Lattice Boltzmann approach for complex nonequilibrium flows.

Science.gov (United States)

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.

Element Free Lattice Boltzmann Method for Fluid-Flow Problems

International Nuclear Information System (INIS)

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

2007-01-01

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

Element Free Lattice Boltzmann Method for Fluid-Flow Problems

Energy Technology Data Exchange (ETDEWEB)

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

2007-10-15

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

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

OpenAIRE

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

2010-01-01

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

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

International Nuclear Information System (INIS)

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

2002-01-01

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

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

Science.gov (United States)

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.

Maxwell iteration for the lattice Boltzmann method with diffusive scaling

Science.gov (United States)

Zhao, Weifeng; Yong, Wen-An

2017-03-01

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

Three-dimensional lattice Boltzmann model for compressible flows.

Science.gov (United States)

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.

Lattice Boltzmann model for numerical relativity.

Science.gov (United States)

Ilseven, E; Mendoza, M

2016-02-01

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

Galilean-Invariant Lattice-Boltzmann Models with H Theorem

National Research Council Canada - National Science Library

Boghosian, Bruce

2003-01-01

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

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

Science.gov (United States)

Verschaeve, Joris C G

2011-06-13

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

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

Directory of Open Access Journals (Sweden)

Zhen Chen

2017-03-01

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

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

Science.gov (United States)

Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

2016-10-01

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

The Lattice Boltzmann Method applied to neutron transport

International Nuclear Information System (INIS)

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

2013-01-01

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

Multispeed models in off-lattice Boltzmann simulations

NARCIS (Netherlands)

Bardow, A.; Karlin, I.V.; Gusev, A.A.

2008-01-01

The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods.

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

DEFF Research Database (Denmark)

Svec, Oldrich; Skoček, Jan

2013-01-01

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

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

Directory of Open Access Journals (Sweden)

El Ganaoui Mohammed

2009-01-01

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

Lattice Boltzmann method for solving the bioheat equation

International Nuclear Information System (INIS)

Zhang Haifeng

2008-01-01

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

Quantum linear Boltzmann equation

International Nuclear Information System (INIS)

Vacchini, Bassano; Hornberger, Klaus

2009-01-01

We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

Lattice Boltzmann model for three-phase viscoelastic fluid flow

Science.gov (United States)

Xie, Chiyu; Lei, Wenhai; Wang, Moran

2018-02-01

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

Topology optimization and lattice Boltzmann methods

DEFF Research Database (Denmark)

Nørgaard, Sebastian Arlund

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

Moving charged particles in lattice Boltzmann-based electrokinetics

Science.gov (United States)

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

2016-12-01

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

Hypersonic Shock Wave Computations Using the Generalized Boltzmann Equation

Science.gov (United States)

Agarwal, Ramesh; Chen, Rui; Cheremisin, Felix G.

2006-11-01

Hypersonic shock structure in diatomic gases is computed by solving the Generalized Boltzmann Equation (GBE), where the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively [1]. The computational framework available for the standard Boltzmann equation [2] is extended by including both the rotational and vibrational degrees of freedom in the GBE. There are two main difficulties encountered in computation of high Mach number flows of diatomic gases with internal degrees of freedom: (1) a large velocity domain is needed for accurate numerical description of the distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 energy levels are needed for accurate representation of the rotational spectrum of the gas. Our methodology addresses these problems, and as a result the efficiency of calculations has increased by several orders of magnitude. The code has been validated by computing the shock structure in Nitrogen for Mach numbers up to 25 including the translational and rotational degrees of freedom. [1] Beylich, A., ``An Interlaced System for Nitrogen Gas,'' Proc. of CECAM Workshop, ENS de Lyon, France, 2000. [2] Cheremisin, F., ``Solution of the Boltzmann Kinetic Equation for High Speed Flows of a Rarefied Gas,'' Proc. of the 24th Int. Symp. on Rarefied Gas Dynamics, Bari, Italy, 2004.

Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena

International Nuclear Information System (INIS)

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

2014-01-01

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

Lattice Boltzmann method for weakly ionized isothermal plasmas

International Nuclear Information System (INIS)

Li Huayu; Ki, Hyungson

2007-01-01

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

Multiphase lattice Boltzmann on the Cell Broadband Engine

International Nuclear Information System (INIS)

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

2009-01-01

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

Lattice Boltzmann method with the cell-population equilibrium

International Nuclear Information System (INIS)

Zhou Xiaoyang; Cheng Bing; Shi Baochang

2008-01-01

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

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

Science.gov (United States)

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)).

Parallel performance and accuracy of lattice Boltzmann and traditional finite difference methods for solving the unsteady two-dimensional Burger's equation

Science.gov (United States)

Velivelli, A. C.; Bryden, K. M.

2006-03-01

Lattice Boltzmann methods are gaining recognition in the field of computational fluid dynamics due to their computational efficiency. In order to quantify the computational efficiency and accuracy of the lattice Boltzmann method, it is compared with efficient traditional finite difference methods such as the alternating direction implicit scheme. The lattice Boltzmann algorithm implemented in previous studies does not approach peak performance for simulations where the data involved in computation per time step is more than the cache size. Due to this, data is obtained from the main memory and this access is much slower than access to cache memory. Using a cache-optimized lattice Boltzmann algorithm, this paper takes into account the full computational strength of the lattice Boltzmann method. The com parison is performed on both a single processor and multiple processors.

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

International Nuclear Information System (INIS)

Zheng, Lin; Zheng, Song; Zhai, Qinglan

2016-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-02-05

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

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

NARCIS (Netherlands)

Sbragaglia, M.; Succi, S.

2006-01-01

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

Straight velocity boundaries in the lattice Boltzmann method

Science.gov (United States)

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

2008-05-01

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

Convection-diffusion lattice Boltzmann scheme for irregular lattices

NARCIS (Netherlands)

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

2000-01-01

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

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

Science.gov (United States)

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

2018-01-01

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

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

International Nuclear Information System (INIS)

Kim, In Chan

2000-01-01

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

Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Jin Licong; Zhang Xinrong; Niu Xiaodong

2012-01-01

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

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

Science.gov (United States)

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

2018-02-01

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

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

Science.gov (United States)

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

2018-02-01

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

Analysis of a bubble coalescence in the multiphase lattice Boltzmann method

International Nuclear Information System (INIS)

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

2008-01-01

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

Lattice Boltzmann model for simulating immiscible two-phase flows

International Nuclear Information System (INIS)

Reis, T; Phillips, T N

2007-01-01

The lattice Boltzmann equation is often promoted as a numerical simulation tool that is particularly suitable for predicting the flow of complex fluids. This paper develops a two-dimensional 9-velocity (D2Q9) lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio using a single relaxation time for each fluid. In the macroscopic limit, this model is shown to recover the Navier-Stokes equations for two-phase flows. This is achieved by constructing a two-phase component of the collision operator that induces the appropriate surface tension term in the macroscopic equations. A theoretical expression for surface tension is determined. The validity of this analysis is confirmed by comparing numerical and theoretical predictions of surface tension as a function of density. The model is also shown to predict Laplace's law for surface tension and Poiseuille flow of layered immiscible binary fluids. The spinodal decomposition of two fluids of equal density but different viscosity is then studied. At equilibrium, the system comprises one large low viscosity bubble enclosed by the more viscous fluid in agreement with theoretical arguments of Renardy and Joseph (1993 Fundamentals of Two-Fluid Dynamics (New York: Springer)). Two other simulations, namely the non-equilibrium rod rest and the coalescence of two bubbles, are performed to show that this model can be used to simulate two fluids with a large density ratio

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

Science.gov (United States)

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

2017-04-01

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

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

Science.gov (United States)

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

2007-03-23

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

Stabilizing the thermal lattice Boltzmann method by spatial filtering.

Science.gov (United States)

Gillissen, J J J

2016-10-01

We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.

Lattice Boltzmann model capable of mesoscopic vorticity computation

Science.gov (United States)

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

2017-11-01

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

Corner-transport-upwind lattice Boltzmann model for bubble cavitation

Science.gov (United States)

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

2018-02-01

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

Modeling and simulation of ocean wave propagation using lattice Boltzmann method

Science.gov (United States)

Nuraiman, Dian

2017-10-01

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

Lattice Boltzmann methods for global linear instability analysis

Science.gov (United States)

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

2017-12-01

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

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

Science.gov (United States)

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

2010-02-01

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

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

Science.gov (United States)

Amaya-Bower, Luz; Lee, Taehun

2011-06-28

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

Simulation of bubble motion under gravity by lattice Boltzmann method

International Nuclear Information System (INIS)

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

2001-01-01

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

Numerical solution of Boltzmann's equation

International Nuclear Information System (INIS)

Sod, G.A.

1976-04-01

The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

CMB spectral distortions as solutions to the Boltzmann equations

Energy Technology Data Exchange (ETDEWEB)

Ota, Atsuhisa, E-mail: a.ota@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)

2017-01-01

We propose to re-interpret the cosmic microwave background spectral distortions as solutions to the Boltzmann equation. This approach makes it possible to solve the second order Boltzmann equation explicitly, with the spectral y distortion and the momentum independent second order temperature perturbation, while generation of μ distortion cannot be explained even at second order in this framework. We also extend our method to higher order Boltzmann equations systematically and find new type spectral distortions, assuming that the collision term is linear in the photon distribution functions, namely, in the Thomson scattering limit. As an example, we concretely construct solutions to the cubic order Boltzmann equation and show that the equations are closed with additional three parameters composed of a cubic order temperature perturbation and two cubic order spectral distortions. The linear Sunyaev-Zel'dovich effect whose momentum dependence is different from the usual y distortion is also discussed in the presence of the next leading order Kompaneets terms, and we show that higher order spectral distortions are also generated as a result of the diffusion process in a framework of higher order Boltzmann equations. The method may be applicable to a wider class of problems and has potential to give a general prescription to non-equilibrium physics.

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

International Nuclear Information System (INIS)

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

2006-01-01

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

Generalized Boltzmann equations for on-shell particle production in a hot plasma

International Nuclear Information System (INIS)

Jakovac, A.

2002-01-01

A novel refinement of the conventional treatment of Kadanoff-Baym equations is suggested. In addition to the Boltzmann equation, another differential equation is used for calculating the evolution of the nonequilibrium two-point function. Although it was usually interpreted as a constraint on the solution of the Boltzmann equation, we argue that its dynamics is relevant to the determination and resummation of the particle production cut contributions. The differential equation for this new contribution is illustrated in the example of the cubic scalar model. The analogue of the relaxation time approximation is suggested. It results in the shift of the threshold location and in a smearing out of the nonanalytic threshold behavior of the spectral function. The possible consequences for the dilepton production are discussed

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

Directory of Open Access Journals (Sweden)

Ahmed M. Ibrahem

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

Entropic multirelaxation lattice Boltzmann models for turbulent flows

Science.gov (United States)

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.

Immiscible multicomponent lattice Boltzmann model for fluids with ...

Indian Academy of Sciences (India)

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

Simulating condensation on microstructured surfaces using Lattice Boltzmann Method

Science.gov (United States)

Alexeev, Alexander; Vasyliv, Yaroslav

2017-11-01

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

Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

Science.gov (United States)

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.

Lattice-Boltzmann simulations of droplet evaporation

KAUST Repository

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

2014-01-01

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

Lattice-Boltzmann simulations of droplet evaporation

KAUST Repository

Ledesma-Aguilar, Rodrigo

2014-09-04

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

Painleve test and discrete Boltzmann equations

International Nuclear Information System (INIS)

Euler, N.; Steeb, W.H.

1989-01-01

The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs

The solution of the Poisson-Boltzmann's equation for self-consistent potential of infinite, random, nonlinear and non-uniform system

International Nuclear Information System (INIS)

Rasulova, M.Yu

1998-01-01

A study has been made of a system of charged particles and inhomogeneities randomly distributed in accordance with the same law in the neighborhoods of corresponding sites of a planar crystal lattice. The existence and uniqueness of the solution of the generalized Poisson-Boltzmann's equation for the average self-consistent potential and average density of surface charges are proved. (author)

An introduction to the theory of the Boltzmann equation

CERN Document Server

Harris, Stewart

2011-01-01

Boltzmann's equation (or Boltzmann-like equations) appears extensively in such disparate fields as laser scattering, solid-state physics, nuclear transport, and beyond the conventional boundaries of physics and engineering, in the fields of cellular proliferation and automobile traffic flow. This introductory graduate-level course for students of physics and engineering offers detailed presentations of the basic modern theory of Boltzmann's equation, including representative applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes

Stabilization of the Lattice Boltzmann Method Using Information Theory

OpenAIRE

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

2018-01-01

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

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

Science.gov (United States)

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

2018-02-01

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

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

Science.gov (United States)

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

2014-04-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-12-15

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

Grid refinement model in lattice Boltzmann method for stream function-vorticity formulations

Energy Technology Data Exchange (ETDEWEB)

Shin, Myung Seob [Dept. of Mechanical Engineering, Dongyang Mirae University, Seoul (Korea, Republic of)

2015-03-15

In this study, we present a grid refinement model in the lattice Boltzmann method (LBM) for two-dimensional incompressible fluid flow. That is, the model combines the desirable features of the lattice Boltzmann method and stream function-vorticity formulations. In order to obtain an accurate result, very fine grid (or lattice) is required near the solid boundary. Therefore, the grid refinement model is used in the lattice Boltzmann method for stream function-vorticity formulation. This approach is more efficient in that it can obtain the same accurate solution as that in single-block approach even if few lattices are used for computation. In order to validate the grid refinement approach for the stream function-vorticity formulation, the numerical simulations of lid-driven cavity flows were performed and good results were obtained.

