Hickey, Owen A; Holm, Christian; Smiatek, Jens
2014-04-28
In this article we examine the electrophoretic stretching of polyelectrolytes between parallel uncharged plates using molecular dynamics simulations. We compare simulations where the fluid is modeled implicitly using a Langevin thermostat, which ignore hydrodynamic interactions, to simulations with an explicit lattice-Boltzmann fluid that take hydrodynamic interactions into account. The difference between simulations with and without hydrodynamic interactions is larger for longer polyelectrolytes, as one would expect. Furthermore, we present simulation results which show that the effects of hydrodynamic interactions are reduced as the distance between the confining plates is diminished. The main result of our study is that hydrodynamic interactions play a larger role in systems with a shorter Debye length, in contrast to conventional wisdom.
Hydrodynamic Force Evaluation by Momentum Exchange Method in Lattice Boltzmann Simulations
Directory of Open Access Journals (Sweden)
Binghai Wen
2015-12-01
Full Text Available As a native scheme to evaluate hydrodynamic force in the lattice Boltzmann method, the momentum exchange method has some excellent features, such as simplicity, accuracy, high efficiency and easy parallelization. Especially, it is independent of boundary geometry, preventing from solving the Navier–Stokes equations on complex boundary geometries in the boundary-integral methods. We review the origination and main developments of the momentum exchange method in lattice Boltzmann simulations. Then several practical techniques to fill newborn fluid nodes are discussed for the simulations of fluid-structure interactions. Finally, some representative applications show the wide applicability of the momentum exchange method, such as movements of rigid particles, interactions of deformation particles, particle suspensions in turbulent flow and multiphase flow, etc.
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 of so...
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.
Lattice Boltzmann approach for complex nonequilibrium flows.
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.
Halliday, I.; Lishchuk, S. V.; Spencer, T. J.; Burgin, K.; Schenkel, T.
2017-10-01
We describe, analyse and reduce micro-current effects in one class of lattice Boltzmann equation simulation method describing immiscible fluids within the continuum approximation, due to Lishchuk et al. (2003). This model's micro-current flow field and associated density adjustment, when considered in the linear, low-Reynolds number regime, may be decomposed into independent, superposable contributions arising from various error terms in its immersed boundary force. Error force contributions which are rotational (solenoidal) are mainly responsible for the micro-current (corresponding density adjustment). Rotationally anisotropic error terms arise from numerical derivatives and from the sampling of the interface-supporting force. They may be removed, either by eliminating the causal error force or by negating it. It is found to be straightforward to design more effective stencils with significantly improved performance. Practically, the micro-current activity arising in Lishchuk's method is reduced by approximately three quarters by using an appropriate stencil and approximately by an order of magnitude when the effects of sampling are removed.
A hydrodynamically-consistent MRT lattice Boltzmann model on a 2D rectangular grid
Peng, Cheng; Min, Haoda; Guo, Zhaoli; Wang, Lian-Ping
2016-12-01
A multiple-relaxation time (MRT) lattice Boltzmann (LB) model on a D2Q9 rectangular grid is designed theoretically and validated numerically in the present work. By introducing stress components into the equilibrium moments, this MRT-LB model restores the isotropy of diffusive momentum transport at the macroscopic level (or in the continuum limit), leading to moment equations that are fully consistent with the Navier-Stokes equations. The model is derived by an inverse design process which is described in detail. Except one moment associated with the energy square, all other eight equilibrium moments can be theoretically and uniquely determined. The model is then carefully validated using both the two-dimensional decaying Taylor-Green vortex flow and lid-driven cavity flow, with different grid aspect ratios. The corresponding results from an earlier model (Bouzidi et al. (2001) [28]) are also presented for comparison. The results of Bouzidi et al.'s model show problems associated with anisotropy of viscosity coefficients, while the present model exhibits full isotropy and is accurate and stable.
Lattices for the lattice Boltzmann method.
Chikatamarla, Shyam S; Karlin, Iliya V
2009-04-01
A recently introduced theory of higher-order lattice Boltzmann models [Chikatamarla and Karlin, Phys. Rev. Lett. 97, 190601 (2006)] is elaborated in detail. A general theory of the construction of lattice Boltzmann models as an approximation to the Boltzmann equation is presented. New lattices are found in all three dimensions and are classified according to their accuracy (degree of approximation of the Boltzmann equation). The numerical stability of these lattices is argued based on the entropy principle. The efficiency and accuracy of many new lattices are demonstrated via simulations in all three dimensions.
Entropic Lattice Boltzmann study of hydrodynamics in a microcavity - Part 1
Energy Technology Data Exchange (ETDEWEB)
Karlin, I. V.; Ansumali, S.; Frouzakis, Ch. E.; Boulouchos, K. [Eidgenoessische Technische Hochschule (ETH), Labor fuer Aerothermochemie und Verbrennungssysteme ETHZ, ETH-Zentrum, Zuerich (Switzerland)
2005-07-01
This yearly report for 2004 presents a review of work being done on behalf of the Swiss Federal Office of Energy (SFOE) at the Laboratory for Aero-thermochemistry and Combustion Systems at the Federal Institute of Technology ETH in Zurich, Switzerland, on the development of a new approximation method for use in micrometer-scale flow calculations. The method, based on recently-developed so-called minimal entropy-kinetic models of the Boltzmann-kinetic equation, is discussed. Two detailed studies of micro-flows in specific geometries are discussed. The potential of the new method as a replacement for costly microscopic simulation methods is examined. The development and testing of a new thermal model - the so-called Thermal D2Q9 model - is discussed. A second study examined flows in a micro-cavity. A detailed parametric study of the quantitative and qualitative properties of the flows for a comprehensive range of dilution is mentioned.
Essentially Entropic Lattice Boltzmann Model
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.
Entropy and Galilean invariance of lattice Boltzmann theories.
Chikatamarla, Shyam S; Karlin, Iliya V
2006-11-10
A theory of lattice Boltzmann (LB) models for hydrodynamic simulation is developed upon a novel relation between entropy construction and roots of Hermite polynomials. A systematic procedure is described for constructing numerically stable and complete Galilean invariant LB models. The stability of the new LB models is illustrated with a shock tube simulation.
Thermal cascaded lattice Boltzmann method
Fei, Linlin
2016-01-01
In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach. A density distribution function relaxed by the cascaded scheme is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve temperature field, where two distribution functions are coupled naturally. The forcing terms are incorporated by means of central moments, which is consistent with the previous force scheme [Premnath \\emph{et al.}, Phys. Rev. E \\textbf{80}, 036702 (2009)] but the derivation is more intelligible and the evolution process is simpler. In the method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, the external force is considered directly without the Boussinesq assumption, and the low-Mach number compressible flows can also be simulated. The forcing scheme is tested by simulating a steady Taylor-Green f...
Fractal and prefractal geometric models have substantial potential of contributing to the analysis of flow and transport in porous media such as soils and reservoir rocks. In this study, geometric and hydrodynamic parameters of saturated 3D mass and pore-solid prefractal porous media were characteri...
Lattice Boltzmann model for incompressible axisymmetric flows.
Chen, Sheng; Tölke, Jonas; Geller, Sebastian; Krafczyk, Manfred
2008-10-01
A lattice Boltzmann model for incompressible axisymmetric flow is proposed in this paper. Unlike previous axisymmetric lattice Boltzmann models, which were based on "primitive-variables" Navier-Stokes equations, the target macroscopic equations of the present model are vorticity-stream-function formulations. Due to the intrinsic features of vorticity-stream-function formulations, the present model is more efficient, more stable, and much simpler than the existing models. The advantages of the present model are validated by numerical experiments.
Lattice Boltzmann algorithm for continuum multicomponent flow
Halliday, I.; Hollis, A. P.; Care, C. M.
2007-08-01
We present a multicomponent lattice Boltzmann simulation for continuum fluid mechanics, paying particular attention to the component segregation part of the underlying algorithm. In the principal result of this paper, the dynamics of a component index, or phase field, is obtained for a segregation method after U. D’Ortona [Phys. Rev. E 51, 3718 (1995)], due to Latva-Kokko and Rothman [Phys. Rev. E 71 056702 (2005)]. The said dynamics accord with a simulation designed to address multicomponent flow in the continuum approximation and underwrite improved simulation performance in two main ways: (i) by reducing the interfacial microcurrent activity considerably and (ii) by facilitating simulational access to regimes of flow with a low capillary number and drop Reynolds number [I. Halliday, R. Law, C. M. Care, and A. Hollis, Phys. Rev. E 73, 056708 (2006)]. The component segregation method studied, used in conjunction with Lishchuk’s method [S. V. Lishchuk, C. M. Care, and I. Halliday, Phys. Rev. E 67, 036701 (2003)], produces an interface, which is distributed in terms of its component index; however, the hydrodynamic boundary conditions which emerge are shown to support the notion of a sharp, unstructured, continuum interface.
Convection-diffusion lattice Boltzmann scheme for irregular lattices
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
Lattice gas cellular automata and lattice Boltzmann models an introduction
Wolf-Gladrow, Dieter A
2000-01-01
Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
Multispeed models in off-lattice Boltzmann simulations
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.
Moving charged particles in lattice Boltzmann-based electrokinetics
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.
Generalized hydrodynamic transport in lattice-gas automata
Luo, Li-Shi; Chen, Hudong; Chen, Shiyi; Doolen, Gary D.; Lee, Yee-Chun
1991-01-01
The generalized hydrodynamics of two-dimensional lattice-gas automata is solved analytically in the linearized Boltzmann approximation. The dependence of the transport coefficients (kinematic viscosity, bulk viscosity, and sound speed) upon wave number k is obtained analytically. Anisotropy of these coefficients due to the lattice symmetry is studied for the entire range of wave number, k. Boundary effects due to a finite mean free path (Knudsen layer) are analyzed, and accurate comparisons are made with lattice-gas simulations.
Lattice-Boltzmann simulations of droplet evaporation
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
Convergence of Convective-Diffusive Lattice Boltzmann Methods
Elton, B H; Levermore, C D; Elton, Bracy H.; Rodrigue, Garry H.
1993-01-01
Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence, consistency, and stability are defined through truncated Hilbert expansions. In this setting it is shown that consistency and stability imply convergence. Monotone lattice Boltzmann methods are defined and shown to be stable, hence convergent when consistent. Examples of diffusive and convective-diffusive lattice Boltzmann methods that are both consistent and monotone are presented.
Lattice Boltzmann model for numerical relativity.
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.
Lattice Boltzmann simulations of genuinely multidimensional rarefied flows in microchannels
Dellar, Paul; Reis, Tim
2012-11-01
We present lattice Boltzmann simulations of rarefied slip flows driven by applied pressure differences across microchannels of finite length. We correctly capture the nonlinear streamwise pressure variation and the cross-channel velocity component, as well as the streamwise velocity and volume flux. The former effects are both absent from almost all previous work that approximated the pressure difference using a uniform body force. We demonstrate second-order convergence of both velocity components towards the asymptotic solution for long microchannels, and slower convergence of the pressure. We use the standard lattice Boltzmann formulation that reduces to a second-order recurrence relation for the streamwise velocity in uniform shear, and whose analytical solution gives a parabolic profile from wall to wall. We therefore cannot capture Knudsen boundary layers, but instead implement Maxwell-Navier slip boundary conditions directly on the hydrodynamic moments of our discrete velocity model. Our only parameter is the tangential momentum accommodation coefficient, so we require no fitting to known solutions. Our moment-based approach shows that existing boundary conditions impose conditions on higher non-hydrodynamic moments rather than on the tangential fluid velocity itself. Supported by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST) and by EPSRC grant EP/E054625/1.
Immersed boundary lattice Boltzmann model based on multiple relaxation times
Lu, Jianhua; Han, Haifeng; Shi, Baochang; Guo, Zhaoli
2012-01-01
As an alterative version of the lattice Boltzmann models, the multiple relaxation time (MRT) lattice Boltzmann model introduces much less numerical boundary slip than the single relaxation time (SRT) lattice Boltzmann model if some special relationship between the relaxation time parameters is chosen. On the other hand, most current versions of the immersed boundary lattice Boltzmann method, which was first introduced by Feng and improved by many other authors, suffer from numerical boundary slip as has been investigated by Le and Zhang. To reduce such a numerical boundary slip, an immerse boundary lattice Boltzmann model based on multiple relaxation times is proposed in this paper. A special formula is given between two relaxation time parameters in the model. A rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single-relaxation-time-based model.
Adaptive filtering for the lattice Boltzmann method
Marié, Simon; Gloerfelt, Xavier
2017-03-01
In this study, a new selective filtering technique is proposed for the Lattice Boltzmann Method. This technique is based on an adaptive implementation of the selective filter coefficient σ. The proposed model makes the latter coefficient dependent on the shear stress in order to restrict the use of the spatial filtering technique in sheared stress region where numerical instabilities may occur. Different parameters are tested on 2D test-cases sensitive to numerical stability and on a 3D decaying Taylor-Green vortex. The results are compared to the classical static filtering technique and to the use of a standard subgrid-scale model and give significant improvements in particular for low-order filter consistent with the LBM stencil.
The Lattice Boltzmann method principles and practice
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...
Multiple-Relaxation-Time Lattice Boltzmann Models in 3D
dHumieres, Dominique; Ginzburg, Irina; Krafczyk, Manfred; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
This article provides a concise exposition of the multiple-relaxation-time lattice Boltzmann equation, with examples of fifteen-velocity and nineteen-velocity models in three dimensions. Simulation of a diagonally lid-driven cavity flow in three dimensions at Re=500 and 2000 is performed. The results clearly demonstrate the superior numerical stability of the multiple-relaxation-time lattice Boltzmann equation over the popular lattice Bhatnagar-Gross-Krook equation.
Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation Project
National Aeronautics and Space Administration — The overall objective of the proposed project is to develop a generalized lattice Boltzmann (GLB) approach as a potential computational aeroacoustics (CAA) tool for...
Lattice Boltzmann method fundamentals and engineering applications with computer codes
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.
Extended lattice Boltzmann scheme for droplet combustion.
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.
Two Dimensional Lattice Boltzmann Method for Cavity Flow Simulation
Panjit MUSIK; Krisanadej JAROENSUTASINEE
2004-01-01
This paper presents a simulation of incompressible viscous flow within a two-dimensional square cavity. The objective is to develop a method originated from Lattice Gas (cellular) Automata (LGA), which utilises discrete lattice as well as discrete time and can be parallelised easily. Lattice Boltzmann Method (LBM), known as discrete Lattice kinetics which provide an alternative for solving the Navier–Stokes equations and are generally used for fluid simulation, is chosen for the study. A spec...
Finite-element lattice Boltzmann simulations of contact line dynamics
Matin, Rastin; Krzysztof Misztal, Marek; Hernández-García, Anier; Mathiesen, Joachim
2018-01-01
The lattice Boltzmann method has become one of the standard techniques for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular lattices. Alternative off-lattice Boltzmann schemes exist for both single- and multiphase flows that decouple the velocity discretization from the underlying spatial grid. The current study extends the applicability of these off-lattice methods by introducing a finite element formulation that enables simulating contact line dynamics for partially wetting fluids. This work exemplifies the implementation of the scheme and furthermore presents benchmark experiments that show the scheme reduces spurious currents at the liquid-vapor interface by at least two orders of magnitude compared to a nodal implementation and allows for predicting the equilibrium states accurately in the range of moderate contact angles.
