Lastly, the relationship between the relative permeability and these parameters under different capillary numbers is explored in this paper.« less

Electro-osmosis of non-Newtonian fluids in porous media using lattice Poisson-Boltzmann method.

PubMed

Chen, Simeng; He, Xinting; Bertola, Volfango; Wang, Moran

2014-12-15

Electro-osmosis in porous media has many important applications in various areas such as oil and gas exploitation and biomedical detection. Very often, fluids relevant to these applications are non-Newtonian because of the shear-rate dependent viscosity. The purpose of this study was to investigate the behaviors and physical mechanism of electro-osmosis of non-Newtonian fluids in porous media. Model porous microstructures (granular, fibrous, and network) were created by a random generation-growth method. The nonlinear governing equations of electro-kinetic transport for a power-law fluid were solved by the lattice Poisson-Boltzmann method (LPBM). The model results indicate that: (i) the electro-osmosis of non-Newtonian fluids exhibits distinct nonlinear behaviors compared to that of Newtonian fluids; (ii) when the bulk ion concentration or zeta potential is high enough, shear-thinning fluids exhibit higher electro-osmotic permeability, while shear-thickening fluids lead to the higher electro-osmotic permeability for very low bulk ion concentration or zeta potential; (iii) the effect of the porous medium structure depends significantly on the constitutive parameters: for fluids with large constitutive coefficients strongly dependent on the power-law index, the network structure shows the highest electro-osmotic permeability while the granular structure exhibits the lowest permeability on the entire range of power law indices considered; when the dependence of the constitutive coefficient on the power law index is weaker, different behaviors can be observed especially in case of strong shear thinning. Copyright © 2014 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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.

Effective Wettability of Heterogenous Fracture Surfaces Using the Lattice-Boltzmann Method

NASA Astrophysics Data System (ADS)

E Santos, J.; Prodanovic, M.; Landry, C. J.

2017-12-01

Fracture walls in the subsurface are often structured by minerals of different composition (potentially further altered in contact with fluids during hydrocarbon extraction or CO2 sequestration), this yields in a heterogeneous wettability of the surface in contact with the fluids. The focus of our work is to study how surfaces presenting different mineralogy and roughness affect multiphase flow in fractures. Using the Shan-Chen model of the lattice-Boltzmann method (LBM) we define fluid interaction and surface attraction parameters to simulate a system of a wetting and a non-wetting fluid. In this work, we use synthetically created fractures presenting different arrangements of wetting and non-wetting patches, and with or without roughness; representative of different mineralogy, similar workflow can be applied to fractures extracted from X-ray microtomography images of fractures porous media. The results from the LBM simulations provide an insight on how the distribution of mineralogy and surface roughness are related with the observed macroscopic contact angle. We present a comparison between the published analytical models, and our results based on surface areas, spatial distribution and local fracture aperture. The understanding of the variables that affect the contact angle is useful for the comprehension of multiphase processes in naturally fractured reservoirs like primary oil production, enhanced oil recovery and CO2 sequestration. The macroscopic contact angle analytical equations for heterogeneous surfaces with variable roughness are no longer valid in highly heterogeneous systems; we quantify the difference thus offering an alternative to analytical models.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Jianlin; Kang, Qinjun; Yao, Jun

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. In this study, 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 themore » 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. Lastly, the relationship between the relative permeability and these parameters under different capillary numbers is explored in this paper.« less

Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

NASA Astrophysics Data System (ADS)

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

2015-04-01

To probe both the hydrodynamic nonequilibrium (HNE) and thermodynamic nonequilibrium (TNE) in the combustion process, a two-dimensional multiple-relaxation-time (MRT) version of lattice Boltzmann kinetic model (LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Aside from describing the evolutions of the conserved quantities, the density, momentum, and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some nonconserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model, both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various nonequilibrium behaviors, including the complex interplays between various HNEs, between various TNEs, and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

PubMed

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Isotropic matrix elements of the collision integral for the Boltzmann equation

NASA Astrophysics Data System (ADS)

Ender, I. A.; Bakaleinikov, L. A.; Flegontova, E. Yu.; Gerasimenko, A. B.

2017-09-01

We have proposed an algorithm for constructing matrix elements of the collision integral for the nonlinear Boltzmann equation isotropic in velocities. These matrix elements have been used to start the recurrent procedure for calculating matrix elements of the velocity-nonisotropic collision integral described in our previous publication. In addition, isotropic matrix elements are of independent interest for calculating isotropic relaxation in a number of physical kinetics problems. It has been shown that the coefficients of expansion of isotropic matrix elements in Ω integrals are connected by the recurrent relations that make it possible to construct the procedure of their sequential determination.

Mean-field message-passing equations in the Hopfield model and its generalizations

NASA Astrophysics Data System (ADS)

Mézard, Marc

2017-02-01

Motivated by recent progress in using restricted Boltzmann machines as preprocessing algorithms for deep neural network, we revisit the mean-field equations [belief-propagation and Thouless-Anderson Palmer (TAP) equations] in the best understood of such machines, namely the Hopfield model of neural networks, and we explicit how they can be used as iterative message-passing algorithms, providing a fast method to compute the local polarizations of neurons. In the "retrieval phase", where neurons polarize in the direction of one memorized pattern, we point out a major difference between the belief propagation and TAP equations: The set of belief propagation equations depends on the pattern which is retrieved, while one can use a unique set of TAP equations. This makes the latter method much better suited for applications in the learning process of restricted Boltzmann machines. In the case where the patterns memorized in the Hopfield model are not independent, but are correlated through a combinatorial structure, we show that the TAP equations have to be modified. This modification can be seen either as an alteration of the reaction term in TAP equations or, more interestingly, as the consequence of message passing on a graphical model with several hidden layers, where the number of hidden layers depends on the depth of the correlations in the memorized patterns. This layered structure is actually necessary when one deals with more general restricted Boltzmann machines.