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

International Nuclear Information System (INIS)

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

2008-01-01

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

Diffusion on unstructured triangular grids using Lattice Boltzmann

NARCIS (Netherlands)

Sman, van der R.G.M.

2004-01-01

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

Lattice-Boltzmann scheme for natural convection in porous media

NARCIS (Netherlands)

Sman, van der R.G.M.

1997-01-01

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

Lattice Boltzmann scheme for diffusion on triangular grids

NARCIS (Netherlands)

Sman, van der R.G.M.

2003-01-01

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

Galilean invariant lattice Boltzmann scheme for natural convection on square and rectangular lattices

NARCIS (Netherlands)

Sman, van der R.G.M.

2006-01-01

In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the

Kinetic Boltzmann, Vlasov and Related Equations

CERN Document Server

Sinitsyn, Alexander; Vedenyapin, Victor

2011-01-01

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in

Flavored quantum Boltzmann equations

International Nuclear Information System (INIS)

Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean

2010-01-01

We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.

Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

Energy Technology Data Exchange (ETDEWEB)

EL Safadi, M

2007-03-15

We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

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

KAUST Repository

Allen, Rebecca

2016-06-29

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

Essentially Entropic Lattice Boltzmann Model

Science.gov (United States)

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

2017-12-01

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

Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

International Nuclear Information System (INIS)

EL Safadi, M.

2007-03-01

We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

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

Energy Technology Data Exchange (ETDEWEB)

Uddin, Rizwan

2012-01-01

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

Stable lattice Boltzmann model for Maxwell equations in media

Science.gov (United States)

Hauser, A.; Verhey, J. L.

2017-12-01

The present work shows a method for stable simulations via the lattice Boltzmann (LB) model for electromagnetic waves (EM) transiting homogeneous media. LB models for such media were already presented in the literature, but they suffer from numerical instability when the media transitions are sharp. We use one of these models in the limit of pure vacuum derived from Liu and Yan [Appl. Math. Model. 38, 1710 (2014), 10.1016/j.apm.2013.09.009] and apply an extension that treats the effects of polarization and magnetization separately. We show simulations of simple examples in which EM waves travel into media to quantify error scaling, stability, accuracy, and time scaling. For conductive media, we use the Strang splitting and check the simulations accuracy at the example of the skin effect. Like pure EM propagation, the error for the static limits, which are constructed with a current density added in a first-order scheme, can be less than 1 % . The presented method is an easily implemented alternative for the stabilization of simulation for EM waves propagating in spatially complex structured media properties and arbitrary transitions.

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

Science.gov (United States)

Wu, Jie; Shen, Meng; Liu, Chen

2018-04-01

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

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

International Nuclear Information System (INIS)

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

2008-01-01

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

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

KAUST Repository

Ibrahem, Ahmed M.

2017-05-04

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

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

KAUST Repository

Reis, Tim

2012-01-01

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

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

Science.gov (United States)

Liou, Tong-Miin; Wang, Chun-Sheng

2018-01-01

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

High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

Science.gov (United States)

Li, Weidong

2017-09-01

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

Global existence proof for relativistic Boltzmann equation

International Nuclear Information System (INIS)

Dudynski, M.; Ekiel-Jezewska, M.L.

1992-01-01

The existence and causality of solutions to the relativistic Boltzmann equation in L 1 and in L loc 1 are proved. The solutions are shown to satisfy physically natural a priori bounds, time-independent in L 1 . The results rely upon new techniques developed for the nonrelativistic Boltzmann equation by DiPerna and Lions

Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations

Science.gov (United States)

Blossey, R.; Maggs, A. C.; Podgornik, R.

2017-06-01

We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)], 10.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

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

KAUST Repository

Xiong, Yuan

2014-04-28

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

Towards a physical interpretation of the entropic lattice Boltzmann method

Science.gov (United States)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-10-06

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2009-07-01

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

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

Science.gov (United States)

Guo, Yangyu; Wang, Moran

2017-10-01

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

Generalized hydrodynamic transport in lattice-gas automata

Science.gov (United States)

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

1991-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-02-15

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

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

International Nuclear Information System (INIS)

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

2013-01-01

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

Lattice Boltzmann Approach to Resistive MHD

Czech Academy of Sciences Publication Activity Database

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

2002-01-01

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

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

KAUST Repository

Neumann, Philipp

2015-09-01

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

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

DEFF Research Database (Denmark)

Pingen, Georg; Evgrafov, Anton; Maute, Kurt

2009-01-01

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

Contact angle determination in multicomponent lattice Boltzmann simultations

NARCIS (Netherlands)

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

2011-01-01

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

MRT Lattice Boltzmann schemes for confined suspension flows

NARCIS (Netherlands)

Sman, van der R.G.M.

2010-01-01

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

Consistent forcing scheme in the cascaded lattice Boltzmann method.

Science.gov (United States)

Fei, Linlin; Luo, Kai Hong

2017-11-01

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

Consistent forcing scheme in the cascaded lattice Boltzmann method

Science.gov (United States)

Fei, Linlin; Luo, Kai Hong

2017-11-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-06-27

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

Non-linear effects in the Boltzmann equation

International Nuclear Information System (INIS)

Barrachina, R.O.

1985-01-01

The Boltzmann equation is studied by defining an integral transformation of the energy distribution function for an isotropic and homogeneous gas. This transformation may be interpreted as a linear superposition of equilibrium states with variable temperatures. It is shown that the temporal evolution features of the distribution function are determined by the singularities of said transformation. This method is applied to Maxwell and Very Hard Particle interaction models. For the latter, the solution of the Boltzmann equation with the solution of its linearized version is compared, finding out many basic discrepancies and non-linear effects. This gives a hint to propose a new rational approximation method with a clear physical meaning. Applying this technique, the relaxation features of the BKW (Bobylev, Krook anf Wu) mode is analyzed, finding a conclusive counter-example for the Krook and Wu conjecture. The anisotropic Boltzmann equation for Maxwell models is solved as an expansion in terms of the eigenfunctions of the corresponding linearized collision operator, finding interesting transient overpopulation and underpopulation effects at thermal energies as well as a new preferential spreading effect. By analyzing the initial collision, a criterion is established to deduce the general features of the final approach to equilibrium. Finally, it is shown how to improve the convergence of the eigenfunction expansion for high energy underpopulated distribution functions. As an application of this theory, the linear cascade model for sputtering is analyzed, thus finding out that many differences experimentally observed are due to non-linear effects. (M.E.L.) [es

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

Science.gov (United States)

Zergani, Sara; Aziz, Z. A.; Viswanathan, K. K.

2015-01-01

An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory.

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

International Nuclear Information System (INIS)

Zergani, Sara; Aziz, Z A; Viswanathan, K K

2015-01-01

An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory

Hot electrons in superlattices: quantum transport versus Boltzmann equation

DEFF Research Database (Denmark)

Wacker, Andreas; Jauho, Antti-Pekka; Rott, S.

1999-01-01

A self-consistent solution of the transport equation is presented for semiconductor superlattices within different approaches: (i) a full quantum transport model based on nonequilibrium Green functions, (ii) the semiclassical Boltzmann equation for electrons in a miniband, and (iii) Boltzmann...

Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

International Nuclear Information System (INIS)

Ayissi, Raoul Domingo; Noutchegueme, Norbert

2015-01-01

Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the

Lattice Boltzmann simulation of endothermal catalytic reaction in catalyst porous media

International Nuclear Information System (INIS)

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

2013-01-01

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

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

DEFF Research Database (Denmark)

Matin, Rastin

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

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

Directory of Open Access Journals (Sweden)

Javier A. Dottori

2015-01-01

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

Energy Dependent Streaming in Lattice Boltzmann Simulations

Czech Academy of Sciences Publication Activity Database

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

2001-01-01

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

Extended lattice Boltzmann scheme for droplet combustion.

Science.gov (United States)

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

2017-05-01

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

Boltzmann equations for a binary one-dimensional ideal gas.

Science.gov (United States)

Boozer, A D

2011-09-01

We consider a time-reversal invariant dynamical model of a binary ideal gas of N molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the N-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large N. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann's H theorem.

Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

CERN Document Server

Farhat, Hassan; Kondaraju, Sasidhar

2014-01-01

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

Modelling viscoacoustic wave propagation with the lattice Boltzmann method.

Science.gov (United States)

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

2017-08-31

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

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

International Nuclear Information System (INIS)

Maroufi, Arman; Aghanajafi, Cyrus

2013-01-01

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

Lattice Boltzmann simulation of flow across a staggered tube bundle array

Energy Technology Data Exchange (ETDEWEB)

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

2016-04-15

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

Lattice Boltzmann simulation of flow around a confined circular cyclinder

International Nuclear Information System (INIS)

Ashrafizaadeh, M.; Zadehgol, A.

2002-01-01

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

Critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics

International Nuclear Information System (INIS)

Diestler, D.J.; Riley, M.E.

1985-01-01

We consider the classical motion of a harmonic lattice in which only those atoms in a certain subset of the lattice (primary zone) may interact with an external force. The formally exact generalized Langevin equation (GLE) for the primary zone is an appropriate description of the dynamics. We examine a previously proposed Brownian, or frictional damping, approximation that reduces the GLE to a set of coupled ordinary Langevin equations for the primary atoms. It is shown that the solution of these equations can contain undamped motion if there is more than one atom in the primary zone. Such motion is explicitly demonstrated for a model that has been used to describe energy transfer in atom--surface collisions. The inability of the standard Brownian approximation to yield an acceptable, physically meaningful result for primary zones comprising more than one atom suggests that the Brownian approximation may introduce other spurious dynamical effects. Further work on damping of correlated motion in lattices is needed

Entropic Lattice Boltzmann: an implicit Large-Eddy Simulation?

Science.gov (United States)

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

2017-11-01

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

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

International Nuclear Information System (INIS)

Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.

2016-01-01

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.

Science.gov (United States)

Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

Energy Technology Data Exchange (ETDEWEB)

Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

Lattice Boltzmann method fundamentals and engineering applications with computer codes

CERN Document Server

Mohamad, A A

2014-01-01

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

Simulating colloid hydrodynamics with lattice Boltzmann methods

International Nuclear Information System (INIS)

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

2004-01-01

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

Lattice-Boltzmann simulation of the sedimentation of charged disks

NARCIS (Netherlands)

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

2006-01-01

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

Convection in multiphase fluid flows using lattice Boltzmann methods

NARCIS (Netherlands)

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

2012-01-01

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

Lattice Boltzmann simulations of attenuation-driven acoustic streaming

International Nuclear Information System (INIS)

Haydock, David; Yeomans, J M

2003-01-01

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

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

Science.gov (United States)

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

2013-01-01

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

Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times

Directory of Open Access Journals (Sweden)

Kosuke Hayashi

2012-06-01

Full Text Available An immersed boundary-lattice Boltzmann method (IB-LBM using a two-relaxation time model (TRT is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. A direct-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1 the proposed method does not cause non-physical velocity distribution in circular Couette flows even at high relaxation times, whereas the single-relaxation time (SRT model causes a large non-physical velocity distortion at a high relaxation time, (2 the multi-direct forcing reduces the errors in the velocity profile of a circular Couette flow at a high relaxation time, (3 the two-point delta function is better than the four-point delta function at low relaxation times, but worse at high relaxation times, (4 the functional form of the direct-forcing term does not affect predictions, and (5 circular and spherical particles falling in liquids are well predicted by using the proposed method both for two-dimensional and three-dimensional cases.

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-06-01

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

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

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Helmut Schomburg

2013-03-01

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

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

International Nuclear Information System (INIS)

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

2016-01-01

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

Generalized Kapchinskij-Vladimirskij Distribution and Envelope Equation for High-intensity Beams in a Coupled Transverse Focusing Lattice

International Nuclear Information System (INIS)

Qin, Hong; Chung, Moses; Davidson, Ronald C.

2009-01-01

In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high- intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation.

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

DEFF Research Database (Denmark)

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

2015-01-01

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

Temperature waves and the Boltzmann kinetic equation for phonons

International Nuclear Information System (INIS)

Urushev, D.; Borisov, M.; Vavrek, A.

1988-01-01

The ordinary parabolic equation for thermal conduction based on the Fourier empiric law as well as the generalized thermal conduction equation based on the Maxwell law have been derived from the Boltzmann equation for the phonons within the relaxation time approximation. The temperature waves of the so-called second sound in crystals at low temperatures are transformed into Fourier waves at low frequencies with respect to the characteristic frequency of the U-processes. These waves are transformed into temperature waves similar to the second sound waves in He II at frequences higher than the U-processes characteristic. 1 fig., 19 refs

Analysis of spectral methods for the homogeneous Boltzmann equation

KAUST Repository

Filbet, Francis; Mouhot, Clé ment

2011-01-01

The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.