Lattice Boltzmann scheme for diffusion on triangular grids
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
Diffusion on unstructured triangular grids using Lattice Boltzmann
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
Magnetic nanoparticles in fluid environment: combining molecular dynamics and Lattice-Boltzmann
Melenev, Petr
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.
Lattice Boltzmann Large Eddy Simulation Model of MHD
Flint, Christopher
2016-01-01
The work of Ansumali \\textit{et al.}\\cite{Ansumali} is extended to Two Dimensional Magnetohydrodynamic (MHD) turbulence in which energy is cascaded to small spatial scales and thus requires subgrid modeling. Applying large eddy simulation (LES) modeling of the macroscopic fluid equations results in the need to apply ad-hoc closure schemes. LES is applied to a suitable mesoscopic lattice Boltzmann representation from which one can recover the MHD equations in the long wavelength, long time scale Chapman-Enskog limit (i.e., the Knudsen limit). Thus on first performing filter width expansions on the lattice Boltzmann equations followed by the standard small Knudsen expansion on the filtered lattice Boltzmann system results in a closed set of MHD turbulence equations provided we enforce the physical constraint that the subgrid effects first enter the dynamics at the transport time scales. In particular, a multi-time relaxation collision operator is considered for the density distribution function and a single rel...
High-order regularization in lattice-Boltzmann equations
Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.
2017-04-01
A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.
Galilean-invariant lattice-Boltzmann models with H theorem.
Boghosian, Bruce M; Love, Peter J; Coveney, Peter V; Karlin, Iliya V; Succi, Sauro; Yepez, Jeffrey
2003-08-01
We 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. The required H function has the form of the Burg entropy for D=2, and of a Tsallis entropy with q=1-(2/D) for D>2, where D is the number of spatial dimensions. We use this observation to construct a fully explicit, unconditionally stable, Galilean-invariant, lattice-Boltzmann model for the incompressible Navier-Stokes equations, for which attainable Reynolds number is limited only by grid resolution.
Immiscible multicomponent lattice Boltzmann model for fluids with ...
Indian Academy of Sciences (India)
An immiscible multicomponent lattice Boltzmann model is developed for fluids with high relaxation time ratios, which is based on the model proposed by Shan and Chen (SC). In the SC model, ... Ruofan Qiu1 Anlin Wang1. College of Mechanical Engineering, Tongji University, 4800# Cao'an Road, Shanghai 201804, China ...
Lattice Boltzmann simulations of droplet formation during microchannel emulsification
Zwan, van der E.A.; Sman, van der R.G.M.; Schroën, C.G.P.H.; Boom, R.M.
2009-01-01
In this study, we compared microchannel droplet formation in a microfluidics device with a two phase lattice Boltzmann simulation. The droplet formation was found to be qualitatively described, with a slightly smaller droplet in the simulation. This was due to the finite thickness of the interface
Matin, Rastin; Hernandez, Anier; Misztal, Marek; Mathiesen, Joachim
2015-04-01
Many hydrodynamic phenomena ranging from flows at micron scale in porous media, large Reynolds numbers flows, non-Newtonian and multiphase flows have been simulated on computers using the lattice Boltzmann (LB) method. By solving the Lattice Boltzmann Equation on unstructured meshes in three dimensions, we have developed methods to efficiently model the fluid flow in real rock samples. We use this model to study the spatio-temporal statistics of the velocity field inside three-dimensional real geometries and investigate its relation to the, in general, anomalous transport of passive tracers for a wide range of Peclet and Reynolds numbers. We extend this model by free-energy based method, which allows us to simulate binary systems with large-density ratios in a thermodynamically consistent way and track the interface explicitly. In this presentation we will present our recent results on both anomalous transport and multiphase segregation.
Matin, Rastin; Misztal, Marek K.; Hernandez-Garcia, Anier; Mathiesen, Joachim
2015-11-01
Many hydrodynamic phenomena such as flows at micron scale in porous media, large Reynolds numbers flows, non-Newtonian and multiphase flows have been simulated numerically using the lattice Boltzmann method. By solving the Lattice Boltzmann Equation on three-dimensional unstructured meshes, we efficiently model single-phase fluid flow in real rock samples. We use the flow field to estimate the permeability and further investigate the anomalous dispersion of passive tracers in porous media. By extending our single-phase model with a free-energy based method, we are able to simulate binary systems with moderate density ratios in a thermodynamically consistent way. In this presentation we will present our recent results on both anomalous transport and multiphase segregation.
Sman, van der R.G.M.
2014-01-01
In this paper we present a novel numerical scheme for simulating the one-dimensional deformation of hydrogel material due to drying or rehydration. The scheme is based on the versatile Lattice Boltzmann method, which has been extended such that the computational grid (lattice) deforms due to
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
Entropic multirelaxation lattice Boltzmann models for turbulent flows.
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)] 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.
Lattice Boltzmann method with restored Galilean invariance.
Prasianakis, N I; Karlin, I V; Mantzaras, J; Boulouchos, K B
2009-06-01
An isothermal model on the standard two-dimension nine-velocity lattice (D2Q9) is proposed and analyzed. It originates from the thermal model with energy conservation introduced by N. I. Prasianakis and I. V. Karlin [Phys. Rev. E 76, 016702 (2007)]. The isothermal and the thermal equivalent models are tested through the simulation of the decay of a shear wave and of a temperature wave. Both are shown to be Galilean invariant, reference temperature independent, and rotational isotropic through the measurement of the transport coefficients on a rotated moving frame of reference.
Lattice Boltzmann Model for Electronic Structure Simulations
Mendoza, M; Succi, S
2015-01-01
Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a suitable single-particle kinetic equation. By using a discrete version of this new formalism, the exchange and correlation energies of simple atoms and the geometrical configuration of the methane molecule were calculated accurately. Here, we discuss the main ideas behind the lattice kinetic approach to electronic structure computations, offer some considerations for prospective extensions, and also show additional numerical results, namely the geometrical configuration of the water molecule.
Modelling thermal fluctuations in non-ideal fluids with the lattice Boltzmann method.
Gross, M; Adhikari, R; Cates, M E; Varnik, F
2011-06-13
Recently, we proposed a theoretical framework to include thermal fluctuations into the Lattice Boltzmann (LB) method for non-ideal fluids. Here, we apply a variant thereof to a certain class of force-based non-ideal fluid LB models. We find that ideal-gas-like noise is an exact result of the fluctuation-dissipation theorem in the hydrodynamic regime. It is shown that satisfactory equilibration of the density and fluid momentum can be obtained in a simulation over a wide range of length scales.
Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities
Allen, Rebecca
2016-06-29
We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.
Lattice Boltzmann modeling and simulation of liquid jet breakup
Saito, Shimpei; Abe, Yutaka; Koyama, Kazuya
2017-07-01
A three-dimensional color-fluid lattice Boltzmann model for immiscible two-phase flows is developed in the framework of a three-dimensional 27-velocity (D3Q27) lattice. The collision operator comprises the D3Q27 versions of three suboperators: a multiple-relaxation-time (MRT) collision operator, a generalized Liu-Valocchi-Kang perturbation operator, and a Latva-Kokko-Rothman recoloring operator. A D3Q27 version of an enhanced equilibrium distribution function is also incorporated into this model to improve the Galilean invariance. Three types of numerical tests, namely, a static droplet, an oscillating droplet, and the Rayleigh-Taylor instability, show a good agreement with analytical solutions and numerical simulations. Following these numerical tests, this model is applied to liquid-jet-breakup simulations. The simulation conditions are matched to the conditions of the previous experiments. In this case, numerical stability is maintained throughout the simulation, although the kinematic viscosity for the continuous phase is set as low as 1.8 ×10-4 , in which case the corresponding Reynolds number is 3.4 ×103 ; the developed lattice Boltzmann model based on the D3Q27 lattice enables us to perform the simulation with parameters directly matched to the experiments. The jet's liquid column transitions from an asymmetrical to an axisymmetrical shape, and entrainment occurs from the side of the jet. The measured time history of the jet's leading-edge position shows a good agreement with the experiments. Finally, the reproducibility of the regime map for liquid-liquid systems is assessed. The present lattice Boltzmann simulations well reproduce the characteristics of predicted regimes, including varicose breakup, sinuous breakup, and atomization.
Three-dimensional lattice Boltzmann model for compressible flows.
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.
Regulski, Wojciech; Szumbarski, Jacek
2016-01-01
In this paper, the performance of two lattice Boltzmann method formulations for yield-stress (i.e. viscoplastic) fluids has been investigated. The first approach is based on the popular Papanastasiou regularisation of the fluid rheology in conjunction with explicit modification of the lattice Boltzmann relaxation rate. The second approach uses a locally-implicit formulation to simultaneously solve for the fluid stress and the underlying particle distribution functions. After investigating issues related to the lattice symmetry and non-hydrodynamic Burnett stresses, the two models were compared in terms of spatial convergence and their behaviour in transient and inertial flows. The choice of lattice and the presence of Burnett stresses was found to influence the results of both models, however the latter did not significantly degrade the velocity field. Using Bingham flows in ducts and synthetic porous media, it was found that the implicitly-regularised model was superior in capturing transient and inertial fl...
Lattice Boltzmann simulation of flow around a confined circular cyclinder
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Ashrafizaadeh, M.; Zadehgol, A. [Isfahan Univ. of Technology , Mechanical Engineering, Isfahan (Iran, Islamic Republic of)]. E-mail: mahmud@cc.iut.ac.ir
2002-07-01
A two dimensional lattice Boltzmann model (LBM) based on a single time relaxation BGK model has been developed. Several benchmark problems including the Poiseuille flow, the lid driven cavity flow and the flow around a circular cylinder have been performed employing a d2q9 lattice. The laminar flow around a circular cylinder within a channel has been extensively investigated using the present lattice Boltzmann model. Both symmetric and asymmetric placement configurations of the circular cylinder within the channel have been considered. A new treatment for the outlet velocity and pressure (density) boundary conditions has been proposed and validated. The present LBM results are in excellent agreement with those of the other existing CFD results. Careful examination of the LBM results and an appropriate calculation of the lift coefficient based on the rectangular lattice representation of the circular cylinder reveals that the periodic oscillation of the lift coefficient has a second harmonic when the cylinder is placed asymmetrically within the channel. The second harmonic could be associated with an asymmetrical shedding pattern of the vortices behind the cylinder from the upper and lower sides of the cylinder. (author)
Element Free Lattice Boltzmann Method for Fluid-Flow Problems
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.
A dynamic mesh refinement technique for Lattice Boltzmann simulations on octree-like grids
Neumann, Philipp
2012-04-27
In this contribution, we present our new adaptive Lattice Boltzmann implementation within the Peano framework, with special focus on nanoscale particle transport problems. With the continuum hypothesis not holding anymore on these small scales, new physical effects - such as Brownian fluctuations - need to be incorporated. We explain the overall layout of the application, including memory layout and access, and shortly review the adaptive algorithm. The scheme is validated by different benchmark computations in two and three dimensions. An extension to dynamically changing grids and a spatially adaptive approach to fluctuating hydrodynamics, allowing for the thermalisation of the fluid in particular regions of interest, is proposed. Both dynamic adaptivity and adaptive fluctuating hydrodynamics are validated separately in simulations of particle transport problems. The application of this scheme to an oscillating particle in a nanopore illustrates the importance of Brownian fluctuations in such setups. © 2012 Springer-Verlag.
Lattice Boltzmann 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.
Lattice Boltzmann method for the fractional advection-diffusion equation.
Zhou, J G; Haygarth, P M; Withers, P J A; Macleod, C J A; Falloon, P D; Beven, K J; Ockenden, M C; Forber, K J; Hollaway, M J; Evans, R; Collins, A L; Hiscock, K M; Wearing, C; Kahana, R; Villamizar Velez, M L
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β, the fractional order α, and the single relaxation time τ, the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.
Thrombosis modeling in intracranial aneurysms: a lattice Boltzmann numerical algorithm
Ouared, R.; Chopard, B.; Stahl, B.; Rüfenacht, D. A.; Yilmaz, H.; Courbebaisse, G.
2008-07-01
The lattice Boltzmann numerical method is applied to model blood flow (plasma and platelets) and clotting in intracranial aneurysms at a mesoscopic level. The dynamics of blood clotting (thrombosis) is governed by mechanical variations of shear stress near wall that influence platelets-wall interactions. Thrombosis starts and grows below a shear rate threshold, and stops above it. Within this assumption, it is possible to account qualitatively well for partial, full or no occlusion of the aneurysm, and to explain why spontaneous thrombosis is more likely to occur in giant aneurysms than in small or medium sized aneurysms.
Lattice Boltzmann Modeling of Thrombosis in Giant Aneurysms
Chopard, B.; Ouared, R.; Ruefenacht, D. A.; Yilmaz, H.
We propose a numerical model of blood flow and blood clotting whose purpose is to describe thrombus formation in cerebral aneurysms. We identify possible mechanisms that can cause occurence of spontaneous thrombosis in unruptured giant intracranial aneurysms. Our main claim is that, under normal conditions, there is a low shear rate threshold below which thrombosis starts and growths. This assumption is supported by several evidences from literature. The proposed mechanisms are incorporated into a Lattice Boltzmann (LB) model for blood flow and platelets adhesion and aggregation. Numerical simulations show that the low shear rate threshold assumption together with aneurysm geometry account well for the observations.
Multi-component lattice-Boltzmann model with interparticle interaction
Shan, X; Shan, Xiaowen; Doolen, Gary
1995-01-01
Abstract: A previously proposed [X. Shan and H. Chen, Phys. Rev. E {\\bf 47}, 1815, (1993)] lattice Boltzmann model for simulating fluids with multiple components and interparticle forces is described in detail. Macroscopic equations governing the motion of each component are derived by using Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirmed by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confirmed numerically.
A large eddy lattice Boltzmann simulation of magnetohydrodynamic turbulence
Flint, Christopher; Vahala, George
2018-02-01
Large eddy simulations (LES) of a lattice Boltzmann magnetohydrodynamic (LB-MHD) model are performed for the unstable magnetized Kelvin-Helmholtz jet instability. This algorithm is an extension of Ansumali et al. [1] to MHD in which one performs first an expansion in the filter width on the kinetic equations followed by the usual low Knudsen number expansion. These two perturbation operations do not commute. Closure is achieved by invoking the physical constraint that subgrid effects occur at transport time scales. The simulations are in very good agreement with direct numerical simulations.
Differentiated heated lid driven cavity interacting with tube: A lattice Boltzmann study
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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.