Ab initio computational study on the lattice thermal conductivity of Zintl clathrates [Si19P4] Cl4 and Na4[Al4Si19

NASA Astrophysics Data System (ADS)

Härkönen, Ville J.; Karttunen, Antti J.

2016-08-01

The lattice thermal conductivity of silicon clathrate framework Si23 and two Zintl clathrates, [Si19P4] Cl4 and Na4[Al4Si19] , is investigated by using an iterative solution of the linearized Boltzmann transport equation in conjunction with ab initio lattice dynamical techniques. At 300 K, the lattice thermal conductivities for Si23, [Si19P4] Cl4 , and Na4[Al4Si19] were found to be 43 W/(m K), 25 W/(m K), and 2 W/(m K), respectively. In the case of Na4[Al4Si19] , the order-of-magnitude reduction in the lattice thermal conductivity was found to be mostly due to relaxation times and group velocities differing from Si23 and [Si19P4] Cl4 . The difference in the relaxation times and group velocities arises primarily due to the phonon spectrum at low frequencies, resulting eventually from the differences in the second-order interatomic force constants (IFCs). The obtained third-order IFCs were rather similar for all materials considered here. The present findings are similar to those obtained earlier for some skutterudites. The predicted lattice thermal conductivity of Na4[Al4Si19] is in line with the experimentally measured thermal conductivity of recently synthesized type-I Zintl clathrate Na8[Al8Si38] (polycrystalline samples).

Spatial variation of permittivity of an electrolyte solution in contact with a charged metal surface: a mini review

PubMed Central

Gongadze, E.; van Rienen, U.; Kralj-Iglič, V.; Iglič, A.

2012-01-01

Contact between a charged metal surface and an electrolyte implies a particular ion distribution near the charged surface, i.e. the electrical double layer. In this mini review, different mean-field models of relative (effective) permittivity are described within a simple lattice model, where the orientational ordering of water dipoles in the saturation regime is taken into account. The Langevin-Poisson-Boltzmann (LPB) model of spatial variation of the relative permittivity for point-like ions is described and compared to a more general Langevin-Bikerman (LB) model of spatial variation of permittivity for finite-sized ions. The Bikerman model and the Poisson-Boltzmann model are derived as limiting cases. It is shown that near the charged surface, the relative permittivity decreases due to depletion of water molecules (volume-excluded effect) and orientational ordering of water dipoles (saturation effect). At the end, the LPB and LB models are generalised by also taking into account the cavity field. PMID:22263808

First principles Peierls-Boltzmann phonon thermal transport: A topical review

DOE PAGES

Lindsay, Lucas

2016-08-05

The advent of coupled thermal transport calculations with interatomic forces derived from density functional theory has ushered in a new era of fundamental microscopic insight into lattice thermal conductivity. Subsequently, significant new understanding of phonon transport behavior has been developed with these methods, and because they are parameter free and successfully benchmarked against a variety of systems, they also provide reliable predictions of thermal transport in systems for which little is known. This topical review will describe the foundation from which first principles Peierls-Boltzmann transport equation methods have been developed, and briefly describe important necessary ingredients for accurate calculations. Samplemore » highlights of reported work will be presented to illustrate the capabilities and challenges of these techniques, and to demonstrate the suite of tools available, with an emphasis on thermal transport in micro- and nano-scale systems. In conclusion, future challenges and opportunities will be discussed, drawing attention to prospects for methods development and applications.« less

Counting in Lattices: Combinatorial Problems from Statistical Mechanics.

NASA Astrophysics Data System (ADS)

Randall, Dana Jill

In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and self-avoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kasteleyn and Temperley discovered an elegant technique to exactly count the number of perfect matchings in two dimensional lattices, but it is not applicable for matchings of arbitrary size, or in higher dimensional lattices. We present the first efficient approximation algorithm for computing the number of matchings of any size in any periodic lattice in arbitrary dimension. The algorithm is based on Monte Carlo simulation of a suitable Markov chain and has rigorously derived performance guarantees that do not rely on any assumptions. In addition, we show that these results generalize to counting matchings in any graph which is the Cayley graph of a finite group. The second problem is counting self-avoiding walks in lattices. This problem arises in the study of the thermodynamics of long polymer chains in dilute solution. While there are a number of Monte Carlo algorithms used to count self -avoiding walks in practice, these are heuristic and their correctness relies on unproven conjectures. In contrast, we present an efficient algorithm which relies on a single, widely-believed conjecture that is simpler than preceding assumptions and, more importantly, is one which the algorithm itself can test. Thus our algorithm is reliable, in the sense that it either outputs answers that are guaranteed, with high probability, to be correct, or finds a counterexample to the conjecture. In either case we know we can trust our results and the algorithm is guaranteed to run in polynomial time. This is the first algorithm for counting self-avoiding walks in which the error bounds are rigorously controlled. This work was supported in part by an AT&T graduate fellowship, a University of California dissertation year fellowship and Esprit working group "RAND". Part of this work was done while visiting ICSI and the University of Edinburgh.