Analysis of spectral methods for the homogeneous Boltzmann equation

KAUST Repository

Filbet, Francis

2011-04-01

The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.

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

Science.gov (United States)

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

2018-06-01

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

Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

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

2010-09-15

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

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

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TEKIC, P. M.

2012-02-01

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

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

Science.gov (United States)

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.

Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

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Florian Thüroff

2014-11-01

Full Text Available Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system’s dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system’s ordered state nematic, despite purely polar interactions on the level of single particles.

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

CERN Document Server

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

2003-01-01

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

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

Science.gov (United States)

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

2003-03-01

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

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

International Nuclear Information System (INIS)

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

2003-01-01

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

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

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Stuart Bartlett

2017-08-01

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

Recursive regularization step for high-order lattice Boltzmann methods

Science.gov (United States)

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

2017-09-01

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

Singularities in the nonisotropic Boltzmann equation

International Nuclear Information System (INIS)

Garibotti, C.R.; Martiarena, M.L.; Zanette, D.

1987-09-01

We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs

One-dimensional transient radiative transfer by lattice Boltzmann method.

Science.gov (United States)

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.

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

Directory of Open Access Journals (Sweden)

Ping Wang

2014-01-01

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

High energy ion range and deposited energy calculation using the Boltzmann-Fokker-Planck splitting of the Boltzmann transport equation

International Nuclear Information System (INIS)

Mozolevski, I.E.

2001-01-01

We consider the splitting of the straight-ahead Boltzmann transport equation in the Boltzmann-Fokker-Planck equation, decomposing the differential cross-section into a singular part, corresponding to small energy transfer events, and in a regular one, which corresponds to large energy transfer. The convergence of implantation profile, nuclear and electronic energy depositions, calculated from the Boltzmann-Fokker-Planck equation, to the respective exact distributions, calculated from Monte-Carlo method, was exanimate in a large-energy interval for various values of splitting parameter and for different ion-target mass relations. It is shown that for the universal potential there exists an optimal value of splitting parameter, for which range and deposited energy distributions, calculated from the Boltzmann-Fokker-Planck equation, accurately approximate the exact distributions and which minimizes the computational expenses

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

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

2013-01-01

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

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed

2013-06-01

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

Metamaterial characterization using Boltzmann's kinetic equation for electrons

DEFF Research Database (Denmark)

Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.

2013-01-01

Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows...

A maximum principle for the first-order Boltzmann equation, incorporating a potential treatment of voids

International Nuclear Information System (INIS)

Schofield, S.L.

1988-01-01

Ackroyd's generalized least-squares method for solving the first-order Boltzmann equation is adapted to incorporate a potential treatment of voids. The adaptation comprises a direct least-squares minimization allied with a suitably-defined bilinear functional. The resulting formulation gives rise to a maximum principle whose functional does not contain terms of the type that have previously led to difficulties in treating void regions. The maximum principle is derived without requiring continuity of the flux at interfaces. The functional of the maximum principle is concluded to have an Euler-Lagrange equation given directly by the first-order Boltzmann equation. (author)

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

Science.gov (United States)

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

2016-04-01

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

Comment on ''Boltzmann equation and the conservation of particle number''

International Nuclear Information System (INIS)

Zanette, D.

1990-09-01

In a recent paper (Z. Banggu, Phys. Rev. A 42, 761 (1990)) it is argued that some solutions of the Boltzmann equation do not satisfy particle conservation as a consequence of the independence of velocity on position. In this comment, the arguments and conclusions of that paper are discussed. In particular, it is stressed that the temporal series used for solving the kinetic equation are generally divergent. A discussion about the particle conservation in its solutions is also provided. (author). 4 refs

Parallel-plate rheometer calibration using oil and lattice Boltzmann simulation

DEFF Research Database (Denmark)

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

2007-01-01

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

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

Science.gov (United States)

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

2017-08-01

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

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

International Nuclear Information System (INIS)

Xu Kun; He Xiaoyi

2003-01-01

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

Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation

International Nuclear Information System (INIS)

Dou, Nicholas G.; Minnich, Austin J.

2016-01-01

Materials that possess low density, low thermal conductivity, and high stiffness are desirable for engineering applications, but most materials cannot realize these properties simultaneously due to the coupling between them. Nanotrusses, which consist of hollow nanoscale beams architected into a periodic truss structure, can potentially break these couplings due to their lattice architecture and nanoscale features. In this work, we study heat conduction in the exact nanotruss geometry by solving the frequency-dependent Boltzmann transport equation using a variance-reduced Monte Carlo algorithm. We show that their thermal conductivity can be described with only two parameters, solid fraction and wall thickness. Our simulations predict that nanotrusses can realize unique combinations of mechanical and thermal properties that are challenging to achieve in typical materials

Lattice Boltzmann methods for moving boundary flows

International Nuclear Information System (INIS)

Inamuro, Takaji

2012-01-01

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

Lattice Boltzmann methods for moving boundary flows

Energy Technology Data Exchange (ETDEWEB)

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

2012-04-01

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

New Poisson–Boltzmann type equations: one-dimensional solutions

International Nuclear Information System (INIS)

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

2011-01-01

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

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

Science.gov (United States)

Ding, E. J.

2015-06-01

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

The lattice Boltzmann method and the problem of turbulence

Energy Technology Data Exchange (ETDEWEB)

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

2015-03-10

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

The lattice Boltzmann method and the problem of turbulence

International Nuclear Information System (INIS)

Djenidi, L.

2015-01-01

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

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

Science.gov (United States)

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

2012-01-01

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

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

Science.gov (United States)

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

2011-08-01

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

Topology optimization of unsteady flow problems using the lattice Boltzmann method

DEFF Research Database (Denmark)

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

2016-01-01

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

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

Science.gov (United States)

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

2018-03-01

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

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

Science.gov (United States)

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 heat transfer model for permeable voxels

Science.gov (United States)

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

2017-12-01

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

Lattice-Boltzmann Simulation of Tablet Disintegration

Science.gov (United States)

Jiang, Jiaolong; Sun, Ning; Gersappe, Dilip

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

Multiple-relaxation-time lattice Boltzmann model for compressible fluids

International Nuclear Information System (INIS)

Chen Feng; Xu Aiguo; Zhang Guangcai; Li Yingjun

2011-01-01

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

Lattice Boltzmann method to study the contraction of a viscous ligament

NARCIS (Netherlands)

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

2013-01-01

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

A particle method with adjustable transport properties - the generalized consistent Boltzmann algorithm

International Nuclear Information System (INIS)

Garcia, A.L.; Alexander, F.J.; Alder, B.J.

1997-01-01

The consistent Boltzmann algorithm (CBA) for dense, hard-sphere gases is generalized to obtain the van der Waals equation of state and the corresponding exact viscosity at all densities except at the highest temperatures. A general scheme for adjusting any transport coefficients to higher values is presented

On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

International Nuclear Information System (INIS)

Kawashima, S.; Matsumara, A.; Nishida, T.

1979-01-01

The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate tsup(-5/4)) as t → + infinitely to that of the compressible Navier-Stokes equation for the corresponding initial data. (orig.) 891 HJ/orig. 892 MKO

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

KAUST Repository

Atanasov, Atanas

2016-10-17

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

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

International Nuclear Information System (INIS)

Mishra, Subhash C.; Vernekar, Rohan Ranganath

2012-01-01

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

A fast iterative scheme for the linearized Boltzmann equation

Science.gov (United States)

Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

2017-06-01

Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference

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

Directory of Open Access Journals (Sweden)

Y. Peng

2017-01-01

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

On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

Directory of Open Access Journals (Sweden)

Nikolai N. Bogoliubov (Jr.

2007-01-01

Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

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

KAUST Repository

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

2016-01-01

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

The Boltzmann equation in the difference formulation

Energy Technology Data Exchange (ETDEWEB)

Szoke, Abraham [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Brooks III, Eugene D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-05-06

First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation

Directory of Open Access Journals (Sweden)

Bertrand Lods

2015-06-01

Full Text Available Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set Ɛ of mutually absolutely continuous densities. We study in particular the fine properties of the Kullback-Liebler divergence in this context. We also show that this setting is well-suited for the study of the spatially homogeneous Boltzmann equation if Ɛ is a set of positive densities with finite relative entropy with respect to the Maxwell density. More precisely, we analyze the Boltzmann operator in the geometric setting from the point of its Maxwell’s weak form as a composition of elementary operations in the exponential manifold, namely tensor product, conditioning, marginalization and we prove in a geometric way the basic facts, i.e., the H-theorem. We also illustrate the robustness of our method by discussing, besides the Kullback-Leibler divergence, also the property of Hyvärinen divergence. This requires us to generalize our approach to Orlicz–Sobolev spaces to include derivatives.

A multi scale approximation solution for the time dependent Boltzmann-transport equation

International Nuclear Information System (INIS)

Merk, B.

2004-03-01

The basis of all transient simulations for nuclear reactor cores is the reliable calculation of the power production. The local power distribution is generally calculated by solving the space, time, energy and angle dependent neutron transport equation known as Boltzmann equation. The computation of exact solutions of the Boltzmann equation is very time consuming. For practical numerical simulations approximated solutions are usually unavoidable. The objective of this work is development of an effective multi scale approximation solution for the Boltzmann equation. Most of the existing methods are based on separation of space and time. The new suggested method is performed without space-time separation. This effective approximation solution is developed on the basis of an expansion for the time derivative of different approximations to the Boltzmann equation. The method of multiple scale expansion is used for the expansion of the time derivative, because the problem of the stiff time behaviour can't be expressed by standard expansion methods. This multiple scale expansion is used in this work to develop approximation solutions for different approximations of the Boltzmann equation, starting from the expansion of the point kinetics equations. The resulting analytic functions are used for testing the applicability and accuracy of the multiple scale expansion method for an approximation solution with 2 delayed neutron groups. The results are tested versus the exact analytical results for the point kinetics equations. Very good agreement between both solutions is obtained. The validity of the solution with 2 delayed neutron groups to approximate the behaviour of the system with 6 delayed neutron groups is demonstrated in an additional analysis. A strategy for a solution with 4 delayed neutron groups is described. A multiple scale expansion is performed for the space-time dependent diffusion equation for one homogenized cell with 2 delayed neutron groups. The result is

Volumetric formulation of lattice Boltzmann models with energy conservation

OpenAIRE

Sbragaglia, M.; Sugiyama, K.

2010-01-01

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

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

DEFF Research Database (Denmark)

Christensen, Britt Stenhøj Baun

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

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

Science.gov (United States)

Huang, Rongzong; Wu, Huiying; Adams, Nikolaus A.

2018-05-01

It is well recognized that there exist additional cubic terms of velocity in the lattice Boltzmann (LB) model based on the standard lattice. In this work, elimination of these cubic terms in the pseudopotential LB model for multiphase flow is investigated, where the force term and density gradient are considered. By retaining high-order (≥3 ) Hermite terms in the equilibrium distribution function and the discrete force term, as well as introducing correction terms in the LB equation, the additional cubic terms of velocity are entirely eliminated. With this technique, the computational simplicity of the pseudopotential LB model is well maintained. Numerical tests, including stationary and moving flat and circular interface problems, are carried out to show the effects of such cubic terms on the simulation of multiphase flow. It is found that the elimination of additional cubic terms is beneficial to reduce the numerical error, especially when the velocity is relatively large. Numerical results also suggest that these cubic terms mainly take effect in the interfacial region and that the density-gradient-related cubic terms are more important than the other cubic terms for multiphase flow.

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

Energy Technology Data Exchange (ETDEWEB)

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

2010-10-15

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

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

International Nuclear Information System (INIS)

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

2010-01-01

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

MRT-lattice Boltzmann computations of natural convection and volumetric radiation in a tilted square enclosure

Energy Technology Data Exchange (ETDEWEB)

Moufekkir, F.; Moussaoui, M.A.; Mezrhab, A. [Laboratoire de Mecanique and Energetique, Faculte des sciences, Departement de physique 60000 Oujda (Morocco); Lemonnier, D. [Institut Pprime, CNRS-ENSMA-Univ. Poitiers, ENSMA, BP 40109, 86961 Futuroscope Chasseneuil cedex (France); Naji, H. [Universite Lille Nord de France, F-59000 Lille (France); Laboratoire Genie Civil and geo-Environnement - LGCgE- EA 4515, UArtois/FSA Bethune, F-62400 Bethune (France)

2012-04-15

A numerical analysis is carried out for natural convection while in an asymmetrically heated square cavity containing an absorbing emitting medium. The numerical approach adopted uses a hybrid thermal lattice Boltzmann method (HTLBM) in which the mass and momentum conservation equations are solved by using multiple relaxation time (MRT) model and the energy equation is solved separately by using the finite difference method (FDM). In addition, the radiative transfer equation (RTE) is treated by the discrete ordinates method (DOM) using the S8 quadrature to evaluate the source term of the energy equation. The effects of parameters such as the Rayleigh number Ra, the optical thickness {tau} and the inclination angle {phi}, are studied numerically to assess their impact on the flow and temperature distribution. The results presented in terms of isotherms, streamlines and averaged Nusselt number, show that in the absence of the radiation, the temperature and the flow fields are centro-symmetric and the cavity core is thermally stratified. However, radiation causes an overall increase in temperature and velocity gradients along both thermally active walls

A Class of Two-Component Adler—Bobenko—Suris Lattice Equations

International Nuclear Information System (INIS)

Fu Wei; Zhang Da-Jun; Zhou Ru-Guang

2014-01-01

We study a class of two-component forms of the famous list of the Adler—Bobenko—Suris lattice equations. The obtained two-component lattice equations are still consistent around the cube and they admit solutions with ‘jumping properties’ between two levels. (general)

Transport methods: general. 7. Formulation of a Fourier-Boltzmann Transformation to Solve the Three-Dimensional Transport Equation

International Nuclear Information System (INIS)

Stancic, V.