Ma, Xiaoyan; Pellerin, Nicolas; Reggio, Marcelo; Bennacer, Rachid
2017-05-01
The method of lattice-Boltzmann multiple relaxation time (MRT) is commonly applied to study the conversion system consisting in a combination of forced convection and natural convection occurred in a cavity. Moving the top surface horizontally at a fixed speed, while two vertical walls are applied with constant different temperatures, assuming adiabatic case on both bottom and top walls. We consider a "non-cooperating" situation, where dynamics and buoyancy forces counterbalance. The cavity contains a circular cylinder placed at various positions. Boundary conditions for velocity and temperature have been applied to handle the non-Cartesian boundary of the cylinder. In lattice Boltzmann methods we adopt the double distribution model for calculating both the thermal and hydrodynamic fields. The D2Q5 and D2Q9 lattice are chosen to perform the simulations for a wide range of Reynolds and Rayleigh numbers. By calculating the average Nusselt number, we also investigated the influence of different obstacle positions on characteristics of flow and heat transfer. The results show the influence of the obstacle position on the dimensionless numbers, so as to effect the heat transfer behaviors inside the cavity. It is also indicates that the governing parameters are also related to driven power for the upper surface sliding. Contribution to the topical issue "Materials for Energy harvesting, conversion and storage II (ICOME 2016)", edited by Jean-Michel Nunzi, Rachid Bennacer and Mohammed El Ganaoui
van der Sman, R G M
2006-08-01
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 equilibrium distributions equal those of the Maxwell-Boltzmann distribution. These constraints can be satisfied for the rectangular D2Q9 lattice for only fluid flow in the weakly compressible regime. The analysis of source terms shows that fluxes are really defined on the boundaries of the Wigner-Seitz cells, and not on the lattice sites where the densities are defined-which is quite similar to the staggered grid finite-volume schemes. Our theoretical findings are confirmed by numerical solutions of benchmark problems for convection diffusion and natural convection. The lattice Boltzmann scheme shows remarkably good performance for convection diffusion, showing little to non-numerical diffusion or numerical dispersion, even at high grid Peclet numbers.
Recursive regularization step for high-order lattice Boltzmann methods
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.
An integrated Boltzmann+hydrodynamics approach to heavy ion collisions
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Petersen, Hannah
2009-04-22
In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. Predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies. Studies of phase diagram trajectories using hydrodynamics are performed. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The full (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. Three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent v{sub 2} values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from E{sub lab}=2-160 A GeV. The HBT correlation of the negatively charged pion source
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.
Lattice Boltzmann equation method for multiple immiscible continuum fluids
Spencer, T. J.; Halliday, I.; Care, C. M.
2010-12-01
This paper generalizes the two-component algorithm of Sec. , extending it, in Sec. , to describe N>2 mutually immiscible fluids in the isothermal continuum regime. Each fluid has an independent interfacial tension. While retaining all its computational advantages, we remove entirely the empiricism associated with contact behavior in our previous multiple immiscible fluid models [M. M. Dupin , Phys. Rev. E 73, 055701(R) (2006)10.1103/PhysRevE.73.055701; Med. Eng. Phys. 28, 13 (2006)10.1016/j.medengphy.2005.04.015] while solidifying the physical foundations. Moreover, the model relies upon a fluid-fluid segregation which is simpler, computationally faster, more free of artifacts (i.e., the interfacial microcurrent), and upon an interface-inducing force distribution which is analytic. The method is completely symmetric between any numbers of immiscible fluids and stable over a wide range of directly input interfacial tension. We present data on the steady-state properties of multiple interface model, which are in good agreement with theory [R. E. Johnson and S. S. Sadhal, Annu. Rev. Fluid Mech. 17, 289 (1985)10.1146/annurev.fl.17.010185.001445], specifically on the shapes of multidrop systems. Section is an analysis of the kinetic and continuum-scale descriptions of the underlying two-component lattice Boltzmann model for immiscible fluids, extendable to more than two immiscible fluids. This extension requires (i) the use of a more local kinetic equation perturbation which is (ii) free from a reliance on measured interfacial curvature. It should be noted that viewed simply as a two-component method, the continuum algorithm is inferior to our previous methods, reported by Lishchuk [Phys. Rev. E 67, 036701 (2003)]10.1103/PhysRevE.76.036701 and Halliday [Phys. Rev. E 76, 026708 (2007)]10.1103/PhysRevE.76.026708. Greater stability and parameter range is achieved in multiple drop simulations by using the forced multi-relaxation-time lattice Boltzmann method developed
Thermohydrodynamics of an evaporating droplet studied using a multiphase lattice Boltzmann method.
Zarghami, Ahad; Van den Akker, Harry E A
2017-04-01
In this paper, the thermohydrodynamics of an evaporating droplet is investigated by using a single-component pseudopotential lattice Boltzmann model. The phase change is applied to the model by adding source terms to the thermal lattice Boltzmann equation in such a way that the macroscopic energy equation of multiphase flows is recovered. In order to gain an exhaustive understanding of the complex hydrodynamics during evaporation, a single droplet is selected as a case study. At first, some tests for a stationary (non-)evaporating droplet are carried out to validate the method. Then the model is used to study the thermohydrodynamics of a falling evaporating droplet. The results show that the model is capable of reproducing the flow dynamics and transport phenomena of a stationary evaporating droplet quite well. Of course, a moving droplet evaporates faster than a stationary one due to the convective transport. Our study shows that our single-component model for simulating a moving evaporating droplet is limited to low Reynolds numbers.
Two-relaxation-time lattice Boltzmann method for the anisotropic dispersive Henry problem
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).
Thermohydrodynamics of an evaporating droplet studied using a multiphase lattice Boltzmann method
Zarghami, Ahad; Van den Akker, Harry E. A.
2017-04-01
In this paper, the thermohydrodynamics of an evaporating droplet is investigated by using a single-component pseudopotential lattice Boltzmann model. The phase change is applied to the model by adding source terms to the thermal lattice Boltzmann equation in such a way that the macroscopic energy equation of multiphase flows is recovered. In order to gain an exhaustive understanding of the complex hydrodynamics during evaporation, a single droplet is selected as a case study. At first, some tests for a stationary (non-)evaporating droplet are carried out to validate the method. Then the model is used to study the thermohydrodynamics of a falling evaporating droplet. The results show that the model is capable of reproducing the flow dynamics and transport phenomena of a stationary evaporating droplet quite well. Of course, a moving droplet evaporates faster than a stationary one due to the convective transport. Our study shows that our single-component model for simulating a moving evaporating droplet is limited to low Reynolds numbers.
Large-scale lattice-Boltzmann simulations over lambda networks
Saksena, R.; Coveney, P. V.; Pinning, R.; Booth, S.
Amphiphilic molecules are of immense industrial importance, mainly due to their tendency to align at interfaces in a solution of immiscible species, e.g., oil and water, thereby reducing surface tension. Depending on the concentration of amphiphiles in the solution, they may assemble into a variety of morphologies, such as lamellae, micelles, sponge and cubic bicontinuous structures exhibiting non-trivial rheological properties. The main objective of this work is to study the rheological properties of very large, defect-containing gyroidal systems (of up to 10243 lattice sites) using the lattice-Boltzmann method. Memory requirements for the simulation of such large lattices exceed that available to us on most supercomputers and so we use MPICH-G2/MPIg to investigate geographically distributed domain decomposition simulations across HPCx in the UK and TeraGrid in the US. Use of MPICH-G2/MPIg requires the port-forwarder to work with the grid middleware on HPCx. Data from the simulations is streamed to a high performance visualisation resource at UCL (London) for rendering and visualisation. Lighting the Blue Touchpaper for UK e-Science - Closing Conference of ESLEA Project March 26-28 2007 The George Hotel, Edinburgh, UK
Lattice Boltzmann method for simulation of compressible flows on standard lattices.
Prasianakis, Nikolaos I; Karlin, Iliya V
2008-07-01
The recently introduced lattice Boltzmann model for thermal flow simulation on a standard lattice [Prasianakis and Karlin, Phys. Rev. E 76, 016702 (2007)] is studied numerically in the case where compressibility effects are essential. It is demonstrated that the speed of sound and shock propagation are described correctly in a wide temperature range, and that it is possible to take into account additional physics such as heat sources and sinks. A remarkable simplicity of the model makes it viable for engineering applications in subsonic flows with large temperature and density variations.
Lattice Boltzmann Simulation of Multiple Bubbles Motion under Gravity
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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.
Lattice Boltzmann modeling an introduction for geoscientists and engineers
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.
Lattice Boltzmann model for melting with natural convection
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Huber, Christian [Department of Earth and Planetary Science, University of California - Berkeley, 307 McCone Hall 4767, Berkeley, CA 94720-4767 (United States)], E-mail: chuber@seismo.berkeley.edu; Parmigiani, Andrea [Computer Science Department, University of Geneva, 24, Rue du General Dufour, 1211 Geneva 4 (Switzerland)], E-mail: andrea.parmigiani@terre.unige.ch; Chopard, Bastien [Computer Science Department, University of Geneva, 24, Rue du General Dufour, 1211 Geneva 4 (Switzerland)], E-mail: Bastien.Chopard@cui.unige.ch; Manga, Michael [Department of Earth and Planetary Science, University of California - Berkeley, 177 McCone Hall 4767, Berkeley, CA 94720-4767 (United States)], E-mail: manga@seismo.berkeley.edu; Bachmann, Olivier [Department of Earth and Space Science, University of Washington, Johnson Hall 070, Seattle WA 98195-1310 (United States)], E-mail: bachmano@u.washington.edu
2008-10-15
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.
Boundary slip from the immersed boundary lattice Boltzmann models.
Le, Guigao; Zhang, Junfeng
2009-02-01
We report an interesting and important observation of the velocity fields from immersed boundary lattice Boltzmann methods (IB-LBM). The computed velocity profiles can deviate from theoretical predictions greatly even for very simple flow situations, both in the immersed boundary layer and the bulk region. A rigorous analysis of the IB-LBM simulated velocity for a symmetric shear flow is carried out, and the analytical solutions indicate a strong dependence of velocity on the relaxation parameter (kinetic viscosity). Also our simulations demonstrate that simply increasing the immersed boundary layer thickness is not an efficient approach to reduce such velocity discrepancy. We hope this work will bring the awareness of this essential issue to people using IB-LBM for various flow situations.
Using an Interactive Lattice Boltzmann Solver in Fluid Mechanics Instruction
Directory of Open Access Journals (Sweden)
Mirjam S. Glessmer
2017-07-01
Full Text Available This article gives an overview of the diverse range of teaching applications that can be realized using an interactive lattice Boltzmann simulation tool in fluid mechanics instruction and outreach. In an inquiry-based learning framework, examples are given of learning scenarios that address instruction on scientific results, scientific methods or the scientific process at varying levels of student activity, from consuming to applying to researching. Interactive live demonstrations on portable hardware enable new and innovative teaching concepts for fluid mechanics, also for large audiences and in the early stages of the university education. Moreover, selected examples successfully demonstrate that the integration of high-fidelity CFD methods into fluid mechanics teaching facilitates high-quality student research work within reach of the current state of the art in the respective field of research.
Chemical-potential-based lattice Boltzmann method for nonideal fluids
Wen, Binghai; Zhou, Xuan; He, Bing; Zhang, Chaoying; Fang, Haiping
2017-06-01
Chemical potential, as an important thermodynamic quantity, has been popularly used in thermodynamic modeling for complex systems, especially for those involving the phase transitions and chemical reactions. Here we present a chemical-potential-based multiphase lattice Boltzmann model, in which the nonideal force is directly evaluated by a chemical potential. The numerical computation is more efficient than the pressure-tensor-based model [Wen et al. Europhys. Lett. 112, 44002 (2015), 10.1209/0295-5075/112/44002] because the calculations of the pressure tensor and its divergence are avoided. We have derived several chemical potentials of the popular equations of state from the free-energy density function. The theoretical analyses and numerical results support that the present model satisfies thermodynamics and Galilean invariance. An effective chemical-potential boundary condition is also implemented to investigate the wettability of a solid surface, and the contact angle can be linearly tuned by the surface chemical potential.
Simulating condensation on microstructured surfaces using Lattice Boltzmann Method
Alexeev, Alexander; Vasyliv, Yaroslav
2017-11-01
We simulate a single component fluid condensing on 2D structured surfaces with different wettability. To simulate the two phase fluid, we use the athermal Lattice Boltzmann Method (LBM) driven by a pseudopotential force. The pseudopotential force results in a non-ideal equation of state (EOS) which permits liquid-vapor phase change. To account for thermal effects, the athermal LBM is coupled to a finite volume discretization of the temperature evolution equation obtained using a thermal energy rate balance for the specific internal energy. We use the developed model to probe the effect of surface structure and surface wettability on the condensation rate in order to identify microstructure topographies promoting condensation. Financial support is acknowledged from Kimberly-Clark.
Lattice Boltzmann simulations of convection heat transfer in porous media
Liu, Qing; He, Ya-Ling
2017-01-01
A non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed to study convection heat transfer in porous media at the representative elementary volume scale based on the generalized non-Darcy model. In the method, two different LB models are constructed: one is constructed in the framework of the double-distribution-function approach, and the other is constructed in the framework of the hybrid approach. In particular, the transformation matrices used in the MRT-LB models are non-orthogonal matrices. The present method is applied to study mixed convection flow in a porous channel and natural convection flow in a porous cavity. It is found that the numerical results are in good agreement with the analytical solutions and/or other results reported in previous studies. Furthermore, the non-orthogonal MRT-LB method shows better numerical stability in comparison with the BGK-LB method.
Consistent forcing scheme in the cascaded lattice Boltzmann method
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.
Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times
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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.
Prestininzi, P.; Abdolali, A.; Montessori, A.; Kirby, J. T.; La Rocca, Michele
2016-11-01
Tsunami waves are generated by sea bottom failures, landslides and faults. The concurrent generation of hydro-acoustic waves (HAW), which travel much faster than the tsunami, has received much attention, motivated by their possible exploitation as precursors of tsunamis. This feature makes the detection of HAW particularly well-suited for building an early-warning system. Accuracy and efficiency of the modeling approaches for HAW thus play a pivotal role in the design of such systems. Here, we present a Lattice Boltzmann Method (LBM) for the generation and propagation of HAW resulting from tsunamigenic ground motions and verify it against commonly employed modeling solutions. LBM is well known for providing fast and accurate solutions to both hydrodynamics and acoustics problems, thus it naturally becomes a candidate as a comprehensive computational tool for modeling generation and propagation of HAW.
Lattice Boltzmann simulations for wall-flow dynamics in porous ceramic diesel particulate filters
Lee, Da Young; Lee, Gi Wook; Yoon, Kyu; Chun, Byoungjin; Jung, Hyun Wook
2018-01-01
Flows through porous filter walls of wall-flow diesel particulate filter are investigated using the lattice Boltzmann method (LBM). The microscopic model of the realistic filter wall is represented by randomly overlapped arrays of solid spheres. The LB simulation results are first validated by comparison to those from previous hydrodynamic theories and constitutive models for flows in porous media with simple regular and random solid-wall configurations. We demonstrate that the newly designed randomly overlapped array structures of porous walls allow reliable and accurate simulations for the porous wall-flow dynamics in a wide range of solid volume fractions from 0.01 to about 0.8, which is beyond the maximum random packing limit of 0.625. The permeable performance of porous media is scrutinized by changing the solid volume fraction and particle Reynolds number using Darcy's law and Forchheimer's extension in the laminar flow region.
Towards a unified lattice kinetic scheme for relativistic hydrodynamics
Gabbana, A.; Mendoza, M.; Succi, S.; Tripiccione, R.
2017-05-01
We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultrarelativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Jüttner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard tests and solvers in relativistic fluid dynamics such as Boltzmann approach multiparton scattering and previous relativistic lattice Boltzmann models. This work provides a significant step towards the formulation of a unified relativistic lattice kinetic scheme, covering both massive and near-massless particles regimes.
Modelling viscoacoustic wave propagation with the lattice Boltzmann method.
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.
Stability and stabilization of the lattice Boltzmann method.
Brownlee, R A; Gorban, A N; Levesley, J
2007-03-01
We revisit the classical stability versus accuracy dilemma for the lattice Boltzmann methods (LBM). Our goal is a stable method of second-order accuracy for fluid dynamics based on the lattice Bhatnager-Gross-Krook method (LBGK). The LBGK scheme can be recognized as a discrete dynamical system generated by free flight and entropic involution. In this framework the stability and accuracy analysis are more natural. We find the necessary and sufficient conditions for second-order accurate fluid dynamics modeling. In particular, it is proven that in order to guarantee second-order accuracy the distribution should belong to a distinguished surface--the invariant film (up to second order in the time step). This surface is the trajectory of the (quasi)equilibrium distribution surface under free flight. The main instability mechanisms are identified. The simplest recipes for stabilization add no artificial dissipation (up to second order) and provide second-order accuracy of the method. Two other prescriptions add some artificial dissipation locally and prevent the system from loss of positivity and local blowup. Demonstration of the proposed stable LBGK schemes are provided by the numerical simulation of a one-dimensional (1D) shock tube and the unsteady 2D flow around a square cylinder up to Reynolds number Re approximately 20,000.
Volumetric lattice Boltzmann simulation for blood flow in aorta arteries
Deep, Debanjan; Yu, Huidan (Whitney); Teague, Shawn
2012-11-01
Complicated moving boundaries pose a major challenge in computational fluid dynamics for complex flows, especially in the biomechanics of both blood flow in the cardiovascular system and air flow in the respiratory system where the compliant nature of the vessels can have significant effects on the flow rate and wall shear stress. We develop a computation approach to treat arbitrarily moving boundaries using a volumetric representation of lattice Boltzmann method, which distributes fluid particles inside lattice cells. A volumetric bounce-back procedure is applied in the streaming step while momentum exchange between the fluid and moving solid boundary are accounted for in the collision sub-step. Additional boundary-induced migration is introduced to conserve fluid mass as the boundary moves across fluid cells. The volumetric LBM (VLBM) is used to simulate blood flow in both normal and dilated aorta arteries. We first compare flow structure and pressure distribution in steady state with results from Navier-Stokes based solver and good agreements are achieved. Then we focus on wall stress within the aorta for different heart pumping condition and present quantitative measurement of wall shear and normal stress.
Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices
Li, Q; He, Y L; Gao, Y J; Tao, W Q
2011-01-01
In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard D2Q9 lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small....
Knotted Vortices: Entropic Lattice Boltzmann Method for Simulation of Vortex dynamics
Boesch, Fabian; Chikatamarla, Shyam; Karlin, Ilya
2013-11-01
Knotted and interlinked vortex structures in real fluids are conjectured to play a major role in hydrodynamic flow dissipation. Much interest lies in determining their temporal stability and the mechanism through which knots dissolve. Kleckner and Irvine recently have shown the existence of such knotted vortices experimentally by accelerating hydrofoils in water. In the present work we employ the entropic lattice Boltzmann method (ELBM) to perform DNS simulations of the creation and dynamics of knotted vortex rings inspired by the experimental setup in. ELBM renders LBM scheme unconditionally stable by restoring the second law of thermodynamics (the Boltzmann H-theorem), and thus enables simulations of large domains and high Reynolds numbers with DNS quality. The results presented in this talk provide an in-depth study of the dynamics of knotted vortices and vortex reconnection events and confirm the existence of trefoil knots in silicio for the first time. This work was supported by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID s347.
A lattice Boltzmann model for multiphase flows with moving contact line and variable density
Huang, Jizu; Wang, Xiao-Ping
2018-01-01
In this paper, we develop an efficient lattice Boltzmann model for the two-phase moving contact line problem with variable density. The Navier-Stokes and Cahn-Hilliard equations are recovered from the lattice Boltzmann model proposed by Fakhari and Rahimian [5]. To improve numerical stability, we present a semi-implicit lattice Boltzmann method together with a mixed finite difference scheme. In order to describe the behavior of the contact line motion on the boundary, we incorporate the generalized Navier boundary condition [25] by the nonequilibrium extrapolation method [8]. The proposed method is easy to implement and retains the advantage of the standard lattice Boltzmann method. Numerical tests are carried out to verify the proposed method. Our numerical results show that the present approach is able to model two-phase flows with variable density and moving contact line.
National Research Council Canada - National Science Library
TAMAGAWA, Masaaki; MATSUO, Sumiaki
2004-01-01
...) with Lattice Boltzmann Method (LBM), applying to orifice-pipe blood flow and flow around a cylinder, which is simple model of turbulent shear stress in the high speed rotary blood pumps and complicated geometry of medical fluid machines...
Implementing the lattice Boltzmann model on commodity graphics hardware
Kaufman, Arie; Fan, Zhe; Petkov, Kaloian
2009-06-01
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
Flow visualisation of downhill skiers using the lattice Boltzmann method
Asai, Takeshi; Hong, Sungchan; Ijuin, Koichi
2017-03-01
In downhill alpine skiing, skiers often exceed speeds of 120 km h-1, with air resistance substantially affecting the overall race times. To date, studies on air resistance in alpine skiing have used wind tunnels and actual skiers to examine the relationship between the gliding posture and magnitude of drag and for the design of skiing equipment. However, these studies have not revealed the flow velocity distribution and vortex structure around the skier. In the present study, computational fluid dynamics are employed with the lattice Boltzmann method to derive the relationship between total drag and the flow velocity around a downhill skier in the full-tuck position. Furthermore, the flow around the downhill skier is visualised, and its vortex structure is examined. The results show that the total drag force in the downhill skier model is 27.0 N at a flow velocity of 15 m s-1, increasing to 185.8 N at 40 m s-1. From analysis of the drag distribution and the flow profile, the head, upper arms, lower legs, and thighs (including buttocks) are identified as the major sources of drag on a downhill skier. Based on these results, the design of suits and equipment for reducing the drag from each location should be the focus of research and development in ski equipment. This paper describes a pilot study that introduces undergraduate students of physics or engineering into this research field. The results of this study are easy to understand for undergraduate students.
Lattice Boltzmann heat transfer model for permeable voxels
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 Optimization on Leading Multicore Platforms
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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.
Stable lattice Boltzmann model for Maxwell equations in media
Hauser, A.; Verhey, J. L.
2017-12-01
The present work shows a method for stable simulations via the lattice Boltzmann (LB) model for electromagnetic waves (EM) transiting homogeneous media. LB models for such media were already presented in the literature, but they suffer from numerical instability when the media transitions are sharp. We use one of these models in the limit of pure vacuum derived from Liu and Yan [Appl. Math. Model. 38, 1710 (2014), 10.1016/j.apm.2013.09.009] and apply an extension that treats the effects of polarization and magnetization separately. We show simulations of simple examples in which EM waves travel into media to quantify error scaling, stability, accuracy, and time scaling. For conductive media, we use the Strang splitting and check the simulations accuracy at the example of the skin effect. Like pure EM propagation, the error for the static limits, which are constructed with a current density added in a first-order scheme, can be less than 1 % . The presented method is an easily implemented alternative for the stabilization of simulation for EM waves propagating in spatially complex structured media properties and arbitrary transitions.
Lattice Boltzmann method for one-dimensional vector radiative transfer.
Zhang, Yong; Yi, Hongliang; Tan, Heping
2016-02-08
A one-dimensional vector radiative transfer (VRT) model based on lattice Boltzmann method (LBM) that considers polarization using four Stokes parameters is developed. The angular space is discretized by the discrete-ordinates approach, and the spatial discretization is conducted by LBM. LBM has such attractive properties as simple calculation procedure, straightforward and efficient handing of boundary conditions, and capability of stable and accurate simulation. To validate the performance of LBM for vector radiative transfer, four various test problems are examined. The first case investigates the non-scattering thermal-emitting atmosphere with no external collimated solar. For the other three cases, the external collimated solar and three different scattering types are considered. Particularly, the LBM is extended to solve VRT in the atmospheric aerosol system where the scattering function contains singularities and the hemisphere space distributions for the Stokes vector are presented and discussed. The accuracy and computational efficiency of this algorithm are discussed. Numerical results show that the LBM is accurate, flexible and effective to solve one-dimensional polarized radiative transfer problems.
Dynamic permeability of porous media by the lattice Boltzmann method
Adler, P.; Pazdniakou, A.
2012-04-01
The main objective of our work is to determine the dynamic permeability of three dimensional porous media by means of the Lattice Boltzmann method (LBM). The Navier-Stokes equation can be numerically solved by LBM which is widely used to address various fluid dynamics problems. Space is discretized by a three-dimensional cubic lattice and time is discretized as well. The generally accepted notation for lattice Boltzmann models is DdQq where D stands for space dimension and Q for the number of discrete velocities. The present model is denoted by D3Q19. Moreover, the Two Relaxation Times variant of the Multi Relaxation Times model is implemented. Bounce back boundary conditions are used on the solid-fluid interfaces. The porous medium is spatially periodic. Reconstructed media were used; they are obtained by imposing a porosity and a correlation function characterized by a correlation length. Real samples can be obtained by MicroCT. In contrast with other previous contributions, the dynamic permeability K(omega) which is a complex number, is derived by imposing an oscillating body force of pulsation omega on the unit cell and by deriving the amplitude and the phase shift of the resulting time dependent seepage velocity. The influence of two limiting parameters, namely the Knudsen number Kn and the discretization for high frequencies, on K(omega) is carefully studied for the first time. Kn is proportional to nu/(cs H) where nu is the kinematic viscosity, cs the speed of sound in the fluid and H a characteristic length scale of the porous medium. Several porous media such as the classical plane Poiseuille flow and the reconstructed media are used to show that it is only for small enough values of Kn that reliable results are obtained. Otherwise, the data depend on Kn and may even be totally unphysical. However, it should be noticed that the limiting value of Kn could not be derived in general since it depends very much on the structure of the medium. Problems occur at
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.
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.
Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring.
Zhang, Rui; Roberts, Tyler; Aranson, Igor S; de Pablo, Juan J
2016-02-28
Liquid crystals (LCs) display many of the flow characteristics of liquids but exhibit long range orientational order. In the nematic phase, the coupling of structure and flow leads to complex hydrodynamic effects that remain to be fully elucidated. Here, we consider the hydrodynamics of a nematic LC in a hybrid cell, where opposite walls have conflicting anchoring boundary conditions, and we employ a 3D lattice Boltzmann method to simulate the time-dependent flow patterns that can arise. Due to the symmetry breaking of the director field within the hybrid cell, we observe that at low to moderate shear rates, the volumetric flow rate under Couette and Poiseuille flows is different for opposite flow directions. At high shear rates, the director field may undergo a topological transition which leads to symmetric flows. By applying an oscillatory pressure gradient to the channel, a net volumetric flow rate is found to depend on the magnitude and frequency of the oscillation, as well as the anchoring strength. Taken together, our findings suggest several intriguing new applications for LCs in microfluidic devices.
Peristaltic particle transport using the Lattice Boltzmann method
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Connington, Kevin William [Los Alamos National Laboratory; Kang, Qinjun [Los Alamos National Laboratory; Viswanathan, Hari S [Los Alamos National Laboratory; Abdel-fattah, Amr [Los Alamos National Laboratory; Chen, Shiyi [JOHNS HOPKINS UNIV.
2009-01-01
Peristaltic transport refers to a class of internal fluid flows where the periodic deformation of flexible containing walls elicits a non-negligible fluid motion. It is a mechanism used to transport fluid and immersed solid particles in a tube or channel when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical moving parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a two-dimensional channel using the lattice Boltzmann method. We systematically investigate the effect of variation of the relevant dimensionless parameters of the system on the particle transport. We find, among other results, a case where an increase in Reynolds number can actually lead to a slight increase in particle transport, and a case where, as the wall deformation increases, the motion of the particle becomes non-negative only. We examine the particle behavior when the system exhibits the peculiar phenomenon of fluid trapping. Under these circumstances, the particle may itself become trapped where it is subsequently transported at the wave speed, which is the maximum possible transport in the absence of a favorable pressure gradient. Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shear-sensitive particles. We find that the levels of shear stress are most hazardous near the throat of the channel. We advise that shear-sensitive particles should be transported under conditions where trapping occurs as the particle is typically situated in a region of innocuous shear stress levels.
Two-Dimensional Lattice Boltzmann for Reactive Rayleigh–Bénard and Bénard–Poiseuille Regimes
Directory of Open Access Journals (Sweden)
Suemi Rodríguez-Romo
2015-09-01
Full Text Available We perform a computer simulation of the reaction-diffusion and convection that takes place in Rayleigh–Bénard and Bénard–Poiseuille regimes. The lattice Boltzmann equation (LBE is used along with the Boussinesq approximation to solve the non-linear coupled differential equations that govern the systems’ thermo-hydrodynamics. Another LBE, is introduced to calculate the evolution concentration of the chemical species involved in the chemical reactions. The simulations are conducted at low Reynolds numbers and in terms of steady state between the first and second thermo-hydrodynamics instability. The results presented here (with no chemical reactions are in good agreement with those reported in the scientific literature which gives us high expectations about the reliability of the chemical kinetics simulation. Some examples are provided.