2001-01-01

This paper presents some elements of a new approach to solve analytically the linearized three-dimensional (3-D) transport equation of neutral particles. Since this task is of such special importance, we present some results of a paper that is still in progress. The most important is that using this transformation, an integro-differential equation with an analytical solution is obtained. For this purpose, a simplest 3-D equation is being considered which describes the transport process in an infinite medium. Until now, this equation has been analytically considered either using the Laplace transform with respect to time parameter t or applying the Fourier transform over the space coordinate. Both of them reduce the number of differential terms in the equation; however, evaluation of the inverse transformation is complicated. In this paper, we introduce for the first time a Fourier transform induced by the Boltzmann operator. For this, we use a complete set of 3-D eigenfunctions of the Boltzmann transport operator defined in a similar way as those that have been already used in 3-D transport theory as a basic set to transform the transport equation. This set consists of a continuous part and a discrete one with spectral measure. The density distribution equation shows the known form asymptotic behavior. Several applications are to be performed using this equation and compared to the benchmark one. Such an analysis certainly would be out of the available space

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

Science.gov (United States)

Januszewski, M.; Kostur, M.

2014-09-01

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

An optimized D2Q37 Lattice Boltzmann code on GP-GPUs

NARCIS (Netherlands)

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

2013-01-01

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

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

NARCIS (Netherlands)

Kamali, M.R.

2013-01-01

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

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

Science.gov (United States)

Osiptsov, Andrei A.

2017-06-01

The goal of this study is to evaluate the conductivity of random close packings of non-spherical, rod-shaped proppant particles under the closure stress using numerical simulation and lab tests, with application to the conductivity of hydraulic fractures created in subterranean formation to stimulate production from oil and gas reservoirs. Numerical simulations of a steady viscous flow through proppant packs are carried out using the lattice Boltzmann method for the Darcy flow regime. The particle packings were generated numerically using the sequential deposition method. The simulations are conducted for packings of spheres, ellipsoids, cylinders, and mixtures of spheres with cylinders at various volumetric concentrations. It is demonstrated that cylinders provide the highest permeability among the proppants studied. The dependence of the nondimensional permeability (scaled by the equivalent particle radius squared) on porosity obtained numerically is well approximated by the power-law function: K /Rv2 = 0.204ϕ4.58 in a wide range of porosity: 0.3 ≤ ϕ ≤ 0.7. Lattice-Boltzmann simulations are cross-verified against finite-volume simulations using Navier-Stokes equations for inertial flow regime. Correlations for the normalized beta-factor as a function of porosity and normalized permeability are presented as well. These formulae are in a good agreement with the experimental measurements (including packings of rod-shaped particles) and existing laboratory data, available in the porosity range 0.3 ≤ ϕ ≤ 0.5. Comparison with correlations by other authors is also given.

Lattice Boltzmann method used to simulate particle motion in a conduit

Czech Academy of Sciences Publication Activity Database

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

2017-01-01

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

Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes.

Science.gov (United States)

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2015-04-05

The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson-Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev-Bashford-Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson-Boltzmann model. © 2015 Wiley Periodicals, Inc.

Boltzmann equation for a mixture of gases with non-conservative processes

International Nuclear Information System (INIS)

Martiarena, M.L.

1989-01-01

The nonlinear and non-isotropic Boltzmann equation (NLBE) including several molecular species, non-conservative channels and external forces. The general solution of that equation is obtained for a spatially homogeneous mixture of L gases, consisting of Maxwell particles, as a Generalized Laguerre expansion, within a Hilbert space. Removal and self-generation effects are included in presence of a time-dependent external force. An exact particular solution is studied generalizing the well-known BKW-mode for a mixture of L gases with inelastic processes. An homogeneous gas of test particles, in d dimension, is considered which interacts with a background host medium in the presence of an external space and time dependent force. Scattering, removal and self-generation collisions are included. The inhomogeneous Boltzmann equation for this system to an homogeneous one is reduced without background or external forces, using a generalized Nilkoskii transform. It is shown that a background of field particles can confine the test gas, even in absence of external forces. Furthermore, the solution of NLBE with non-isotropic singular initial conditions, is analyzed. The NLBE is transformed into an integral equation which is solved iteratively. The evolution of delta and step singularities in the distribution function is discussed during the initial layer and compared with the isotropic case. As an application of the methods abovementioned, the collision of a beam of ions or neutral atoms with a carbon-foil is considered. The electron experimental spectra from a transport equation is described. It is supposed that convoy electron may be produced inside the solid by single ion-atom collisions as ELC or ECC. The produced electrons lost energy by collision with the atoms of the material, which are considered at rest. The electron distribution function is numerically calculated. The ratio between the intrinsic convoy electron peak height to the background electron intensity

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

International Nuclear Information System (INIS)

Ebihara, Ken-ichi

2005-03-01

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

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

Science.gov (United States)

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

2018-03-01

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

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

Directory of Open Access Journals (Sweden)

Liping Chen

2018-05-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2012-12-15

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

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

Science.gov (United States)

Ginzburg, Irina; Steiner, Konrad

2002-03-15

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

Boltzmann-Langevin equation, dynamical instability and multifragmentation

International Nuclear Information System (INIS)

Feng-Shou Zhang

1993-02-01

By using simulations of the Boltzmann-Langevin equation which incorporates dynamical fluctuations beyond usual transport theories and by coupling it with a coalescence model, we obtain information on multifragmentation in heavy-ion collisions. From a calculation of the 40 Ca + 40 Ca system, we recover some trends of recent multifragmentation data

The Quark-Gluon Plasma Equation of State and the Generalized Uncertainty Principle

Directory of Open Access Journals (Sweden)

L. I. Abou-Salem

2015-01-01

Full Text Available The quark-gluon plasma (QGP equation of state within a minimal length scenario or Generalized Uncertainty Principle (GUP is studied. The Generalized Uncertainty Principle is implemented on deriving the thermodynamics of ideal QGP at a vanishing chemical potential. We find a significant effect for the GUP term. The main features of QCD lattice results were quantitatively achieved in case of nf=0, nf=2, and nf=2+1 flavors for the energy density, the pressure, and the interaction measure. The exciting point is the large value of bag pressure especially in case of nf=2+1 flavor which reflects the strong correlation between quarks in this bag which is already expected. One can notice that the asymptotic behavior which is characterized by Stephan-Boltzmann limit would be satisfied.

Boltzmann equation and hydrodynamics beyond Navier-Stokes.

Science.gov (United States)

Bobylev, A V

2018-04-28

We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Weighted particle method for solving the Boltzmann equation

International Nuclear Information System (INIS)

Tohyama, M.; Suraud, E.

1990-01-01

We propose a new, deterministic, method of solution of the nuclear Boltzmann equation. In this Weighted Particle Method two-body collisions are treated by a Master equation for an occupation probability of each numerical particle. We apply the method to the quadrupole motion of 12 C. A comparison with usual stochastic methods is made. Advantages and disadvantages of the Weighted Particle Method are discussed

New variational principles for locating periodic orbits of differential equations.

Science.gov (United States)

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.

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

Science.gov (United States)

Salomons, Erik M; Lohman, Walter J A; Zhou, Han

2016-01-01

Propagation of sound waves in air can be considered as a special case of fluid dynamics. Consequently, the lattice Boltzmann method (LBM) for fluid flow can be used for simulating sound propagation. In this article application of the LBM to sound propagation is illustrated for various cases: free-field propagation, propagation over porous and non-porous ground, propagation over a noise barrier, and propagation in an atmosphere with wind. LBM results are compared with solutions of the equations of acoustics. It is found that the LBM works well for sound waves, but dissipation of sound waves with the LBM is generally much larger than real dissipation of sound waves in air. To circumvent this problem it is proposed here to use the LBM for assessing the excess sound level, i.e. the difference between the sound level and the free-field sound level. The effect of dissipation on the excess sound level is much smaller than the effect on the sound level, so the LBM can be used to estimate the excess sound level for a non-dissipative atmosphere, which is a useful quantity in atmospheric acoustics. To reduce dissipation in an LBM simulation two approaches are considered: i) reduction of the kinematic viscosity and ii) reduction of the lattice spacing.

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

International Nuclear Information System (INIS)

Sukop, M.C.; Or, Dani

2003-01-01

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

Flux Limiter Lattice Boltzmann for Compressible Flows

International Nuclear Information System (INIS)

Chen Feng; Li Yingjun; Xu Aiguo; Zhang Guangcai

2011-01-01

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

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

2016-01-01

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

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

International Nuclear Information System (INIS)

Esfahanian, Vahid; Ghadyani, Mohsen

2015-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-05-15

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

A multi-GPU implementation of a D2Q37 lattice Boltzmann code

NARCIS (Netherlands)

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

2012-01-01

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

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

DEFF Research Database (Denmark)

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

2007-01-01

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

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

DEFF Research Database (Denmark)

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

2006-01-01

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

Lattice Boltzmann simulation of droplet formation in T-junction geometries

Science.gov (United States)

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

2017-01-01

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

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

International Nuclear Information System (INIS)

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

2011-01-01

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

Lattice Boltzmann model for three-dimensional decaying homogeneous isotropic turbulence

International Nuclear Information System (INIS)

Xu Hui; Tao Wenquan; Zhang Yan

2009-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2012-12-15

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

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

KAUST Repository

Neumann, Philipp; Rohrmann, Till

2012-01-01

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

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

Directory of Open Access Journals (Sweden)

Bennacer Rachid

2017-01-01

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

Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows.

Science.gov (United States)

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

2012-07-01

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

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

KAUST Repository

Reis, Tim; Dellar, Paul J.

2012-01-01

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

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

KAUST Repository

Neumann, Philipp

2012-01-01

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

Exact results for the Boltzmann equation and Smoluchowski's coagulation equation

International Nuclear Information System (INIS)

Hendriks, E.M.

1983-01-01

Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

International Nuclear Information System (INIS)

Gamba, Irene M.; Haack, Jeffrey R.

2014-01-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation

Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

Energy Technology Data Exchange (ETDEWEB)

Uchaikin, V V; Sibatov, R T, E-mail: vuchaikin@gmail.com, E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432000, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation)

2011-04-08

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

International Nuclear Information System (INIS)

Uchaikin, V V; Sibatov, R T

2011-01-01

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

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

Science.gov (United States)

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

2018-05-01

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

Thermal lattice Boltzmann simulation for multispecies fluid equilibration

International Nuclear Information System (INIS)

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

2000-01-01

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

Thermal lattice Boltzmann simulation for multispecies fluid equilibration

Energy Technology Data Exchange (ETDEWEB)

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

2000-07-01

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

Lattice Boltzmann model for melting with natural convection

International Nuclear Information System (INIS)

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

2008-01-01

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

Applications of Boltzmann Langevin equation to nuclear collisions

International Nuclear Information System (INIS)

Suraud, E.; Belkacem, M.; Stryjewski, J.; Ayik, S.

1991-01-01

An approximate method for obtaining numerical solutions of the Boltzmann-Langevin equation is proposed. The method is applied to calculate the time evolution of the mean value and dispersion of the quadrupole and octupole moments of the momentum distribution in nucleus-nucleus collisions, and some consequences are discussed

A discontinuous Galerkin finite-element method for a 1D prototype of the Boltzmann equation

NARCIS (Netherlands)

Hoitinga, W.; Brummelen, van E.H.

2011-01-01

To develop and analyze new computational techniques for the Boltzmann equation based on model or approximation adaptivity, it is imperative to have disposal of a compliant model problem that displays the essential characteristics of the Boltzmann equation and that admits the extraction of highly

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

NARCIS (Netherlands)

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

2011-01-01

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

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

African Journals Online (AJOL)

JOSLIN

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

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

NARCIS (Netherlands)

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

2013-01-01

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

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

Science.gov (United States)

Yu, H.; Wang, Z.; Zhang, C.; Chen, N.; Zhao, Y.; Sawchuk, A. P.; Dalsing, M. C.; Teague, S. D.; Cheng, Y.

2014-11-01

Existing research of patient-specific computational hemodynamics (PSCH) heavily relies on software for anatomical extraction of blood arteries. Data reconstruction and mesh generation have to be done using existing commercial software due to the gap between medical image processing and CFD, which increases computation burden and introduces inaccuracy during data transformation thus limits the medical applications of PSCH. We use lattice Boltzmann method (LBM) to solve the level-set equation over an Eulerian distance field and implicitly and dynamically segment the artery surfaces from radiological CT/MRI imaging data. The segments seamlessly feed to the LBM based CFD computation of PSCH thus explicit mesh construction and extra data management are avoided. The LBM is ideally suited for GPU (graphic processing unit)-based parallel computing. The parallel acceleration over GPU achieves excellent performance in PSCH computation. An application study will be presented which segments an aortic artery from a chest CT dataset and models PSCH of the segmented artery.