Application of Lattice Boltzmann Methods in Complex Mass Transfer Systems
Sun, Ning
Lattice Boltzmann Method (LBM) is a novel computational fluid dynamics method that can easily handle complex and dynamic boundaries, couple local or interfacial interactions/reactions, and be easily parallelized allowing for simulation of large systems. While most of the current studies in LBM mainly focus on fluid dynamics, however, the inherent power of this method makes it an ideal candidate for the study of mass transfer systems involving complex/dynamic microstructures and local reactions. In this thesis, LBM is introduced to be an alternative computational method for the study of electrochemical energy storage systems (Li-ion batteries (LIBs) and electric double layer capacitors (EDLCs)) and transdermal drug design on mesoscopic scale. Based on traditional LBM, the following in-depth studies have been carried out: (1) For EDLCs, the simulation of diffuse charge dynamics is carried out for both the charge and the discharge processes on 2D systems of complex random electrode geometries (pure random, random spheres and random fibers). Steric effect of concentrated solutions is considered by using modified Poisson-Nernst-Plank (MPNP) equations and compared with regular Poisson-Nernst-Plank (PNP) systems. The effects of electrode microstructures (electrode density, electrode filler morphology, filler size, etc.) on the net charge distribution and charge/discharge time are studied in detail. The influence of applied potential during discharging process is also discussed. (2) For the study of dendrite formation on the anode of LIBs, it is shown that the Lattice Boltzmann model can capture all the experimentally observed features of microstructure evolution at the anode, from smooth to mossy to dendritic. The mechanism of dendrite formation process in mesoscopic scale is discussed in detail and compared with the traditional Sand's time theories. It shows that dendrite formation is closely related to the inhomogeneous reactively at the electrode-electrolyte interface
Liang, H; Shi, B C; Guo, Z L; Chai, Z H
2014-05-01
In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is proposed for incompressible multiphase flow systems. In this model, one distribution function is used to solve the Chan-Hilliard equation and the other is adopted to solve the Navier-Stokes equations. Unlike previous phase-field-based LB models, a proper source term is incorporated in the interfacial evolution equation such that the Chan-Hilliard equation can be derived exactly and also a pressure distribution is designed to recover the correct hydrodynamic equations. Furthermore, the pressure and velocity fields can be calculated explicitly. A series of numerical tests, including Zalesak's disk rotation, a single vortex, a deformation field, and a static droplet, have been performed to test the accuracy and stability of the present model. The results show that, compared with the previous models, the present model is more stable and achieves an overall improvement in the accuracy of the capturing interface. In addition, compared to the single-relaxation-time LB model, the present model can effectively reduce the spurious velocity and fluctuation of the kinetic energy. Finally, as an application, the Rayleigh-Taylor instability at high Reynolds numbers is investigated.
Chatterjee, Dipankar; Amiroudine, Sakir
2011-02-01
A comprehensive non-isothermal Lattice Boltzmann (LB) algorithm is proposed in this article to simulate the thermofluidic transport phenomena encountered in a direct-current (DC) magnetohydrodynamic (MHD) micropump. Inside the pump, an electrically conducting fluid is transported through the microchannel by the action of an electromagnetic Lorentz force evolved out as a consequence of the interaction between applied electric and magnetic fields. The fluid flow and thermal characteristics of the MHD micropump depend on several factors such as the channel geometry, electromagnetic field strength and electrical property of the conducting fluid. An involved analysis is carried out following the LB technique to understand the significant influences of the aforementioned controlling parameters on the overall transport phenomena. In the LB framework, the hydrodynamics is simulated by a distribution function, which obeys a single scalar kinetic equation associated with an externally imposed electromagnetic force field. The thermal history is monitored by a separate temperature distribution function through another scalar kinetic equation incorporating the Joule heating effect. Agreement with analytical, experimental and other available numerical results is found to be quantitative.
Zhao, Mingfei; Yong, Xin
2017-11-01
Nanoparticle deposition coupled to hydrodynamics plays important roles in materials printing and thin-film processing. Investigations of nanoparticle dynamics in evaporating colloidal dispersions could elicit a greater understanding of the processing-structure relationship for evaporation-induced self-assembly and deposition. A 3D free-energy lattice Boltzmann method combined with Brownian dynamics is developed to simulate evaporating colloidal droplets and rivulets. In this work, we explore the deposition on solid substrates with different wetting properties, namely static contact angle and contact line motion. We highlight the influence of convective flows on the assembly kinetics and deposit patterns using the developed model. We introduce a novel approach to impose a pinned contact line for most of droplet lifetime. The time evolutions of contact angle and droplet volume are examined to characterize the pinning scheme. We observe the process of nanoparticle self-assembly during the evaporation of droplets and rivulets and quantitatively analyze the deposit structure. This work was supported by the National Science Foundation under Grant No. CMMI-1538090.
An immersed boundary-lattice Boltzmann model for biofilm growth in porous media
Benioug, M.; Golfier, F.; Oltéan, C.; Buès, M. A.; Bahar, T.; Cuny, J.
2017-09-01
In this paper, we present a two-dimensional pore-scale numerical model to investigate the main mechanisms governing biofilm growth in porous media. The fluid flow and solute transport equations are coupled with a biofilm evolution model. Fluid flow is simulated with an immersed boundary-lattice Boltzmann model while solute transport is described with a volume-of-fluid-type approach. A cellular automaton algorithm combined with immersed boundary methods was developed to describe the spreading and distribution of biomass. Bacterial attachment and detachment mechanisms are also taken into account. The capability of this model to describe correctly the couplings involved between fluid circulation, nutrient transport and bacterial growth is tested under different hydrostatic and hydrodynamic conditions (i) on a flat medium and (ii) for a complex porous medium. For the second case, different regimes of biofilm growth are identified and are found to be related to the dimensionless parameters of the model, Damköhler and Péclet numbers and dimensionless shear stress. Finally, the impact of biofilm growth on the macroscopic properties of the porous medium is investigated and we discuss the unicity of the relationships between hydraulic conductivity and biofilm volume fraction.
Lattice Boltzmann accelerated direct simulation Monte Carlo for dilute gas flow simulations.
Di Staso, G; Clercx, H J H; Succi, S; Toschi, F
2016-11-13
Hybrid particle-continuum computational frameworks permit the simulation of gas flows by locally adjusting the resolution to the degree of non-equilibrium displayed by the flow in different regions of space and time. In this work, we present a new scheme that couples the direct simulation Monte Carlo (DSMC) with the lattice Boltzmann (LB) method in the limit of isothermal flows. The former handles strong non-equilibrium effects, as they typically occur in the vicinity of solid boundaries, whereas the latter is in charge of the bulk flow, where non-equilibrium can be dealt with perturbatively, i.e. according to Navier-Stokes hydrodynamics. The proposed concurrent multiscale method is applied to the dilute gas Couette flow, showing major computational gains when compared with the full DSMC scenarios. In addition, it is shown that the coupling with LB in the bulk flow can speed up the DSMC treatment of the Knudsen layer with respect to the full DSMC case. In other words, LB acts as a DSMC accelerator.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'. © 2016 The Author(s).
Lattice-Boltzmann simulation of inertial particle-laden flow around an obstacle
Haddadi, Hamed; Shojaei-Zadeh, Shahab; Morris, Jeffrey F.
2016-06-01
The lattice-Boltzmann method is used to compute the flow of a particle suspension of dilute volume fraction ϕ ≤0.08 around obstacles. The work focuses on the interaction of particles with the obstacle and the flow behavior in and around the recirculating wake behind the obstacle. Motivated by microfluidic experiments of dilute suspension flow over obstacles of circular, square, and other shapes showing depletion of particles in the wake behind the obstacle, we focus on the entry and exit from the wake for isolated particles, small groups of particles, and a suspension of many particles. All work is at conditions well below the Reynolds number for the transition to unsteady flow and vortex shedding. The dynamics of an isolated particle inside the recirculating wake flow exhibits motion toward a limit cycle near the outer boundary of the wake. By increasing particle density above the fluid and increasing the size of the particle, we determine the upper limits of these variables yielding a limit cycle trajectory. Hydrodynamic interaction between particles in a many-particle suspension is shown to lead to exchange of particles between the wake zone and free stream.
Turbulent jet computations based on MRT and Cascaded Lattice Boltzmann models
Geller, S; Uphoff, S.; Krafczyk, M.
2012-01-01
In this contribution a numerical study of a turbulent jet flow is presented. The simulation results of two different variants of the Lattice Boltzmann method (LBM) are compared. The first is the well-established D3Q19 MRT model extended by a Smagorinsky Large Eddy Simulation (LES) model. The second is the D3Q27 Factorized Cascaded Lattice Boltzmann (FCLB) model without any additional explicit turbulence model. For this model no studies of turbulent flow with high resolution on nonuniform grid...
A double-distribution-function lattice Boltzmann method for bed-load sediment transport
Cai, Li; Xu, Wenjing; Luo, Xiaoyu
2017-01-01
The governing equations of bed-load sediment transport are the shallow water equations and the Exner equation. To embody the advantages of the lattice Boltzmann method (e.g., simplicity, efficiency), the three-velocity (D1Q3) and five-velocity (D1Q5) double-distribution-function lattice Boltzmann models (DDF-LBMs), which can present the numerical solution for one-dimensional bed-load sediment transport, are proposed here based on the quasi-steady approach. The so-called DDF-LBM means we use t...
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.
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...
Incorporating forcing terms in cascaded lattice Boltzmann approach by method of central moments.
Premnath, Kannan N; Banerjee, Sanjoy
2009-09-01
Cascaded lattice Boltzmann method (cascaded-LBM) employs a class of collision operators aiming to stabilize computations and remove certain modeling artifacts for simulation of fluid flow on lattice grids with sizes arbitrarily larger than the smallest physical dissipation length scale [Geier, Phys. Rev. E 63, 066705 (2006)]. It achieves this and distinguishes from other collision operators, such as in the standard single or multiple relaxation-time approaches, by performing relaxation process due to collisions in terms of moments shifted by the local hydrodynamic fluid velocity, i.e., central moments, in an ascending order by order at different relaxation rates. In this paper, we propose and derive source terms in the cascaded-LBM to represent the effect of external or internal forces on the dynamics of fluid motion. This is essentially achieved by matching the continuous form of the central moments of the source or forcing terms with its discrete version. Different forms of continuous central moments of sources, including one that is obtained from a local Maxwellian, are considered in this regard. As a result, the forcing terms obtained in this formulation are Galilean invariant by construction. To alleviate lattice artifacts due to forcing terms in the emergent macroscopic fluid equations, they are proposed as temporally semi-implicit and second order, and the implicitness is subsequently effectively removed by means of a transformation to facilitate computation. It is shown that the impressed force field influences the cascaded collision process in the evolution of the transformed distribution function. The method of central moments along with the associated orthogonal properties of the moment basis completely determines the analytical expressions for the source terms as a function of the force and macroscopic velocity fields. In contrast to the existing forcing schemes, it is found that they involve higher-order terms in velocity space. It is shown that the
Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models.
Shan, Xiaowen
2006-04-01
We show that the spurious current present near a curved interface in a class of multiphase lattice Boltzmann (LB) models is due to the insufficient isotropy of the discrete gradient operator. A method of obtaining highly isotropic gradient operators on a lattice is given. Numerical simulations show that both the magnitude and the spatial extent of the spurious current are significantly reduced as gradient operators of increasingly higher order of isotropy is adopted in multiphase LB models.
A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method
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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.
Sman, van der R.G.M.
2013-01-01
We have investigated the performance of an alternative wetting boundary condition for complex geometries in a phase field Lattice Boltzmann scheme, which is an alternative to the commonly used formulation by Yeomans and coworkers. Though our boundary condition is much simpler in its implementation,
A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects
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
Corrected momentum exchange method for lattice Boltzmann simulations of suspension flow
Lorenz, E.; Caiazzo, A.; Hoekstra, A.G.
2009-01-01
Standard methods for lattice Boltzmann simulations of suspended particles, based on the momentum exchange algorithm, might lack accuracy or violate Galilean invariance in some particular situations. Aiming at simulations of dense suspensions in high-shear flows, we motivate and investigate necessary
Lattice-Boltzmann-based two-phase thermal model for simulating phase change
Kamali, M.R.; Gillissen, J.J.J.; Van den Akker, H.E.A.; Sundaresan, S.
2013-01-01
A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A
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...... at the walls, which corroborates experimental measurements in cylindrical pipes....
Development of a Prototype Lattice Boltzmann Code for CFD of Fusion Systems.
Energy Technology Data Exchange (ETDEWEB)
Pattison, Martin J; Premnath, Kannan N; Banerjee, Sanjoy; Dwivedi, Vinay
2007-02-26
ability of the LBM to scale almost linearly. The equation for magnetic induction was also solved using a lattice Boltzmann method. This approach has the advantage that it fits in well to the framework used for the hydrodynamic equations, but more importantly that it preserves the ability of the code to run efficiently on parallel architectures. Since the LBM is a relatively recent model, a number of new developments were needed to solve the magnetic induction equation for practical problems. Existing methods were only suitable for cases where the fluid viscosity and the magnetic resistivity are of the same order, and a preconditioning method was used to allow the simulation of liquid metals, where these properties differ by several orders of magnitude. An extension of this method to the hydrodynamic equations allowed faster convergence to steady state. A new method of imposing boundary conditions using an extrapolation technique was derived, enabling the magnetic field at a boundary to be specified. Also, a technique by which the grid can be stretched was formulated to resolve thin layers at high imposed magnetic fields, allowing flows with Hartmann numbers of several thousand to be quickly and efficiently simulated. In addition, a module has been developed to calculate the temperature field and heat transfer. This uses a total variation diminishing scheme to solve the equations and is again very amenable to parallelisation. Although, the module was developed with thermal modelling in mind, it can also be applied to passive scalar transport. The code is fully three dimensional and has been applied to a wide variety of cases, including both laminar and turbulent flows. Validations against a series of canonical problems involving both MHD effects and turbulence have clearly demonstrated the ability of the LBM to properly model these types of flow. As well as applications to fusion engineering, the resulting code is flexible enough to be applied to a wide range of other
Liao, Qiang; Yang, Yan-Xia; Zhu, Xun; Wang, Hong; Ding, Yu-Dong
2015-06-01
The lattice Boltzmann method is adopted to simulate hydrodynamics and mass transfer accompanying with biochemical reaction in a channel with cylinder bundle, which is the scenario of biohydrogen production by photosynthetic bacteria in the biofilm attached on the surface of cylinder bundle in photobioreactor. The effects of cylinder spacing, Reynolds number and cylinder arrangement are investigated. The numerical results reveal that highest glucose concentration and the lowest hydrogen concentration are obtained at the front of the first row cylinders for all cases. The staggered arrangement leads to an increment in average drag coefficient, Sherwood number and consumption efficiency of substrate under a given condition, and the increment in Sherwood number reaches up to 30 %, while that in drag coefficient is around 1 %, moreover, the increment in consumption efficiency reaches the maximum value of 12 %. The results indicate that the staggered arrangement is beneficial to the mass transfer and biochemical reaction.
Mino, Yasushi; Shinto, Hiroyuki; Sakai, Shohei; Matsuyama, Hideto
2017-04-01
A computational method for the simulation of particulate flows that can efficiently treat the particle-fluid boundary in systems containing many particles was developed based on the smoothed-profile lattice Boltzmann method (SPLBM). In our proposed method, which we call the improved SPLBM (iSPLBM), for an accurate and stable simulation of particulate flows, the hydrodynamic force on a moving solid particle is exactly formulated with consideration of the effect of internal fluid mass. To validate the accuracy and stability of iSPLBM, we conducted numerical simulations of several particulate flow systems and compared our results with those of other simulations and some experiments. In addition, we performed simulations on flotation of many lightweight particles with a wide range of particle size distribution, the results of which demonstrated the effectiveness of iSPLBM. Our proposed model is a promising method to accurately and stably simulate extensive particulate flows.
Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology
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...
Reis, T.
2010-09-06
Existing lattice Boltzmann models that have been designed to recover a macroscopic description of immiscible liquids are only able to make predictions that are quantitatively correct when the interface that exists between the fluids is smeared over several nodal points. Attempts to minimise the thickness of this interface generally leads to a phenomenon known as lattice pinning, the precise cause of which is not well understood. This spurious behaviour is remarkably similar to that associated with the numerical simulation of hyperbolic partial differential equations coupled with a stiff source term. Inspired by the seminal work in this field, we derive a lattice Boltzmann implementation of a model equation used to investigate such peculiarities. This implementation is extended to different spacial discretisations in one and two dimensions. We shown that the inclusion of a quasi-random threshold dramatically delays the onset of pinning and facetting.
Lattice-Boltzmann simulation of laser interaction with weakly ionized helium plasmas.
Li, Huayu; Ki, Hyungson
2010-07-01
This paper presents a lattice Boltzmann method for laser interaction with weakly ionized plasmas considering electron impact ionization and three-body recombination. To simulate with physical properties of plasmas, the authors' previous work on the rescaling of variables is employed and the electromagnetic fields are calculated from the Maxwell equations by using the finite-difference time-domain method. To calculate temperature fields, energy equations are derived separately from the Boltzmann equations. In this way, we attempt to solve the full governing equations for plasma dynamics. With the developed model, the continuous-wave CO2 laser interaction with helium is simulated successfully.
Energy Technology Data Exchange (ETDEWEB)
Li, Baoming; Kwok, Daniel Y. [Nanoscale Technology and Engineering Laboratory, Department of Mechanical Engineering, University of Alberta, Edmonton, AB (Canada)
2004-09-01
We present here a lattice Boltzmann model with high Reynolds number in the presence of external force fields to describe electrokinetic phenomena in microfluidics, by considering pressure as the only external force for liquid flow. Our results from a 9-bit square lattice Boltzmann model are in excellent agreement with experimental data in pressure-driven microchannel flow that could not be fully described by electrokinetic theory. The difference between the predicted and experimental Reynolds numbers from pressure gradients are well within 5%. Our results suggest that the lattice Boltzmann model described here is an effective computational tool to predict the more complex microfluidic systems that might be problematic using conventional methods. (orig.)
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 (0â2% added to water-base fluid and Rayleigh numbers of 103â105. 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
Energy Technology Data Exchange (ETDEWEB)
Karlin, I.; Frouzakis, Ch.; Boulouchos, K.
2007-07-01
This final report for the Swiss Federal Office of Energy (SFOE) reports on work done in 2007 at the Swiss Federal Institute of Technology ETH in Zurich on simulation methods for chemically reactive systems at the micrometer scale. The Lattice-Boltzmann method using lattice models is examined and the results obtained are discussed. A three-dimensional thermal model was developed and used to analyse flows with considerable temperature and density variations. The model was also used for the analysis of flows in diluted gases. A method for the reduction of complex reaction mechanisms was developed and tested for future combustion applications. 30 publications are noted and new possibilities for the analysis of flows in micro-channels and porous media - as used in reformers, catalyzers and fuel cells - are discussed.
A Review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer
Directory of Open Access Journals (Sweden)
D. Arumuga Perumal
2015-12-01
Full Text Available The Lattice Boltzmann Method (LBM is introduced in the Computational Fluid Dynamics (CFD field as a tool for research and development, but its ultimate importance lies in various industrial and academic applications. Owing to its excellent numerical stability and constitutive versatility it plays an essential role as a simulation tool for understanding micro and macro fluid flows. The LBM received a tremendous impetus with their spectacular use in incompressible and compressible fluid flow and heat transfer problems. The applications of LBM to incompressible flows with simple and complex geometries are much less spectacular. From a computational point of view, the present LBM is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. The present paper reviews the philosophy and the formal concepts behind the lattice Boltzmann approach and gives progress in the area of incompressible fluid flows, compressible fluid flows and free surface flows.
On the Stability of the Finite Difference based Lattice Boltzmann Method
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.
Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers
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.
Turbulent jet computations based on MRT and Cascaded Lattice Boltzmann models
Geller, S; Krafczyk, M
2012-01-01
In this contribution a numerical study of a turbulent jet flow is presented. The simulation results of two different variants of the Lattice Boltzmann method (LBM) are compared. The first is the well-established D3Q19 MRT model extended by a Smagorinsky Large Eddy Simulation (LES) model. The second is the D3Q27 Factorized Cascaded Lattice Boltzmann (FCLB) model without any additional explicit turbulence model. For this model no studies of turbulent flow with high resolution on nonuniform grids existed so far. The underlying computational procedure uses a time nested refinement technique and a grid with more than a billion DOF. The simulations were conducted with the parallel multi physics solver VIRTUALFLUIDS. It is shown that both models are feasible for the present flow case, but the FCLB outperforms the traditional approach in some aspects.
Obliger, Amaël; Duvail, Magali; Jardat, Marie; Coelho, Daniel; Békri, Samir; Rotenberg, Benjamin
2013-07-01
We report the calculation of all the transfer coefficients which couple the solvent and ionic fluxes through a charged pore under the effect of pressure, electrostatic potential, and concentration gradients. We use a combination of analytical calculations at the Poisson-Nernst-Planck and Navier-Stokes levels of description and mesoscopic lattice simulations based on kinetic theory. In the absence of added salt, i.e., when the only ions present in the fluid are the counterions compensating the charge of the surface, exact analytical expressions for the fluxes in cylindrical pores allow us to validate a new lattice-Boltzmann electrokinetics (LBE) scheme which accounts for the osmotic contribution to the transport of all species. The influence of simulation parameters on the numerical accuracy is thoroughly investigated. In the presence of an added salt, we assess the range of validity of approximate expressions of the fluxes computed from the linearized Poisson-Boltzmann equation by a systematic comparison with LBE simulations.
Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework
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.
Conservative phase-field lattice Boltzmann model for interface tracking equation.
Geier, Martin; Fakhari, Abbas; Lee, Taehun
2015-06-01
Based on the phase-field theory, we propose a conservative lattice Boltzmann method to track the interface between two different fluids. The presented model recovers the conservative phase-field equation and conserves mass locally and globally. Two entirely different approaches are used to calculate the gradient of the phase field, which is needed in computation of the normal to the interface. One approach uses finite-difference stencils similar to many existing lattice Boltzmann models for tracking the two-phase interface, while the other one invokes central moments to calculate the gradient of the phase field without any finite differences involved. The former approach suffers from the nonlocality of the collision operator while the latter is entirely local making it highly suitable for massive parallel implementation. Several benchmark problems are carried out to assess the accuracy and stability of the proposed model.
Liu, Qing
2016-01-01
As a numerically accurate and computationally efficient mesoscopic numerical method, the lattice Boltzmann (LB) method has achieved great success in simulating microscale rarefied gas flows. In this paper, an LB method based on the cascaded collision operator is presented to simulate microchannel gas flows in the transition flow regime. The Bosanquet-type effective viscosity is incorporated into the cascaded lattice Boltzmann (CLB) method to account for the rarefaction effects. In order to gain accurate simulations and match the Bosanquet-type effective viscosity, the combined bounce-back/specular-reflection scheme with a modified second-order slip boundary condition is employed in the CLB method. The present method is applied to study gas flow in a microchannel with periodic boundary condition and gas flow in a long microchannel with pressure boundary condition over a wide range of Knudsen numbers. The predicted results, including the velocity profile, the mass flow rate, and the non-linear pressure deviatio...
Simulation of droplet formation and coalescence using lattice Boltzmann-based single-phase model.
Xing, Xiu Qing; Butler, David Lee; Ng, Sum Huan; Wang, Zhenfeng; Danyluk, Steven; Yang, Chun
2007-07-15
A lattice Boltzmann method-based single-phase free surface model is developed to study the interfacial dynamics of coalescence, droplet formation and detachment phenomena related to surface tension and wetting effects. Compared with the conventional multiphase models, the lattice Boltzmann-based single-phase model has a higher computational efficiency since it is not necessary to simulate the motion of the gas phase. A perturbation, which is given in the same fashion as the perturbation step in Gunstensen's color model, is added to the distribution functions of the interface cells for incorporating the surface tension into the single-phase model. The assignment of different mass gradients along the fluid-wall interface is used to model the wetting properties of the solid surface. Implementations of the model are demonstrated for simulating the processes of the droplet coalescence, the droplet formation and detachment from ceiling and from nozzles with different shapes and different wall wetting properties.
Evaluation of the Finite Element Lattice Boltzmann Method for Binary Fluid Flows
Matin, Rastin; Hernandez-Garcia, Anier; Mathiesen, Joachim
2016-01-01
In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex boundaries. The current work combines characteristic-based integration of the streaming step with the free-energy based multiphase model by Lee et. al. [Journal of Computational Physics, 206 (1), 2005 ]. This allows for simulation time steps more than an order of magnitude larger than the relaxation time. Unlike previous work by Wardle et. al. [Computers and Mathematics with Applications, 65 (2), 2013 ] that integrated intermolecular forcing terms in the advection term, the current scheme applies collision and forcing terms locally for a simpler finite element formulation. A series of thorough benchmark studies reveal that this does not compromise stability and that the scheme is able to accurately simulate flows at large density and viscosity contrasts.
Investigation of a lattice Boltzmann model with a variable speed of sound
Buick, J.M.; Cosgrove, J. A.
2007-01-01
A lattice Boltzmann model is considered in which the speed of sound can be varied independently of the other parameters. The range over which the speed of sound can be varied is investigated and good agreement is found between simulations and theory. The onset of nonlinear effects due to variations in the speed of sound is also investigated and good agreement is again found with theory. It is also shown that the fluid viscosity is not altered by changing the speed of sound.
Lattice Boltzmann simulation of solute transport in a single rough fracture
Dou, Zhi; Zhi-fang ZHOU
2014-01-01
In this study, the lattice Boltzmann method (LBM) was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves (BTCs) for continuous injection sources in ro...
Dorschner, B.; Chikatamarla, S. S.; Karlin, I. V.
2017-06-01
Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015), 10.1016/j.jcp.2015.04.017] as well as for three-dimensional one-way coupled simulations of engine-type geometries in B . Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016), 10.1017/jfm.2016.448] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases, including two-way coupling between fluid and structure and then turbulence and deforming geometries. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil in the transitional regime at a Reynolds number of Re =40 000 and, finally, to access the model's performance for deforming geometries, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.
Dynamically adaptive Lattice Boltzmann simulation of shallow water flows with the Peano framework
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.
Increasing stability and accuracy of the lattice Boltzmann scheme: recursivity and regularization
Malaspinas, Orestis
2015-01-01
In the present paper a lattice Boltzmann scheme is presented which exhibits an increased stability and accuracy with respect to standard single- or multi-relaxation-time (MRT) approaches. The scheme is based on a single-relaxation-time model where a special regularization procedure is applied. This regularization is based on the fact that, for a-thermal flows, there exists a recursive way to express the velocity distribution function at any order (in the Hermite series sense) in terms of the ...
Chequerboard effects on spurious currents in the lattice Boltzmann equation for two-phase flows.
Guo, Zhaoli; Shi, Baochang; Zheng, Chuguang
2011-06-13
Spurious currents near an interface between different phases are a common undesirable feature of the lattice Boltzmann equation (LBE) method for two-phase systems. In this paper, we show that the spurious currents of a kinetic theory-based LBE have a significant dependence on the parity of the grid number of the underlying lattice, which can be attributed to the chequerboard effect. A technique that uses a Lax-Wendroff streaming is proposed to overcome this anomaly, and its performance is verified numerically.
Higher-order Galilean-invariant lattice Boltzmann model for microflows: single-component gas.
Yudistiawan, Wahyu Perdana; Kwak, Sang Kyu; Patil, D V; Ansumali, Santosh
2010-10-01
We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox. Finally, we present numerical results corresponding to Couette flow for two representative Knudsen numbers. We show that the off-lattice D3Q27 model exhibits better accuracy as compared to more widely used on-lattice D3Q19 or D3Q27 model. Finally, our construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.
A mass-conserving multiphase lattice Boltzmann model for simulation of multiphase flows
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
Fakhari, Abbas; Mitchell, Travis; Leonardi, Christopher; Bolster, Diogo
2017-11-01
Based on phase-field theory, we introduce a robust lattice-Boltzmann equation for modeling immiscible multiphase flows at large density and viscosity contrasts. Our approach is built by modifying the method proposed by Zu and He [Phys. Rev. E 87, 043301 (2013), 10.1103/PhysRevE.87.043301] in such a way as to improve efficiency and numerical stability. In particular, we employ a different interface-tracking equation based on the so-called conservative phase-field model, a simplified equilibrium distribution that decouples pressure and velocity calculations, and a local scheme based on the hydrodynamic distribution functions for calculation of the stress tensor. In addition to two distribution functions for interface tracking and recovery of hydrodynamic properties, the only nonlocal variable in the proposed model is the phase field. Moreover, within our framework there is no need to use biased or mixed difference stencils for numerical stability and accuracy at high density ratios. This not only simplifies the implementation and efficiency of the model, but also leads to a model that is better suited to parallel implementation on distributed-memory machines. Several benchmark cases are considered to assess the efficacy of the proposed model, including the layered Poiseuille flow in a rectangular channel, Rayleigh-Taylor instability, and the rise of a Taylor bubble in a duct. The numerical results are in good agreement with available numerical and experimental data.
Mei, Ren-Wei; Shyy, Wei; Yu, Da-Zhi; Luo, Li-Shi; Rudy, David (Technical Monitor)
2001-01-01
The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2014-05-01
We study the coupling between hydraulic and electric flows in a porous medium at small scale using the Lattice Boltzmann method. This method is a computational fluid dynamics technique that is used for advection and diffusion modeling. We implement a coupled Lattice Boltzmann algorithm that solves both the mass transport and the electric field arising from charges displacements. The streaming potential and electroosmosis phenomena occur in a variety of situations and derive from this coupling. We focus on the streaming potential which is described using the ratio between the created potential difference and the applied pressure gradient. The streaming potential is assumed to be a linear function of the fluid conductivity, but experimental results highlight anomalous behaviors at low and high salinity. We try to account for them by setting extreme conditions that are likely to generate non-linearities. Several pore radii are tested so as to determine what is the effect of a radius that is comparable to the Debye length, the screening length of the electric potential, due to the ions in the electrolyte. The volumetric integral of the electrical current is calculated for comparison with the 2D simulations. High values of zeta potential are tested to verify if the discrepancy regarding the theoretical result is concentration-dependent. We try to include a surface conductivity term in the coefficient formulation. Some tests including a rugosity on the channel walls are performed. All of these attempts show a normal behaviour of the streaming potential at high salinity. We observe a decrease of the ratio at low conductivity, showing that this ratio is modified when the pore radius becomes negligible compared with the Debye length, which is physically meaningful in little pores at low concentrations. References : S. Pride. Governing equations for the coupled electromagnetics and acoustics of porous media. Physical Review B, 50 : 15678-15696, 1994. D. A. Wolf
Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel
Liu, Haihu; Valocchi, Albert J.; Zhang, Yonghao; Kang, Qinjun
2014-01-01
To understand how thermocapillary forces manipulate the droplet motion in a confined microchannel, a lattice Boltzmann phase-field model is developed to simulate immiscible thermocapillary flows with consideration of fluid-surface interactions. Based on our recent work of Liu et al., 2013 [54], an interfacial force of potential form is proposed to model the interfacial tension force and the Marangoni stress. As only the first-order derivatives are involved, the proposed interfacial force is easily combined with the wetting boundary condition to account for fluid-surface interactions. The hydrodynamic equations are solved using a multiple-relaxation-time algorithm with the interfacial force treated as a forcing term, while an additional convection-diffusion equation is solved by a passive-scalar approach to obtain the temperature field, which is coupled to the interfacial tension by an equation of state. The model is first validated against analytical solutions for the thermocapillary-driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then demonstrated to produce the correct equilibrium contact angle for a binary fluid with different viscosities when a constant interfacial tension is taken into account. Finally, we numerically simulate the thermocapillary flows for a microfluidic droplet adhering on a solid wall and subject to a simple shear flow when a laser is applied to locally heat the fluids, and investigate the influence of contact angle and fluid viscosity ratio on the droplet dynamical behavior. The droplet motion can be completely blocked provided that the contact angle exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and approximately constant velocity. When the droplet motion is completely blocked, three steady vortices are clearly visible, and the droplet is fully filled by two counter-rotating vortices with the
Macroscopic Surface Tension in a Lattice Boltzmann BGK Model of Two Immiscible Fluids.