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

Science.gov (United States)

Xue, Xiao; Biferale, Luca; Sbragaglia, Mauro; Toschi, Federico

2017-11-01

Thermal fluctuations are essential ingredients in a nanoscale system, driving Brownian motion of particles and capillary waves at non-ideal interfaces. Here we study the influence of thermal fluctuations on the breakup of liquid ligaments at the nanoscale. We offer quantitative characterization of the effects of thermal fluctuations on the Plateau-Rayleigh mechanism that drives the breakup process of ligaments. Due to thermal fluctuations, the droplet sizes after break-up need to be analyzed in terms of their distribution over an ensemble made of repeated experiments. To this aim, we make use of numerical simulations based on the fluctuating lattice Boltzmann method (FLBM) for multicomponent mixtures. The method allows an accurate and efficient simulation of the fluctuating hydrodynamics equations of a binary mixture, where both stochastic viscous stresses and diffusion fluxes are introduced. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No 642069.

Simulation of plume dynamics by the Lattice Boltzmann Method

Science.gov (United States)

Mora, Peter; Yuen, David A.

2017-09-01

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

Parallelization of 2-D lattice Boltzmann codes

International Nuclear Information System (INIS)

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

1996-03-01

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

Parallelization of 2-D lattice Boltzmann codes

Energy Technology Data Exchange (ETDEWEB)

Suzuki, Soichiro; Kaburaki, Hideo; Yokokawa, Mitsuo

1996-03-01

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

Study of the Dynamics of a Condensing Bubble Using Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Shahnawaz Ahmed

2015-06-01

Full Text Available Mesoscopic lattice Boltzmann method (LBM is used to discretize the governing equations for a steam bubble inside a tube filled with water. The bubbles are kept at higher temperature compared to its boiling point while the liquid is kept subcooled. Heat transfer is allowed to take place between the two phases by virtue of which the bubble will condense. Three separate probability distribution functions are used in LBM to handle continuity, momentum and energy equations separately. The interface is considered to be diffused within a narrow zone and it has been modeled using convective Cahn-Hillard equation. Combined diffused interface-LBM framework is adapted accordingly to handle complex interface separating two phases having high density ratio. Developed model is validated with respect to established correlations for instantaneous equivalent radius of a spherical condensing bubble. Numerical snapshots of the simulation depict that the bubble volume decreases faster for higher degree of superheat. The degrees of superheat are varied over a wide range to note its effect on bubble shape and size. Effect of initial volume of the bubble on the condensation rate is also studied. It has been observed that for a fixed degree of superheat, the condensation rate is not exactly proportional to its volume. Due to the variation in interfacial configuration for different sized bubbles, condensation rate changes drastically. Influence of gravity on the rate of condensation is also studied using the developed methodology.

Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

International Nuclear Information System (INIS)

Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T.; Santos, Marcio G.

2015-01-01

This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

Energy Technology Data Exchange (ETDEWEB)

Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte

2015-07-01

This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Rasmussen, Kim; Henning, D.; Gabriel, H.

1996-01-01

We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...

Application of group analysis to the spatially homogeneous and isotropic Boltzmann equation with source using its Fourier image

International Nuclear Information System (INIS)

Grigoriev, Yurii N; Meleshko, Sergey V; Suriyawichitseranee, Amornrat

2015-01-01

Group analysis of the spatially homogeneous and molecular energy dependent Boltzmann equations with source term is carried out. The Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The correspondent determining equation of the admitted Lie group is reduced to a partial differential equation for the admitted source. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation with respect to a source function is given. The representation of invariant solutions and corresponding reduced equations for all obtained source functions are also presented. (paper)

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

DEFF Research Database (Denmark)

Skocek, Jan; Svec, Oldrich; Spangenberg, Jon

2011-01-01

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

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

Science.gov (United States)

Ren, Qinlong

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

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

Energy Technology Data Exchange (ETDEWEB)

Bin Mansoor, Saad; Sami Yilbas, Bekir, E-mail: bsyilbas@kfupm.edu.sa

2015-08-15

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.

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

International Nuclear Information System (INIS)

Bin Mansoor, Saad; Sami Yilbas, Bekir

2015-01-01

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

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

DEFF Research Database (Denmark)

Svec, Oldrich; Skocek, Jan; Stang, Henrik

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

Construction and analysis of lattice Boltzmann methods applied to a 1D convection-diffusion equation

International Nuclear Information System (INIS)

Dellacherie, Stephane

2014-01-01

To solve the 1D (linear) convection-diffusion equation, we construct and we analyze two LBM schemes built on the D1Q2 lattice. We obtain these LBM schemes by showing that the 1D convection-diffusion equation is the fluid limit of a discrete velocity kinetic system. Then, we show in the periodic case that these LBM schemes are equivalent to a finite difference type scheme named LFCCDF scheme. This allows us, firstly, to prove the convergence in L∞ of these schemes, and to obtain discrete maximum principles for any time step in the case of the 1D diffusion equation with different boundary conditions. Secondly, this allows us to obtain most of these results for the Du Fort-Frankel scheme for a particular choice of the first iterate. We also underline that these LBM schemes can be applied to the (linear) advection equation and we obtain a stability result in L∞ under a classical CFL condition. Moreover, by proposing a probabilistic interpretation of these LBM schemes, we also obtain Monte-Carlo algorithms which approach the 1D (linear) diffusion equation. At last, we present numerical applications justifying these results. (authors)

Spherical harmonics and energy polynomial solution of the Boltzmann equation for neutrons, 1

International Nuclear Information System (INIS)

Toledo, P.S. de

1974-01-01

The approximate solution of the source-free energy-dependent Boltzmann transport equation for neutrons in plane geometry and isotropic scattering case was given by Leonard and Ferziger using a truncated development in a series of energy-polynomials for the energy dependent neutron flux and solving exactly for the angular dependence. The presence in the general solution of eigenfunctions belonging to a continuous spectrum gives rise to difficult analytical problems in the application of their method even to simple problems. To avoid such difficulties, the angular dependence is treated by a spherical harmonics method and a general solution of the energy-dependent transport equation in plane geometry and isotropic scattering is obtained, in spite of the appearance of matrices as argument of the angular polynomials [pt

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

International Nuclear Information System (INIS)

Gan Yanbiao; Li Yingjun; Xu Aiguo; Zhang Guangcai

2011-01-01

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

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

International Nuclear Information System (INIS)

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

2000-01-01

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

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

International Nuclear Information System (INIS)

Park, Jong Woon; Choi, Hyun Gyung

2014-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-02-15

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

Entire solutions for bistable lattice differential equations with obstacles

CERN Document Server

Hoffman, Aaron; Vleck, E S Van

2018-01-01

The authors consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by "holes") are present in the lattice. Their work generalizes to the discrete spatial setting the results obtained in Berestycki, Hamel, and Matuno (2009) for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.

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

Science.gov (United States)

Flint, Christopher; Vahala, George

2018-02-01

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

Navier-Stokes Dynamics by a Discrete Boltzmann Model

Science.gov (United States)

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.

A Boltzmann equation approach to the damping of giant resonances in nuclei

International Nuclear Information System (INIS)

Schuck, P.; Winter, J.

1983-01-01

The Vlasov equation plus collision term (Boltzmann equation) represents an appropriate frame for the treatment of giant resonances (zero sound modes) in nuclei. With no adjustable parameters we obtain correct positions and widths for the giant quadrupole resonances. (author)

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

Science.gov (United States)

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=∑_{α}e_{α}f_{α}/ρ, while the actual fluid velocity is defined as u[over ̂]=u+δ_{t}F/(2ρ). 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.

On Traveling Waves in Lattices: The Case of Riccati Lattices

Science.gov (United States)

Dimitrova, Zlatinka

2012-09-01

The method of simplest equation is applied for analysis of a class of lattices described by differential-difference equations that admit traveling-wave solutions constructed on the basis of the solution of the Riccati equation. We denote such lattices as Riccati lattices. We search for Riccati lattices within two classes of lattices: generalized Lotka-Volterra lattices and generalized Holling lattices. We show that from the class of generalized Lotka-Volterra lattices only the Wadati lattice belongs to the class of Riccati lattices. Opposite to this many lattices from the Holling class are Riccati lattices. We construct exact traveling wave solutions on the basis of the solution of Riccati equation for three members of the class of generalized Holling lattices.

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

International Nuclear Information System (INIS)

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

2016-01-01

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

Tracer sorption and macroscopic transport in clay nano-pores: a lattice-Boltzmann study

International Nuclear Information System (INIS)

Levesque, Maximilien; Rotenberg, Benjamin; Duvail, Magali; Benichou, Olivier; Voituriez, Raphael; Pagonabarraga, Ignacio; Frenkel, Daan

2012-01-01

followed by making their associated moment to propagate between nodes of a lattice with a probability defined by evolution equations. This evolution with time gives access to macroscopic transport properties like the tracer effective diffusion coefficient. For now, however, the evolution equations do not satisfactorily account for sorption effects as they do not capture their chemical-specific nature. This is our goal to overtake this lack. We have introduced the specific adsorption and desorption mechanisms in the description of tracers transport. This has been done for neutral tracers, as a first step, by introducing a new possible event during the moment propagation of particles standing at solid-liquid interfacial nodes: they may adsorb (desorb) with a probability related to the adsorption and desorption rates of the underlying mechanism occurring at the molecular scale. In order to validate the method and to determine its numerical limitations, we have compared the Lattice-Boltzmann results to an analytical solution developed purposely in the simple geometry consisting of two parallel walls. This last solution comes from a stochastic approach of the longitudinal dynamics of a particle assumed to be driven by a Langevin equation accounting for bulk diffusion and for the adsorption-desorption rates defined above. It is finally shown how sorption phenomena affect the macroscopic transport properties of neutral tracers in geometries and regimes compatible with water in clay nano-pores. (authors)

Normal solutions of the Boltzmann equation with small Knudsen number

International Nuclear Information System (INIS)

Ding, E.J.; Huang, Z.Q.

1986-01-01

A singular perturbation method is used to find the normal solutions of the Boltzmann equation with small Knudsen number. It is proved that the secular terms may be removed by improving the Hilbert expansion and the Enskog expansion

Multi-relaxation-time lattice Boltzmann modeling of the acoustic field generated by focused transducer

Science.gov (United States)

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.

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

Science.gov (United States)

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

The Boltzmann-Langevin Equation derived from the real-time path formalism

International Nuclear Information System (INIS)

Suraud, E.; Reinhard, P.G.

1991-01-01

We derive the Boltzmann-Langevin equation using Green's functions techniques in the real-time path formalism. We start from the Martin-Schwinger hierarchy and close it approximately at the two-body level. A careful discussion of the initial conditions for the free two-body Green's function provides the flexibility to recover the discarded correlations as fluctuations leading to the Langevin force. The derivation is generalized to the T-matrix approach which allows to prove that one can use the same effective interaction in the mean-field as well as in the collision term and Langevin force

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

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

International Nuclear Information System (INIS)

Mishra, Subhash C.; Roy, Hillol K.

2007-01-01

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 heat 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

Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz—Ladik—Lattice system

International Nuclear Information System (INIS)

Fu Jing-Li; He Yu-Fang; Hong Fang-Yu; Song Duan; Fu Hao

2013-01-01

In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz—Ladik—Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz—Ladik—Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz—Ladik—Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz—Ladik—Lattice method is verified. (general)

The Lattice Boltzmann method principles and practice

CERN Document Server

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

2017-01-01

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

Finite Boltzmann schemes

NARCIS (Netherlands)

Sman, van der R.G.M.

2006-01-01

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

On the Boltzmann Equation of Thermal Transport for Interacting Phonons and Electrons

Directory of Open Access Journals (Sweden)

Amelia Carolina Sparavigna

2016-05-01

Full Text Available The thermal transport in a solid can be determined by means of the Boltzmann equations regarding its distributions of phonons and electrons, when the solid is subjected to a thermal gradient. After solving the coupled equations, the related thermal conductivities can be obtained. Here we show how to determine the coupled equations for phonons and electrons.

Solution of spatially homogeneous model Boltzmann equations by means of Lie groups of transformations

International Nuclear Information System (INIS)

Foroutan, A.

1992-05-01

The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)

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

Science.gov (United States)

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

2007-09-01

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

A modified Poisson-Boltzmann equation applied to protein adsorption.

Science.gov (United States)

Gama, Marlon de Souza; Santos, Mirella Simões; Lima, Eduardo Rocha de Almeida; Tavares, Frederico Wanderley; Barreto, Amaro Gomes Barreto

2018-01-05

Ion-exchange chromatography has been widely used as a standard process in purification and analysis of protein, based on the electrostatic interaction between the protein and the stationary phase. Through the years, several approaches are used to improve the thermodynamic description of colloidal particle-surface interaction systems, however there are still a lot of gaps specifically when describing the behavior of protein adsorption. Here, we present an improved methodology for predicting the adsorption equilibrium constant by solving the modified Poisson-Boltzmann (PB) equation in bispherical coordinates. By including dispersion interactions between ions and protein, and between ions and surface, the modified PB equation used can describe the Hofmeister effects. We solve the modified Poisson-Boltzmann equation to calculate the protein-surface potential of mean force, treated as spherical colloid-plate system, as a function of process variables. From the potential of mean force, the Henry constants of adsorption, for different proteins and surfaces, are calculated as a function of pH, salt concentration, salt type, and temperature. The obtained Henry constants are compared with experimental data for several isotherms showing excellent agreement. We have also performed a sensitivity analysis to verify the behavior of different kind of salts and the Hofmeister effects. Copyright © 2017 Elsevier B.V. All rights reserved.

A lattice Boltzmann model for substrates with regularly structured surface roughness

Science.gov (United States)

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.

Effect of the forcing term in the pseudopotential lattice Boltzmann modeling of thermal flows.

Science.gov (United States)

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); L. Biferale, P. Perlekar, M. Sbragaglia, and F. Toschi, Phys. Rev. Lett. 108, 104502 (2012); S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012); M. R. Kamali et al., Phys. Rev. E 88, 033302 (2013)]. 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.

Lattice Boltzmann modeling an introduction for geoscientists and engineers

CERN Document Server

Sukop, Michael C

2005-01-01

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

A differential equation for the Generalized Born radii.

Science.gov (United States)

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linear second-order partial differential equation for the Generalized Born radius, which may be solved using local iterative algorithms. The equation is derived under the assumption that the usual GB approximation to the reaction field obeys Laplace's equation. The equation admits as particular solutions the correct GB radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and "perfect" Poisson-Boltzmann based values.

Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

2009-01-01

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

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

NARCIS (Netherlands)

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

2004-01-01

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

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

International Nuclear Information System (INIS)

Haydock, David

2005-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2005-04-15

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

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

International Nuclear Information System (INIS)

Schneider, A; Conrad, D; Böhle, M

2013-01-01

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

Inverse analysis of a rectangular fin using the lattice Boltzmann method

International Nuclear Information System (INIS)

Bamdad, Keivan; Ashorynejad, Hamid Reza

2015-01-01

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

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

KAUST Repository

Allen, Rebecca; Reis, Tim

2016-01-01

moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow

Backlund transformations and three-dimensional lattice equations

NARCIS (Netherlands)

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

1984-01-01

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

Lattice Wigner equation

Science.gov (United States)

Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

The C{sub n} method for approximation of the Boltzmann equation; La methode C{sub n} d'approximation de l'equation de Boltzmann

Energy Technology Data Exchange (ETDEWEB)

Benoist, P; Kavenoky, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1968-01-15

In a new method of approximation of the Boltzmann equation, one starts from a particular form of the equation which involves only the angular flux at the boundary of the considered medium and where the space variable does not appear explicitly. Expanding in orthogonal polynomials the angular flux of neutrons leaking from the medium and making no assumption about the angular flux within the medium, very good approximations to several classical plane geometry problems, i.e. the albedo of slabs and the transmission by slabs, the extrapolation length of the Milne problem, the spectrum of neutrons reflected by a semi-infinite slowing down medium. The method can be extended to other geometries. (authors) [French] On etablit une nouvelle methode d'approximation pour l'equation de Boltzmann en partant d'une forme particuliere de cette equation qui n'implique que le flux angulaire a la frontiere du milieu et ou les variables d'espace n'apparaissent pas explicitement. Par un developpement en polynomes orthogonaux du flux angulaire sortant du milieu et sans faire d'hypothese sur le flux angulaire a l'interieur du milieu, on obtient de tres bonnes approximations pour plusieurs problemes classiques en geometrie plane: l'albedo et le facteur de transmission des plaques, la longueur d'extrapolation du probleme de Milne, le spectre des neutrons reflechis par un milieu semi-infini ralentisseur. La methode se generalise a d'autres geometries. (auteurs)

An efficient numerical method for solving the Boltzmann equation in multidimensions

Science.gov (United States)

Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas

2018-01-01

In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme combines a robust and fast method for treating the transport part based on an innovative Lagrangian technique supplemented with conservative fast spectral schemes to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is numerically tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the 3 D × 3 D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different numerical methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.

Implementing the lattice Boltzmann model on commodity graphics hardware

International Nuclear Information System (INIS)

Kaufman, Arie; Fan, Zhe; Petkov, Kaloian

2009-01-01

Modern graphics processing units (GPUs) can perform general-purpose computations in addition to the native specialized graphics operations. Due to the highly parallel nature of graphics processing, the GPU has evolved into a many-core coprocessor that supports high data parallelism. Its performance has been growing at a rate of squared Moore's law, and its peak floating point performance exceeds that of the CPU by an order of magnitude. Therefore, it is a viable platform for time-sensitive and computationally intensive applications. The lattice Boltzmann model (LBM) computations are carried out via linear operations at discrete lattice sites, which can be implemented efficiently using a GPU-based architecture. Our simulations produce results comparable to the CPU version while improving performance by an order of magnitude. We have demonstrated that the GPU is well suited for interactive simulations in many applications, including simulating fire, smoke, lightweight objects in wind, jellyfish swimming in water, and heat shimmering and mirage (using the hybrid thermal LBM). We further advocate the use of a GPU cluster for large scale LBM simulations and for high performance computing. The Stony Brook Visual Computing Cluster has been the platform for several applications, including simulations of real-time plume dispersion in complex urban environments and thermal fluid dynamics in a pressurized water reactor. Major GPU vendors have been targeting the high performance computing market with GPU hardware implementations. Software toolkits such as NVIDIA CUDA provide a convenient development platform that abstracts the GPU and allows access to its underlying stream computing architecture. However, software programming for a GPU cluster remains a challenging task. We have therefore developed the Zippy framework to simplify GPU cluster programming. Zippy is based on global arrays combined with the stream programming model and it hides the low-level details of the

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

International Nuclear Information System (INIS)

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

2017-01-01

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

An introduction to the Boltzmann equation and transport processes in gases

CERN Document Server

Kremer, Gilberto M; Colton, David

2010-01-01

This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.

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

KAUST Repository

Reis, T.

2011-07-01

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

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

KAUST Repository

Reis, T.; Dellar, P.J.

2011-01-01

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

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

Science.gov (United States)

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

2018-03-01

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

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

DEFF Research Database (Denmark)

Svec, Oldrich; Skocek, Jan; Stang, Henrik

2011-01-01

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

Generalized isothermic lattices

International Nuclear Information System (INIS)

Doliwa, Adam

2007-01-01

We study multi-dimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isothermic lattices using Steiner's projective structure of conics, and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two-dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Directory of Open Access Journals (Sweden)

Song Wenyu

2017-06-01

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

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

Directory of Open Access Journals (Sweden)

Giacomo Falcucci

2017-09-01

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

The polaron problem and the Boltzmann equation

International Nuclear Information System (INIS)

Devreese, J.

1979-01-01

A mobility theory for the Feynman polaron is developed. It is shown that the Boltzmann equation for polarons is valid for weak coupling and not too high electric fields. The analytical results indicate that for E → 0 the relaxation time approximation is valid. A comparison is made of three methods to calculate the mobility in a linear electron transport theory. An approximation to the Kubo formula, a mobility calculation using path integrals by Feynman and a calculation based on the displaced Maxwell distribution function are considered. The three methods lead to equivalent results in the weak scattering and small electric field limit

Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations.

Science.gov (United States)

Liu, Haihu; Valocchi, Albert J; Kang, Qinjun

2012-04-01

We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter β=0.7. In the limit of creeping flow, droplet breakup occurs at a critical capillary number 0.35

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

NARCIS (Netherlands)

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

2017-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-03-15

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

Global Well-Posedness of the Boltzmann Equation with Large Amplitude Initial Data

Science.gov (United States)

Duan, Renjun; Huang, Feimin; Wang, Yong; Yang, Tong

2017-07-01

The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new {L^∞_xL^1v\\cap L^∞_{x,v}} approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted {L^∞} norm under some smallness condition on the {L^1_xL^∞_v} norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in the {L^∞_{x,v}} norm with explicit rates of convergence are also studied.

Application of Boltzmann equation to electron transmission and seconary electron emission

International Nuclear Information System (INIS)

Lanteri, H.; Bindi, R.; Rostaing, P.

1979-01-01

A method is presented for numerical treatment of integro-differential equation, based upon finite difference techniques. This method allows to formulate in a satisfactory manner the Boltzmann's equation applied to backscattering, transmission and secondary emission of metallic targets, avoiding must of the restrictive hypothesis, used until now in these models. For aluminium, the calculated energy spectra, angular distribution, transmission and backscattering coefficients, and secondary emission yield, are found to be in good agreement with experiment [fr

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

NARCIS (Netherlands)

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

2016-01-01

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

A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations

International Nuclear Information System (INIS)

Ma Wenxiu; Xu Xixiang

2004-01-01

Starting from a modified Toda spectral problem, a hierarchy of generalized Toda lattice equations with two arbitrary constants is constructed through discrete zero curvature equations. It is shown that the hierarchy possesses a bi-Hamiltonian structure and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals. Two cases of the involved constants present two specific integrable sub-hierarchies, one of which is exactly the Toda lattice hierarchy

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

Science.gov (United States)

Házi, Gábor; Márkus, Attila

2008-02-01

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

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

Science.gov (United States)

Somogyi, Andy; Tagg, Randall

2007-11-01

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

Boundary Slip and Surface Interaction: A Lattice Boltzmann Simulation

International Nuclear Information System (INIS)

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

2008-01-01

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

Lattice Boltzmann Simulation of Multiple Bubbles Motion under Gravity

Directory of Open Access Journals (Sweden)

Deming Nie

2015-01-01

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

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

Science.gov (United States)

Habilomatis, George; Chaloulakou, Archontoula

2013-10-01

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

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

Science.gov (United States)

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.

Nonlinear Boltzmann equation for the homogeneous isotropic case: Minimal deterministic Matlab program

Science.gov (United States)

Asinari, Pietro

2010-10-01

The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains extremely challenging from the computational point of view, in particular by deterministic methods (free of stochastic noise). This work aims to improve a deterministic direct method recently proposed [V.V. Aristov, Kluwer Academic Publishers, 2001] for solving the HIBE with a generic collisional kernel and, in particular, for taking care of the late dynamics of the relaxation towards the equilibrium. Essentially (a) the original problem is reformulated in terms of particle kinetic energy (exact particle number and energy conservation during microscopic collisions) and (b) the computation of the relaxation rates is improved by the DVM-like correction, where DVM stands for Discrete Velocity Model (ensuring that the macroscopic conservation laws are exactly satisfied). Both these corrections make possible to derive very accurate reference solutions for this test case. Moreover this work aims to distribute an open-source program (called HOMISBOLTZ), which can be redistributed and/or modified for dealing with different applications, under the terms of the GNU General Public License. The program has been purposely designed in order to be minimal, not only with regards to the reduced number of lines (less than 1000), but also with regards to the coding style (as simple as possible). Program summaryProgram title: HOMISBOLTZ Catalogue identifier: AEGN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 23 340 No. of bytes in distributed program, including test data, etc.: 7 635 236 Distribution format: tar

Lattice Boltzmann Simulation Optimization on Leading Multicore Platforms

Energy Technology Data Exchange (ETDEWEB)

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

2008-02-01

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

Lattice Boltzmann simulation optimization on leading multicore platforms

Energy Technology Data Exchange (ETDEWEB)

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

2008-01-01

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

Effective Wettability of Heterogenous Fracture Surfaces Using the Lattice-Boltzmann Method

Science.gov (United States)

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.

Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

OpenAIRE

Wu, Lei

2014-01-01

We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

Simulation of Thermal Flow Problems via a Hybrid Immersed Boundary-Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

J. Wu

2012-01-01

Full Text Available A hybrid immersed boundary-lattice Boltzmann method (IB-LBM is presented in this work to simulate the thermal flow problems. In current approach, the flow field is resolved by using our recently developed boundary condition-enforced IB-LBM (Wu and Shu, (2009. The nonslip boundary condition on the solid boundary is enforced in simulation. At the same time, to capture the temperature development, the conventional energy equation is resolved. To model the effect of immersed boundary on temperature field, the heat source term is introduced. Different from previous studies, the heat source term is set as unknown rather than predetermined. Inspired by the idea in (Wu and Shu, (2009, the unknown is calculated in such a way that the temperature at the boundary interpolated from the corrected temperature field accurately satisfies the thermal boundary condition. In addition, based on the resolved temperature correction, an efficient way to compute the local and average Nusselt numbers is also proposed in this work. As compared with traditional implementation, no approximation for temperature gradients is required. To validate the present method, the numerical simulations of forced convection are carried out. The obtained results show good agreement with data in the literature.

Generalized Stefan-Boltzmann Law

Science.gov (United States)

Montambaux, Gilles

2018-03-01

We reconsider the thermodynamic derivation by L. Boltzmann of the Stefan law and we generalize it for various different physical systems whose chemical potential vanishes. Being only based on classical arguments, therefore independent of the quantum statistics, this derivation applies as well to the saturated Bose gas in various geometries as to "compensated" Fermi gas near a neutrality point, such as a gas of Weyl Fermions. It unifies in the same framework the thermodynamics of many different bosonic or fermionic non-interacting gases which were until now described in completely different contexts.