Thompson, S. P.; Halliday, I.; Care, C. M.
1997-08-01
We present a method by which an interface generating algorithm, similar to that of earlier lattice Boltzmann models of immisible fluids, may be extended to a two component, two-speed D2Q9 lattice Bhatnagar Gross Krook fluid. For two-dimensional, microcurrent-free planar interfaces between the two immiscible fluids we derive expressions for static interfacial tensions and interfacial distributions of the two fluids. Extending our analysis to curved interfaces we propose a scheme for incorporating the influence of interfacial microcurrents which is based upon general symmetry arguments and is correct to second order in lattice velocity. The analysis demonstrates that the interfacial microcurrents have only second order influence upon the macroscopic behaviour of the model. We find good agreement between our calculations and simulation results based on the microcurrent stream function and surface tension results from the pressure tensor or Laplace law.
An Eulerian description of the streaming process in the lattice Boltzmann equation
Lee Tae Hun
2003-01-01
This paper presents a novel strategy for solving discrete Boltzmann equation (DBE) for simulation of fluid flows. This strategy splits the solution procedure into streaming and collision steps as in the lattice Boltzmann equation (LBE) method. The streaming step can then be carried out by solving pure linear advection equations in an Eulerian framework. This offers two significant advantages over previous methods. First, the relationship between the relaxation parameter and the discretization of the collision term developed from the LBE method is directly applicable to the DBE method. The resulting DBE collision step remains local and poses no constraint on time step. Second, decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes. An implicit unstructured DBE method is constructed based on this strategy and is evaluated using several test cases of flow over a backward-facing step, lid-driven cavity flow, and flow past a circul...
2014-09-15
Lattice Boltzmann solver with immersible moving boundaries . The primary goal is to validate the model by comparing it with various...FEM: finite element method • FVM: finite volume method • IMB: immersible moving boundary • Kn: Knudsen number • LBM: Lattice Boltzmann method • Ma...2011. “An Efficient Framework for Fluid- Structure Interaction Using the Lattice Boltzmann Method and Immersed Moving Boundaries .” International
A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide
Allen, Rebecca
2013-01-01
The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently
Gray free-energy multiphase lattice Boltzmann model with effective transport and wetting properties
Zalzale, Mohamad; Ramaioli, M.; Scrivener, K. L.; McDonald, P. J.
2016-11-01
The paper shows that it is possible to combine the free-energy lattice Boltzmann approach to multiphase modeling of fluids involving both liquid and vapor with the partial bounce back lattice Boltzmann approach to modeling effective media. Effective media models are designed to mimic the properties of porous materials with porosity much finer than the scale of the simulation lattice. In the partial bounce-back approach, an effective media parameter or bounce-back fraction controls fluid transport. In the combined model, a wetting potential is additionally introduced that controls the wetting properties of the fluid with respect to interfaces between free space (white nodes), effective media (gray nodes), and solids (black nodes). The use of the wetting potential combined with the bounce-back parameter gives the model the ability to simulate transport and sorption of a wide range of fluid in material systems. Results for phase separation, permeability, contact angle, and wicking in gray media are shown. Sorption is explored in small sections of model multiscale porous systems to demonstrate two-step desorption, sorption hysteresis, and the ink-bottle effect.
Effects of Nanoparticles on Melting Process with Phase-Change Using the Lattice Boltzmann Method
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.
A multi-component lattice Boltzmann scheme: towards the mesoscale simulation of blood flow.
Dupin, M M; Halliday, I; Care, C M
2006-01-01
While blood at the macroscopic scale is frequently treated as a continuum by techniques such as computational fluid dynamics, its mesoscale behaviour is not so well investigated or understood. At this scale, the deformability of each cell within the plasma is important and cannot be ignored. However there is currently a lack of efficient computational techniques able to simulate a large number of deformable particles such as blood cells. This paper addresses this problem and demonstrates the applicability of the authors' recent multi-component lattice Boltzmann method for the simulation of a large number of mutually immiscible liquid species [Dupin MM, Halliday I, Care CM. Multi-component lattice boltzmann equation for mesoscale blood flow. J Phys A: Math Gen 2003;36:8517-34]. In here, biological cells are treated as immiscible, deformable, and relatively viscous drops (compared to the surrounding fluid). The validation of the model is based on the work of Goldsmith on the flow of solid particles, deformable particles and red blood cells [Goldsmith HL, Marlow JC. Flow behavior of erythrocytes. II. Particle motions in concentrated suspensions of ghost cells. J Colloid Interf Sci 1979;71:383-407]. We demonstrate, in particular, that the model recovers Goldsmith's observations on the flow properties of red blood cells and also the experimental observations of Frank on the flow of solid beads [Frank M, Anderson D, Weeks ER, Morris JF. Particle migration in pressure-driven flow of a brownian suspension. J Fluid Mech 2003;493:363-78]. The current article is the first validation of our new lattice Boltzmann model for a large number of deformable particles in this context and demonstrates that the method provides a new, and effective, approach for the modeling of mesoscale blood flow.
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.
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2015-04-01
Streaming-potentials are produced by electrokinetic effects in relation to fluid flow, and are used for geophysical prospecting. The electrokinetic coupling is induced by the coupling between the fluid flow and the electrical flow, which results from the presence of an electrical double layer at the rock/pore water interface. When fluid flows through a porous medium, it gives rise to an electric streaming current, counterbalanced by a conduction current, leading to a resulting measurable electrical voltage. Streaming current generation is well understood in water-saturated porous media, but the streaming potential coefficient at very-low and very-high salinities can show a non-linear behaviour. The aim of this study is to model the streaming potential coefficient using Lattice Boltzmann simulations and to quantify the effect of parameters such as fluid conductivity and rugosity. The lattice Boltzmann method is computational fluid dynamics technique that allows to solve advection and diffusion phenomena. We implement a coupled lattice Boltzmann algorithm that solves both the flow in a rock channel and the electrical diffusion to calculate the streaming potential coefficient (ratio between the created potential difference and the applied pressure gradient) in various situations. In this study, we aim at quantifying the change that is brought by taking into account the dependence of the local fluid conductivity on the local concentration. We also observe the influence of a rough surface on the behaviour of this coefficient with the fluid salinity. We try to generate non-linearities regarding the theoretical prediction of the streaming potential coefficient with a view to explaining existing experimental measurements.
Directory of Open Access Journals (Sweden)
Keijo Kalervo Mattila
2014-01-01
Full Text Available We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils.
Mattila, Keijo Kalervo; Hegele Júnior, Luiz Adolfo; Philippi, Paulo Cesar
2014-01-01
We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils.
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 shown that the model is in a good agreement with the classical Nusselt equations for the laminar flow regime. Comparisons of the present model with other empirical models also demonstrate good agreement beyond the laminar regime. This allows the film condensation modeling at high film Reynolds numbers...
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
is necessary. Computational fluid dynamics (CFD) comes to play at this stage. Formulation of a possible CFD model that is able to solve multi-phase and multi component non-Newtonian flow with complex boundary conditions and fiber suspension and preferably in reasonable time brings a very challenging task....... 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....
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.
Effect of Rolling Massage on the Vortex Flow in Blood Vessels with Lattice Boltzmann Simulation
Yi, Hou Hui
The rolling massage manipulation is a classic Chinese Medical Massage, which is a nature therapy in eliminating many diseases. Here, the effect of the rolling massage on the cavity flows in blood vessel under the rolling manipulation is studied by the lattice Boltzmann simulation. The simulation results show that the vortex flows are fully disturbed by the rolling massage. The flow behavior depends on the rolling velocity and the rolling depth. Rolling massage has a better effect on the flows in the cavity than that of the flows in a planar blood vessel. The result is helpful to understand the mechanism of the massage and develop the rolling techniques.
Calculation of drag and torque coefficients by time-independent lattice-Boltzmann method.
Ding, E J
2014-09-01
A method is developed to calculate the drag and torque coefficients of an isolated particle in a Stokes flow. The method is based on solving the time-independent lattice-Boltzmann equation. The advantage of this method is that the algorithm is easy to code, the method can be applied to any shape of the particle without complicated implementation, and the computational cost is independent of the shape of the particle. This method is validated and shown to be accurate by comparing with analytical solutions for certain problems.
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...... for computation of effective viscosities. It is shown that the presented model based on well established methods and without any artificial parameters, numerical tricks or modifications provides an efficient tool that can be applied to a range of engineering problems on different length-scales yielding results...
Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method
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.
Modeling and simulation of ocean wave propagation using lattice Boltzmann method
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.
Wang, Huimin
2017-01-01
In this paper, a new lattice Boltzmann model for the Korteweg-de Vries (KdV) equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher- order moments of equilibrium distribution functions are obtained. In order to make the scheme obey the three conservation laws of the KdV equation, two equilibrium distribution functions are used and a correlation between the first conservation law and the second conservation law is constructed. In numerical examples, the numerical results of the KdV equation obtained by this scheme are compared with those results obtained by the previous lattice Boltzmann model. Numerical experiments demonstrate this scheme can be used to reduce the truncation error of the lattice Boltzmann scheme and preserve the three conservation laws.
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.
Directory of Open Access Journals (Sweden)
Stuart Bartlett
2017-08-01
Full Text Available The lattice Boltzmann method is an efficient computational fluid dynamics technique that can accurately model a broad range of complex systems. As well as single-phase fluids, it can simulate thermohydrodynamic systems and passive scalar advection. In recent years, it also gained attention as a means of simulating chemical phenomena, as interest in self-organization processes increased. This paper will present a widely-used and versatile lattice Boltzmann model that can simultaneously incorporate fluid dynamics, heat transfer, buoyancy-driven convection, passive scalar advection, chemical reactions and enthalpy changes. All of these effects interact in a physically accurate framework that is simple to code and readily parallelizable. As well as a complete description of the model equations, several example systems will be presented in order to demonstrate the accuracy and versatility of the method. New simulations, which analyzed the effect of a reversible reaction on the transport properties of a convecting fluid, will also be described in detail. This extra chemical degree of freedom was utilized by the system to augment its net heat flux. The numerical method outlined in this paper can be readily deployed for a vast range of complex flow problems, spanning a variety of scientific disciplines.
Galilean-invariant lattice-Boltzmann simulation of liquid-vapor interface dynamics.
Kalarakis, A N; Burganos, V N; Payatakes, A C
2002-05-01
A two-dimensional two-phase lattice-Boltzmann model is presented and used for the study of interfacial phenomena under static and flow conditions. The model is based on the nonideal lattice-Boltzmann model proposed originally by Swift, Osborn, and Yeomans [Phys. Rev. Lett. 75, 830 (1995)] and makes it possible to couple a prescribed equation of state with the pressure tensor at the interface and the excess free-energy density formalism. The characteristic feature of the present model is that Galilean invariance is restored in the presence of interfaces without sacrificing any of the merits of the original model and, hence, the Navier-Stokes equation is adequately (to second order) recovered. The fluid properties can be prescribed in a thermodynamically consistent manner, which remains accurate at states close to the critical point. The model is first validated through static equilibrium tests and then applied to flow systems. It is shown that the simulator can reproduce some known two-phase flow configurations, like the motion of deformable droplets under the action of an external flow field. The simulator can also capture some interesting events during jet breakup and can be useful for the parametric study of the process in the two-dimensional case.
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Jin Su
2017-11-01
Full Text Available Elastic instabilities could happen in viscoelastic flows as the Weissenberg number is enlarged, and this phenomenon makes the numerical simulation of viscoelastic fluids more difficult. In this study, we introduce a coupled lattice Boltzmann method to solve the equations of viscoelastic fluids, which has a great capability of simulating the high Weissenberg number problem. Different from some traditional methods, two kinds of distribution functions are defined respectively for the evolution of the momentum and stress tensor equations. We mainly aim to investigate some key factors of the symmetry-breaking transition induced by elastic instability of viscoelastic fluids using this numerical coupled lattice Boltzmann method. In the results, we firstly find that the ratio of kinematical viscosity has an important influence on the transition of the elastic instability; the transition between the single stationary and cycling dominant vortex can be controlled via changing the ratio of kinematical viscosity in a periodic extensional flow. Finally, we can also observe a new transition state of instability for the flow showing the banded structure at higher Weissenberg number.
Chen, Z.; Shu, C.; Tan, D.
2017-05-01
In this paper, a three-dimensional simplified and unconditionally stable lattice Boltzmann method (3D-USLBM) is proposed for simulating incompressible isothermal/thermal flows. This method is developed by reconstructing solutions to the macroscopic governing equations recovered from the lattice Boltzmann equation and resolved in a predictor-corrector scheme. The final formulations of 3D-USLBM only involve the equilibrium and the non-equilibrium distribution functions. Among them, the former is calculated from the macroscopic variables and the latter is evaluated from the difference between two equilibrium distribution functions at different locations and time levels. Thus, 3D-USLBM directly tracks the evolution of macroscopic variables, which yields lower cost in virtual memory and facilitates the implementation of physical boundary conditions. A von Neumann stability analysis was performed on the present method to theoretically prove its unconditional stability. By imposing a regular Lagrange interpolation algorithm, this method can be flexibly extended to a non-uniform Cartesian mesh or body-fitted mesh with curved boundaries. Four numerical tests, that is, plane Poiseuille flow, 3D lid-driven cavity flow and 3D natural convection in a cubic cavity, and concentric annulus, were conducted to verify the stability, accuracy, and flexibility of the presented method.
Lattice Boltzmann simulations of the time evolution of living multicellular systems.