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

OpenAIRE

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

2016-01-01

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

BCS @ 50: derivation of gap equations in different lattice geometries

International Nuclear Information System (INIS)

Saurabh Basu

2007-07-01

We rigorously derive BCS gap equations for a square, triangular and a honeycomb lattice using a two-dimensional t-J model. The gap equations in all the three lattice geometries look usual, with band indices appearing and a minor modification in the separable pair potential for the (two band) honeycomb lattice. In each case, the gap equation is solved (self consistently with the number equation) at low densities assuming singlet pairing. (author)

A Greenian approach to the solution of the Schroedinger equation for periodic lattice potentials

International Nuclear Information System (INIS)

Minelli, T.A.

1976-01-01

A modified structural Green's function (MSGF), exploiting all the information contained in the previously solved Schroedinger equation for the electron interacting with a single lattice site, has been introduced and used in order to obtain, from a Dyson-type equation, a kernel whose poles and residues give the E-vs.-k relation and, respectively, the Bloch functions. Such a formulation suggests an alternative technique for the approximate solution of the KKR equations. The MSGF formalism has been also used in order to determine the structure constants of a one-dimensional lattice in a general representation

A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

Energy Technology Data Exchange (ETDEWEB)

Liu, Chang, E-mail: cliuaa@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Sun, Quanhua, E-mail: qsun@imech.ac.cn [State Key Laboratory of High-temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuan Xi Rd, Beijing 100190 (China); Cai, Qingdong, E-mail: caiqd@mech.pku.edu.cn [Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871 (China)

2016-06-01

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

Science.gov (United States)

Chu, Weiqi; Li, Xiantao

2018-01-01

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori-Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.

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

International Nuclear Information System (INIS)

Zhang, J.; Kwok, D.Y.

2004-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-06-15

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

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

International Nuclear Information System (INIS)

Fakhari, Abbas; Geier, Martin; Lee, Taehun

2016-01-01

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

Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

Science.gov (United States)

Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo

2009-10-01

In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.

Baecklund transformations for integrable lattice equations

International Nuclear Information System (INIS)

Atkinson, James

2008-01-01

We give new Baecklund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of two other kinds. Specifically, it is found that some equations admit additional auto-BTs (with Baecklund parameter), whilst some pairs of apparently distinct equations admit a BT which connects them

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

Science.gov (United States)

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.

Science.gov (United States)

Wang, Nuo; Zhou, Shenggao; Kekenes-Huskey, Peter M; Li, Bo; McCammon, J Andrew

2014-12-26

Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.

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

International Nuclear Information System (INIS)

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

2007-01-01

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

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

International Nuclear Information System (INIS)

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

2007-01-01

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

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

Directory of Open Access Journals (Sweden)

Li-Zhong Huang

2013-01-01

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

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

Science.gov (United States)

Mawson, Mark J.; Revell, Alistair J.

2014-10-01

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

Inelastic Quantum Transport in Superlattices: Success and Failure of the Boltzmann Equation

DEFF Research Database (Denmark)

Wacker, Andreas; Jauho, Antti-Pekka; Rott, Stephan

1999-01-01

the whole held range from linear response to negative differential conductivity. The quantum results are compared with the respective results obtained from a Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the limits of validity for the semiclassical theory in a nonlinear transport...

Numerical simulation of jet breakup behavior by the lattice Boltzmann method

International Nuclear Information System (INIS)

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

2015-01-01

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

Lattice Boltzmann model for free-surface flow and its application to filling process in casting

CERN Document Server

Ginzburg, I

2003-01-01

A generalized lattice Boltzmann model to simulate free-surface is constructed in both two and three dimensions. The proposed model satisfies the interfacial boundary conditions accurately. A distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid. To maintain a sharp interfacial front, the method includes an anti-diffusion algorithm. The unknown distribution functions at the interfacial region are constructed according to the first-order Chapman-Enskog analysis. The interfacial boundary conditions are satisfied exactly by the coefficients in the Chapman-Enskog expansion. The distribution functions are naturally expressed in the local interfacial coordinates. The macroscopic quantities at the interface are extracted from the least-square solutions of a locally linearized system obtained from the known distribution functions. The proposed method does not require any geometric front construction and is robust for any interfacial ...

Generalized multivariate Fokker-Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

International Nuclear Information System (INIS)

Frank, T.D.

2002-01-01

We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions

Recursive integral equations with positive kernel for lattice calculations

International Nuclear Information System (INIS)

Illuminati, F.; Isopi, M.

1990-11-01

A Kirkwood-Salzburg integral equation, with positive defined kernel, for the states of lattice models of statistical mechanics and quantum field theory is derived. The equation is defined in the thermodynamic limit, and its iterative solution is convergent. Moreover, positivity leads to an exact a priori bound on the iteration. The equation's relevance as a reliable algorithm for lattice calculations is therefore suggested, and it is illustrated with a simple application. It should provide a viable alternative to Monte Carlo methods for models of statistical mechanics and lattice gauge theories. 10 refs

New Monte Carlo approach to the adjoint Boltzmann equation

International Nuclear Information System (INIS)

De Matteis, A.; Simonini, R.

1978-01-01

A class of stochastic models for the Monte Carlo integration of the adjoint neutron transport equation is described. Some current general methods are brought within this class, thus preparing the ground for subsequent comparisons. Monte Carlo integration of the adjoint Boltzmann equation can be seen as a simulation of the transport of mathematical particles with reaction kernels not normalized to unity. This last feature is a source of difficulty: It can influence the variance of the result negatively and also often leads to preparation of special ''libraries'' consisting of tables of normalization factors as functions of energy, presently used by several methods. These are the two main points that are discussed and that are taken into account to devise a nonmultigroup method of solution for a certain class of problems. Reactions considered in detail are radiative capture, elastic scattering, discrete levels and continuum inelastic scattering, for which the need for tables has been almost completely eliminated. The basic policy pursued to avoid a source of statistical fluctuations is to try to make the statistical weight of the traveling particle dependent only on its starting and current energies, at least in simple cases. The effectiveness of the sampling schemes proposed is supported by numerical comparison with other more general adjoint Monte Carlo methods. Computation of neutron flux at a point by means of an adjoint formulation is the problem taken as a test for numerical experiments. Very good results have been obtained in the difficult case of resonant cross sections

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

Science.gov (United States)

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

2018-03-01

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

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

International Nuclear Information System (INIS)

Leznov, A.N.

1982-01-01

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

Lattice Boltzmann simulation on the liquid junction potential in a concentration fuel cell. Paper no. IGEC-1-060

International Nuclear Information System (INIS)

Park, J.; Huh, K.Y.; Li, X.

2005-01-01

The lattice Boltzmann method (LBM) is applied to investigate the liquid junction potential (LJP) at an interface between two electrolyte layers. The Poisson equation for electrostatic field is solved to extend the applicable range to micro and nano scales in which electroneutrality does not hold. The LBM solutions are validated against analytical and finite difference method (FDM) results for evolution of concentration, net charge density and electrostatic potential. Noticeable separation of the concentration profiles of positive and negative ions occurs for kd less than 67 in simulation, where k is the inverse of the thickness of electrical double layer and d is the system length. Parametric study is performed for the peak potential and the time to reach the peak with respect to kd and ξ which is the initial thickness ratio of the lower concentration to entire stream. Simple coding and easy parallelization will allow the LBM to make an efficient analysis tool for complex electrochemical systems. (author)

Calculating lattice thermal conductivity: a synopsis

Science.gov (United States)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-01-15

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

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

Directory of Open Access Journals (Sweden)

Niya Ma

2018-02-01

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

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

KAUST Repository

Li, Jun

2013-01-01

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

Lattice gas methods for predicting intrinsic permeability of porous media

Energy Technology Data Exchange (ETDEWEB)

Santos, L.O.E.; Philippi, P.C. [Santa Catarina Univ., Florianopolis, SC (Brazil). Dept. de Engenharia Mecanica. Lab. de Propriedades Termofisicas e Meios Porosos)]. E-mail: emerich@lmpt.ufsc.br; philippi@lmpt.ufsc.br; Damiani, M.C. [Engineering Simulation and Scientific Software (ESSS), Florianopolis, SC (Brazil). Parque Tecnologico]. E-mail: damiani@lmpt.ufsc.br

2000-07-01

This paper presents a method for predicting intrinsic permeability of porous media based on Lattice Gas Cellular Automata methods. Two methods are presented. The first is based on a Boolean model (LGA). The second is Boltzmann method (LB) based on Boltzmann relaxation equation. LGA is a relatively recent method developed to perform hydrodynamic calculations. The method, in its simplest form, consists of a regular lattice populated with particles that hop from site to site in discrete time steps in a process, called propagation. After propagation, the particles in each site interact with each other in a process called collision, in which the number of particles and momentum are conserved. An exclusion principle is imposed in order to achieve better computational efficiency. In despite of its simplicity, this model evolves in agreement with Navier-Stokes equation for low Mach numbers. LB methods were recently developed for the numerical integration of the Navier-Stokes equation based on discrete Boltzmann transport equation. Derived from LGA, LB is a powerful alternative to the standard methods in computational fluid dynamics. In recent years, it has received much attention and has been used in several applications like simulations of flows through porous media, turbulent flows and multiphase flows. It is important to emphasize some aspects that make Lattice Gas Cellular Automata methods very attractive for simulating flows through porous media. In fact, boundary conditions in flows through complex geometry structures are very easy to describe in simulations using these methods. In LGA methods simulations are performed with integers needing less resident memory capability and boolean arithmetic reduces running time. The two methods are used to simulate flows through several Brazilian reservoir petroleum rocks leading to intrinsic permeability prediction. Simulation is compared with experimental results. (author)

General particle transport equation. Final report

International Nuclear Information System (INIS)

Lafi, A.Y.; Reyes, J.N. Jr.

1994-12-01

The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

Science.gov (United States)

Farhat, Hassan

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

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

OpenAIRE

Corre , Samuel; Belmiloudi , Aziz

2016-01-01

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

Electron kinetics with attachment and ionization from higher order solutions of Boltzmann's equation

International Nuclear Information System (INIS)

Winkler, R.; Wilhelm, J.; Braglia, G.L.

1989-01-01

An appropriate approach is presented for solving the Boltzmann equation for electron swarms and nonstationary weakly ionized plasmas in the hydrodynamic stage, including ionization and attachment processes. Using a Legendre-polynomial expansion of the electron velocity distribution function the resulting eigenvalue problem has been solved at any even truncation-order. The technique has been used to study velocity distribution, mean collision frequencies, energy transfer rates, nonstationary behaviour and power balance in hydrodynamic stage, of electrons in a model plasma and a plasma of pure SF 6 . The calculations have been performed for increasing approximation-orders, up to the converged solution of the problem. In particular, the transition from dominant attachment to prevailing ionization when increasing the field strength has been studied. Finally the establishment of the hydrodynamic stage for a selected case in the model plasma has been investigated by solving the nonstationary, spatially homogeneous Boltzmann equation in twoterm approximation. (author)

Lattice Boltzmann simulation for the energy and entropy of excitable systems

Institute of Scientific and Technical Information of China (English)

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

2011-01-01

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

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

Science.gov (United States)

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

2012-04-01

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

Solution of the non-stationary electron Boltzmann equation for a weakly ionized collision dominated plasma

International Nuclear Information System (INIS)

Winkler, R.; Wilhelm, J.

A detailed description is presented of calculating the nonstationary electron distribution function in a weakly ionized collision-dominated plasma from the Boltzmann kinetic equation respecting the effects of the time-dependent electric field, collision processes and the electron formation and loss. The finite difference approximation was used for numerical solution. Using the Crank-Nicolson method and parabolic interpolation between the grid points the Boltzmann equation was transformed to a system of linear equations which was then solved by iterations at a preset accuracy. Using the calculated distribution function values, the macroscopic plasma parameters were determined and the balance of electron density and energy checked in each time step. The mathematical procedure is illustrated using a neon plasma perturbed by a rectangular electric pulse. The time development shown of the distribution function at moments when the pulse was switched on and off demonstrates the great stability of the numerical solution. (J.U.)

Generalized boundary conditions in an existence and uniqueness proof for the solution of the non-stationary electron Boltzmann equation by means of operator-semigroups

International Nuclear Information System (INIS)

Bartolomaeus, G.; Wilhelm, J.

1983-01-01

Recently, based on the semigroup approach a new proof was presented of the existence of a unique solution of the non-stationary Boltzmann equation for the electron component of a collision dominated plasma. The proof underlies some restriction which should be overcome to extend the validity range to other problems of physical interest. One of the restrictions is the boundary condition applied. The choice of the boundary condition is essential for the proof because it determines the range of definition of the infinitesimal generator and thus the operator semigroup itself. The paper proves the existence of a unique solution for generalized boundary conditions, this solution takes non-negative values, which is necessary for a distribution function from the physical point of view. (author)

Nonaligned shocks for discrete velocity models of the Boltzmann equation

Directory of Open Access Journals (Sweden)

J. M. Greenberg

1991-05-01

Full Text Available At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions, Greenberg asked whether such solutions were possible in directions e(α=(cosα ,sinα when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α=(cosα ,sinα.

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

Science.gov (United States)

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

2018-02-20

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

From Lattice Boltzmann to hydrodynamics in dissipative relativistic fluids

Science.gov (United States)

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

2017-11-01

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

From Newton's Law to the Linear Boltzmann Equation Without Cut-Off

Science.gov (United States)

Ayi, Nathalie

2017-03-01

We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. More particularly, we will describe the motion of a tagged particle in a gas close to global equilibrium. The main difficulty in our context is that, due to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford's strategy. Our proof relies then on a combination of Lanford's strategy, of tools developed recently by Bodineau, Gallagher and Saint-Raymond to study the collision process, and of new duality arguments to study the additional terms associated with the long-range interaction, leading to some explicit weak estimates.

Intensity-interferometric test of nuclear collision geometries obtained from the Boltzmann-Uehling-Uhlenbeck equation

International Nuclear Information System (INIS)

Gong, W.G.; Bauer, W.; Gelbke, C.K.; Carlin, N.; de Souza, R.T.; Kim, Y.D.; Lynch, W.G.; Murakami, T.; Poggi, G.; Sanderson, D.P.; Tsang, M.B.; Xu, H.M.; Pratt, S.; Fields, D.E.; Kwiatkowski, K.; Planeta, R.; Viola, V.E. Jr.; Yennello, S.J.

1990-01-01

Two-proton correlation functions measured for the 14 N+ 27 Al reaction at E/A=75 MeV are compared to correlation functions predicted for collision geometries obtained from numerical solutions of the Boltzmann-Uehling-Uhlenbeck (BUU) equation. The calculations are in rather good agreement with the experimental correlation function, indicating that the BUU equation gives a reasonable description of the space-time evolution of the reaction

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

Science.gov (United States)

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

2017-12-01

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

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

International Nuclear Information System (INIS)

Eshghinejadfard, A.; Thévenin, D.

2016-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-12-18

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

Comparison of Einstein-Boltzmann solvers for testing general relativity

Science.gov (United States)

Bellini, E.; Barreira, A.; Frusciante, N.; Hu, B.; Peirone, S.; Raveri, M.; Zumalacárregui, M.; Avilez-Lopez, A.; Ballardini, M.; Battye, R. A.; Bolliet, B.; Calabrese, E.; Dirian, Y.; Ferreira, P. G.; Finelli, F.; Huang, Z.; Ivanov, M. M.; Lesgourgues, J.; Li, B.; Lima, N. A.; Pace, F.; Paoletti, D.; Sawicki, I.; Silvestri, A.; Skordis, C.; Umiltà, C.; Vernizzi, F.

2018-01-01

We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f (R ) gravity, a code that models covariant Galileons, a code that models Hořava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.

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

Science.gov (United States)

Wang, Zimeng; Shang, Helen; Zhang, Junfeng

2017-06-01

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

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

Science.gov (United States)

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

On some problems related to feasibility of statistical mechanics

International Nuclear Information System (INIS)

Bogolyubov, N.N.; Kazaryan, A.R.; Kurbatov, A.M.

1981-01-01

The principle generalization of the method kinetic Boltzmann equation in the theory of electrons, moving in a crystal and interacting both with lattice vibrations and external electric field, is developed. A scheme of constrUction of the kinetic equation from the accurate evolution one is discussed in the framework of the averaged lattice pulse approximation. A kinetic description of the helical polaron motion is performed on the base of the Boltzmann equation obtained. The above approach permits to generalize The Tornber-Feynman formulae, applied in the transport theory in crystals. The Green function equations are dirived for electron-phonon systems

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

International Nuclear Information System (INIS)

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

2013-01-01

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

Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations

CERN Document Server

Riotto, Antonio

1998-01-01

The closed time-path (CPT) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CPT formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ``memory'' effects which are typical of the quantum transp ort t...

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions

DEFF Research Database (Denmark)

Johannessen, Kim

2014-01-01

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...

Nonequilibrium phenomena in QCD and BEC. Boltzmann and beyond

Energy Technology Data Exchange (ETDEWEB)

Stockamp, T.

2006-12-22

In chapter 2 we chose the real time formalism to discuss some basic principles in quantum field theory at finite temperature. This enables us to derive the quantum Boltzmann equation from the Schwinger-Dyson series. We then shortly introduce the basic concepts of QCD which are needed to understand the physics of QGP formation. After a detailed account on the bottom-up scenario we show the consistency of this approach by a diagramatical analysis of the relevant Boltzmann collision integrals. Chapter 3 deals with BEC dynamics out of equilibrium. After an introduction to the fundamental theoretical tool - namely the Gross-Pitaevskii equation - we focus on a generalization to finite temperature developed by Zaremba, Nikuni and Griffin (ZNG). These authors use a Boltzmann equation to describe the interactions between condensed and excited atoms and manage in this way to describe condensate growth. We then turn to a discussion on the 2PI effective action and derive equations of motion for a relativistic scalar field theory. In the nonrelativistic limit these equations are shown to coincide with the ZNG theory when a quasiparticle approximation is applied. Finally, we perform a numerical analysis of the full 2PI equations. These remain valid even at strong coupling and far from equilibrium, and thus go far beyond Boltzmann's approach. For simplicity, we limit ourselves to a homogeneous system and present the first 3+1 dimensional study of condensate melting. (orig.)

Gas-liquid Relative Permeability Estimation in 2D Porous Media by Lattice Boltzmann Method: Low Viscosity Ratio 2D LBM Relative Permeability

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Sadegh Mahmoudi

2013-04-01

Full Text Available This work is a primary achievement in studying the CO2 and N2–oil systems. To predict gas-liquid relative permeability curves, a Shan-Chen type multicomponent multiphase lattice Boltzmann model for two-phase flow through 2D porous media is developed. Periodic and bounce back boundary conditions are applied to the model with the Guo scheme for the external body force (i.e., the pressure gradient. The influence of relationship between cohesion and adsorption parameters and the interfacial tension values in Young's equation, pore structure (micro scan image derived porous media response is compared with corresponding porosity and permeability ideal sphere pack structure, and saturation distribution on relative permeability curves are studied with the aim to achieve the realistic stable condition for the simulation of gas-liquid systems with a low viscosity ratio.

AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

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Koehl, Patrice; Delarue, Marc

2010-02-14

The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE

Description of the approach to equilibrium in the Boltzmann equation

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Barrachina, R.O.; Fujii, D.H.; Garibotti, C.R.

1985-06-01

An integral transform of the Boltzmann equation with a clear physical interpretation is introduced. It is applied to different interaction models and initial conditions, relevant information about the way the equilibrium is reached. This method leads quite naturally to the introduction of an N-pole approximant of the distribution function which seems to be a rather useful technique not only in view of its simplicity but also because of its capability to keep track of the temporal evolution features of the chosen interaction model. 6 references.

Simulation of natural convection in an inclined polar cavity using a finite-difference lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Yang, Fan; Yang, Haicheng; Guo, Xueyan; Ren Dai [University of Shanghai for Science and Technology, Shanghai (China); Yan, Yonghua [Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai (China); Liu, Chaoqun [University of Texas at Arlington, Arlington (United States)

2017-06-15

Natural convection heat transfer in an inclined polar cavity was studied using a Finite-difference lattice Boltzmann method (FDLBM) based on a double-population approach for body-fitted coordinates. A D2G9 model coupled with the simplest TD2Q4 lattice model was applied to determine the velocity field and temperature field. For both velocity and temperature fields, the discrete spatial derivatives were obtained by combining the upwind scheme with the central scheme, and the discrete temporal term is obtained using a fourth-order Runge-Kutta scheme. Studies were carried out for different Rayleigh numbers and different inclination angles. The results in terms of streamlines, isotherms, and Nusselt numbers explain the heat transfer mechanism of natural convection in an inclined polar cavity due to the change of Rayleigh number and inclination angle.

Modelling and nonlinear shock waves for binary gas mixtures by the discrete Boltzmann equation with multiple collisions

International Nuclear Information System (INIS)

Bianchi, M.P.

1991-01-01

The discrete Boltzmann equation is a mathematical model in the kinetic theory of gases which defines the time and space evolution of a system of gas particles with a finite number of selected velocities. Discrete kinetic theory is an interesting field of research in mathematical physics and applied mathematics for several reasons. One of the relevant fields of application of the discrete Boltzmann equation is the analysis of nonlinear shock wave phenomena. Here, a new multiple collision regular plane model for binary gas mixtures is proposed within the discrete theory of gases and applied to the analysis of the classical problems of shock wave propagation

Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations

International Nuclear Information System (INIS)

Yotsuji, K.; Tachi, Y.; Nishimaki, Y.

2012-01-01

Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na + as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m -3

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

International Nuclear Information System (INIS)

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

2015-01-01

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

Lattice Boltzmann method used to simulate particle motion in a conduit

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Dolanský Jindřich

2017-06-01

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

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

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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.

Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

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Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.

2017-10-01

There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

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Sels, Dries; Brosens, Fons

2013-10-01

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

International Nuclear Information System (INIS)

Farrell, Patricio; Koprucki, Thomas; Fuhrmann, Jürgen

2017-01-01

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter–Gummel scheme to non-Boltzmann (e.g. Fermi–Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

Science.gov (United States)

Farrell, Patricio; Koprucki, Thomas; Fuhrmann, Jürgen

2017-10-01

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter-Gummel scheme to non-Boltzmann (e.g. Fermi-Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

Multiple-Relaxation-Time Lattice Boltzmann Approach to Richtmyer-Meshkov Instability

International Nuclear Information System (INIS)

Chen Feng; Li Yingjun; Xu Aiguo; Zhang Guangcai

2011-01-01

The aims of the present paper are twofold. At first, we further study the Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) model proposed in [Europhys. Lett. 90 (2010) 54003]. We discuss the reason why the Gram-Schmidt orthogonalization procedure is not needed in the construction of transformation matrix M; point out a reason why the Kataoka-Tsutahara model [Phys. Rev. E 69 (2004) 035701 (R)] is only valid in subsonic flows. The von Neumann stability analysis is performed. Secondly, we carry out a preliminary quantitative study on the Richtmyer-Meshkov instability using the proposed MRT LB model. When a shock wave travels from a light medium to a heavy one, the simulated growth rate is in qualitative agreement with the perturbation model by Zhang-Sohn. It is about half of the predicted value by the impulsive model and is closer to the experimental result. When the shock wave travels from a heavy medium to a light one, our simulation results are also consistent with physical analysis. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Axisymmetric Lattice Boltzmann Model of Droplet Impact on Solid Surfaces

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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.

Modified momentum exchange method for fluid-particle interactions in the lattice Boltzmann method.

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

2015-03-01

In this paper, a modified momentum exchange method for fluid-particle interactions is proposed based on the finite-volume lattice Boltzmann method. The idea of the improvement is to remove the restriction that the boundary points must be set as the midpoints of the grid lines or the intersection of the grid lines with the solid boundaries. The particle surface is represented by a set of arc (area) elements, and the interior fluid is used which the geometric conservation law is naturally satisfied. The interactions between fluid and arc (area) elements of particle boundary are considered using the momentum exchange method, and the mass of the fluid particles which collide with an arc (area) element is obtained by means of numerical integration in the control volume. The fluid field is corrected with the help of the smooth kernel function. Moreover, a generalized explicit time marching scheme is introduced to resolve the motion of particle in the problems with the ratio of particle density to fluid density is close to or less than 1. Finally, some numerical case studies of particle sedimentation are carried out to validate the present method. The corresponding results have a good agreement with the previous literature, which strongly demonstrates the capability of the improved method.

Ludwig Boltzmann - pioneer of atomistics and evolution

International Nuclear Information System (INIS)

Stiller, W.

1986-01-01

At first a short introduction to Ludwig Boltzmann's life (1844 - 1906) and work is given. Some theoretical results of his work (H-theorem, classical Boltzmann statistics, Boltzmann's kinetic equation) are treated in detail. His experimental work is briefly discussed. In addition Boltzmann's philosophical work is characterized. Finally, the influence of Boltzmann's ideas on our time is investigated. (author)

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

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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.

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

Science.gov (United States)

Succi, Sauro

Over the last three decades, the Lattice Boltzmann (LB) method has gained a prominent role in the numerical simulation of complex flows across an impressively broad range of scales, from fully-developed turbulence in real-life geometries, to multiphase flows in micro-fluidic devices, all the way down to biopolymer translocation in nanopores and lately, even quark-gluon plasmas. After a brief introduction to the main ideas behind the LB method and its historical developments, we shall present a few selected applications to complex flow problems at various scales of motion. Finally, we shall discuss prospects for extreme-scale LB simulations of outstanding problems in the physics of fluids and its interfaces with material sciences and biology, such as the modelling of fluid turbulence, the optimal design of nanoporous gold catalysts and protein folding/aggregation in crowded environments.

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-06-15

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

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

International Nuclear Information System (INIS)

Suga, K

2013-01-01

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

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

Science.gov (United States)

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

2018-04-01

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

Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — The research proposed targets airframe noise (AFN) prediction and reduction. AFN originates from complex interactions of turbulent flow with airframe components that...

Phase-field-lattice Boltzmann study for lamellar eutectic growth in a natural convection melt

Directory of Open Access Journals (Sweden)

Ang Zhang

2017-11-01

Full Text Available In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions.

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