Cristea, Artur; Neagu, Adrian; Sofonea, Victor
2011-01-01
Embryonic tissues and multicellular aggregates of adult cells mimic the behavior of highly viscous liquids. The liquid analogy helps to understand morphogenetic phenomena, such as cell sorting and tissue fusion, observed in developmental biology and tissue engineering. Tissue fusion is vital in tissue printing, an emergent technique based on computer-controlled deposition of tissue fragments and biocompatible materials. Computer simulations proved useful in predicting post-printing shape changes of tissue constructs. The simulation methods available to date, however, are unable to describe the time evolution of living systems made of millions of cells. The Lattice Boltzmann (LB) approach allows the implementation of interaction forces between the constituents of the system and yields time evolution in terms of distribution functions. With tissue engineering applications in mind, we have developed a finite difference Lattice Boltzmann model of a multicellular system and applied it to simulate the sidewise fusion of two contiguous cylinders made of cohesive cells and embedded in a medium (hydrogel). We have identified a biologically relevant range of model parameters. The proposed LB model may be extended to describe the time evolution of more complex multicellular structures such as sheets or tubes produced by tissue printing. © 2011 – IOS Press and the authors. All rights reserved
Ezzatneshan, Eslam
2017-11-01
Cavitating flow through the orifice is numerically solved by implementation of the lattice Boltzmann method. The pseudo-potential single-component multiphase Shan-Chen model is used to resolve inter-particle interactions and phase change between the liquid and its vapor. The effect of surface wettability on the cavity formation and shape is studied by imposing an appropriate wall boundary condition for the contact angle between the liquid-vapor interface and the solid surface. Efficiency of the numerical approach presented is examined by computing the cavitation inception, growth, and collapse for internal cavitating flows over a sack-wall obstacle placed inside a channel and through a convergent-divergent nozzle section. The results obtained demonstrate that hydrophobic walls act as surface nuclei and contribute to the process of cavitation inception even at high cavitation numbers. In contrast, the solid wall with hydrophilic properties shows no contribution to the onset of cavitation in the geometries studied. High values for the flow velocity corresponding to low cavitation numbers are needed to observe the cavitation inception over the geometries studied with the hydrophilic solid wall. The study shows that the present computational technique based on the implementation of the lattice Boltzmann method with the Shan-Chen model employed is robust and efficient to predict the cavitation phenomena by considering surface wettability effects and also accurate enough for computing the cavitating flow properties at different conditions.
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.
Large eddy simulation of rotating turbulent flows and heat transfer by the lattice Boltzmann method
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.
Directory of Open Access Journals (Sweden)
Jifu Tan
2016-02-01
Full Text Available Nanodrug-carrier delivery in the blood stream is strongly influenced by nanoparticle (NP dispersion. This paper presents a numerical study on NP transport and dispersion in red blood cell (RBC suspensions under shear and channel flow conditions, utilizing an immersed boundary fluid-structure interaction model with a lattice Boltzmann fluid solver, an elastic cell membrane model and a particle motion model driven by both hydrodynamic loading and Brownian dynamics. The model can capture the multiphase features of the blood flow. Simulations were performed to obtain an empirical formula to predict NP dispersion rate for a range of shear rates and cell concentrations. NP dispersion rate predictions from the formula were then compared to observations from previous experimental and numerical studies. The proposed formula is shown to accurately predict the NP dispersion rate. The simulation results also confirm previous findings that the NP dispersion rate is strongly influenced by local disturbances in the flow due to RBC motion and deformation. The proposed formula provides an efficient method for estimating the NP dispersion rate in modeling NP transport in large-scale vascular networks without explicit RBC and NP models.
GPU accelerated study of heat transfer and fluid flow by lattice Boltzmann method on CUDA
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
Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei
2017-08-01
Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.
Progress in lattice Boltzmann methods for magnetohydrodynamic flows relevant to fusion applications
Energy Technology Data Exchange (ETDEWEB)
Pattison, M.J. [MetaHeuristics LLC, 3944 State St., Ste. 350, Santa Barbara, CA 93105 (United States)], E-mail: martin@metah.com; Premnath, K.N. [MetaHeuristics LLC, 3944 State St., Ste. 350, Santa Barbara, CA 93105 (United States); UCSB, Chemical Engineering Department, Santa Barbara, CA 93106 (United States); Morley, N.B.; Abdou, M.A. [UCLA, MAE Department, 44-114 Engineering IV, 420 Westwood Pza, Los Angeles, CA 90095-1597 (United States)
2008-05-15
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.
Randles, Amanda Elizabeth
Accurate and reliable modeling of cardiovascular hemodynamics has the potential to improve understanding of the localization and progression of heart diseases, which are currently the most common cause of death in Western countries. However, building a detailed, realistic model of human blood flow is a formidable mathematical and computational challenge. The simulation must combine the motion of the fluid, the intricate geometry of the blood vessels, continual changes in flow and pressure driven by the heartbeat, and the behavior of suspended bodies such as red blood cells. Such simulations can provide insight into factors like endothelial shear stress that act as triggers for the complex biomechanical events that can lead to atherosclerotic pathologies. Currently, it is not possible to measure endothelial shear stress in vivo, making these simulations a crucial component to understanding and potentially predicting the progression of cardiovascular disease. In this thesis, an approach for efficiently modeling the fluid movement coupled to the cell dynamics in real-patient geometries while accounting for the additional force from the expansion and contraction of the heart will be presented and examined. First, a novel method to couple a mesoscopic lattice Boltzmann fluid model to the microscopic molecular dynamics model of cell movement is elucidated. A treatment of red blood cells as extended structures, a method to handle highly irregular geometries through topology driven graph partitioning, and an efficient molecular dynamics load balancing scheme are introduced. These result in a large-scale simulation of the cardiovascular system, with a realistic description of the complex human arterial geometry, from centimeters down to the spatial resolution of red-blood cells. The computational methods developed to enable scaling of the application to 294,912 processors are discussed, thus empowering the simulation of a full heartbeat. Second, further extensions to enable
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
On a two-relaxation-time D2Q9 lattice Boltzmann model for the Navier-Stokes equations
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.
Development and validation of a 3D Lattice Boltzmann model for volcano aeroacoustics
Brogi, Federico; Bonadonna, Costanza; Ripepe, Maurizio; Chopard, Bastien; Malaspinas, Orestis; Latt, Jonas; Falcone, Jean-Luc
2015-04-01
Infrasound measurements have a great potential for the real time characterization of volcanic plume source parameters [Ripepe et al., 2013]. Nonetheless many shortcomings have been highlighted in the understanding of the infrasound monitoring. In particular, the application of the classical acoustic source models to volcanic explosive eruptions has shown to be challenging and a better knowledge of the link between the acoustic radiation and actual volcanic fluid dynamics processes is required. New insights into this subject could be given by the study of realistic aeroacoustic numerical simulations of a volcanic jet. Our work mainly focuses on developing and validating such numerical model to determine when and if classical model source theory can be applied to explain volcanic infrasound data. Lattice Boltzmann strategies (LB) provide the opportunity to develop an accurate, computationally fast, 3D physical model for a volcanic jet and wave propagation. In the field of aeroacoustic applications, dedicated LB schemes has been proven to have the low dispersion and dissipative properties needed for capturing the weak acoustic pressure fluctuations. However, when dealing with simulations of realistic flows, artificial boundaries are defined around the flow region. The reflected waves from these boundaries can have significant influence on the flow field and overwhelm the acoustic field of interest. A special absorbing boundary layer has been implemented in our model to suppress the reflected waves [Xu et al., 2013]. In addition, for highly multi-scale turbulent flows, such as volcanic plumes, the number of grid points needed to represent the smallest scales might become intractable and the most complicated physics happen only in small portions of the computational domain. The implementation of the grid refinement, in our model allow us to insert local finer grids only where is actually needed [Lagrava et al., 2012] and to increase the size of the computational domain
Ambruş, Victor Eugen; Sofonea, Victor
2014-04-01
The Gauss-Laguerre quadrature method is used on the Cartesian semiaxes in the momentum space to construct a family of lattice Boltzmann models. When all quadrature orders Qx, Qy, Qz equal N+1, the Laguerre lattice Boltzmann model LLB(Qx,Qy,Qz) exactly recovers all moments up to order N of the Maxwell-Boltzmann equilibrium distribution function f(eq), calculated over any Cartesian octant of the three-dimensional momentum space. Results of Couette flow simulations at Kn=0.1, 0.5, 1.0 and in the ballistic regime are reported. Specific microfluidic effects (velocity slip, temperature jump, longitudinal heat flux) are well captured up to Kn=0.5, as demonstrated by comparison to direct simulation Monte Carlo results. Excellent agreement with analytic results is obtained in the ballistic regime.
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:
Directory of Open Access Journals (Sweden)
Haiqing Si
2015-03-01
Full Text Available Lattice Boltzmann method combined with large eddy simulation is developed in the article to simulate fluid flow at high Reynolds numbers. A subgrid model is used as a large eddy simulation model in the numerical simulation for high Reynolds flow. The idea of subgrid model is based on an assumption to include the physical effects that the unresolved motion has on the resolved fluid motion. It takes a simple form of eddy viscosity models for the Reynolds stress. Lift and drag evaluation in the lattice Boltzmann equation takes momentum-exchange method for curved body surface. First of all, the present numerical method is validated at low Reynolds numbers. Second, the developed lattice Boltzmann method/large eddy simulation method is performed to solve flow problems at high Reynolds numbers. Some detailed quantitative comparisons are implemented to show the effectiveness of the present method. It is demonstrated that lattice Boltzmann method combined with large eddy simulation model can efficiently simulate high Reynolds numbers’ flows.
Lattice Boltzmann simulations of immiscible displacement process with large viscosity ratios
Rao, Parthib; Schaefer, Laura
2017-11-01
Immiscible displacement is a key physical mechanism involved in enhanced oil recovery and carbon sequestration processes. This multiphase flow phenomenon involves a complex interplay of viscous, capillary, inertial and wettability effects. The lattice Boltzmann (LB) method is an accurate and efficient technique for modeling and simulating multiphase/multicomponent flows especially in complex flow configurations and media. In this presentation we present numerical simulation results of displacement process in thin long channels. The results are based on a new psuedo-potential multicomponent LB model with multiple relaxation time collision (MRT) model and explicit forcing scheme. We demonstrate that the proposed model is capable of accurately simulating the displacement process involving fluids with a wider range of viscosity ratios (>100) and which also leads to viscosity-independent interfacial tension and reduction of some important numerical artifacts.
Grayscale lattice Boltzmann model for multiphase heterogeneous flow through porous media.
Pereira, Gerald G
2016-06-01
The grayscale lattice Boltzmann (LB) model has been recently developed to model single-phase fluid flow through heterogeneous porous media. Flow is allowed in each voxel but the degree of flow depends on that voxel's resistivity to fluid motion. Here we extend the grayscale LB model to multiphase, immiscible flow. The new model is outlined and then applied to a number of test cases, which show good agreement with theory. This method is subsequently used to model the important case where each voxel may have a different resistance to each particular fluid that is passing through it. Finally, the method is applied to model fluid flow through real porous media to demonstrate its capability. Both the capillary and viscous flow regimes are recovered in these simulations.
Lycett-Brown, Daniel; Luo, Kai H
2015-02-01
The pseudopotential lattice Boltzmann method has been widely used to simulate many multiphase flow applications. However, there still exist problems with reproducing realistic values of density ratio and surface tension. In this study, a higher-order analysis of a general forcing term is derived. A forcing scheme is then constructed for the pseudopotential method that is able to accurately reproduce the full range of coexistence curves. As a result, multiphase flow of arbitrarily high density ratios independent of the surface tension can be simulated. Furthermore, the interface width can be tuned to allow for grid refinement and systematic error reduction. Numerical results confirm that the proposed scheme enables independent control of density ratio, surface tension, and interface width simultaneously.
Parallelization of a coupled immersed boundary and lattice Boltzmann method for fluid and heat flow
Kasparek, Andrzej; Łapka, Piotr
2017-07-01
The paper presents first approach to the GPU-based parallelization of the coupled Immersed Boundary and Lattice Boltzmann Method. The proposed numerical simulator deals with fluid and heat flow in a domains with complex internal boundaries using Cartesian grid. The solution algorithm was parallelized with the aid of the CUDA architecture. Several heat and fluid flow problems, i.e., heated lid-driven flow and laminar natural convection in square domains without internal obstacles and isothermal flow past stationary cylinder were investigated. Satisfactory accelerations of the solution times were obtained for problems without internal boundaries. For test case with internal boundaries decrease in the parallel computing efficiency was observed as a results of numerical handling of the internal boundaries.
Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries
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
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 model for free-surface flow and its application to filling process in casting
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 ...
Hybrid Lattice Boltzmann Method for the Simulation of Blending Process in Static Mixers
Latt, Jonas; Kontaxakis, Dimitrios; Chatagny, Laurent; Muggli, Felix; Chopard, Bastien
2013-12-01
A lattice Boltzmann method is proposed to simulate the blending of two fluids in static, laminar mixers. The method uses a mesh-based algorithm to solve for the fluid flow, and a meshless technique to trace the interface between the blended fluids. This hybrid approach is highly accurate, because the position of the interface can be traced beyond the resolution of the grid. The numerical diffusion is negligible in this model, and it is possible to reproduce mixing patterns that contain more than one hundred striations with high fidelity. The implementation of this method in the massively parallel library Palabos is presented, and simulation results are compared with experimental data to emphasize the accuracy of the results.
Phase-field-lattice Boltzmann studies for dendritic growth with natural convection
Takaki, Tomohiro; Rojas, Roberto; Sakane, Shinji; Ohno, Munekazu; Shibuta, Yasushi; Shimokawabe, Takashi; Aoki, Takayuki
2017-09-01
Simulating dendritic growth with natural convection is challenging because of the size of the computational domain required when compared to the dendrite scale. In this study, a phase-field-lattice Boltzmann model was used to simulate dendritic growth in the presence of natural convection due to a difference in solute concentration. To facilitate and accelerate the large-scale simulation, a parallel computing code with multiple graphics processing units was developed. The effects of the computational domain size as well as those of gravity on the dendritic morphologies were examined by performing two-dimensional free dendritic growth simulations with natural convection. The effects of the gravity direction on the dendrite spacing and morphology were also investigated by simulating unidirectional solidification from multiple seeds.
Lattice Boltzmann modeling of self-propelled Leidenfrost droplets on ratchet surfaces
Li, Q; Francois, M M; Hu, A J
2015-01-01
In this paper, the self-propelled motion of Leidenfrost droplets on ratchet surfaces is numerically investigated with a thermal multiphase lattice Boltzmann model with liquid-vapor phase change. The capability of the model for simulating evaporation is validated via the D2 law. Using the model, we first study the performances of Leidenfrost droplets on horizontal ratchet surfaces. It is numerically shown that the motion of self-propelled Leidenfrost droplets on ratchet surfaces is owing to the asymmetry of the ratchets and the vapor flows beneath the droplets. It is found that the Leidenfrost droplets move in the direction toward the slowly inclined side from the ratchet peaks, which agrees with the direction of droplet motion in experiments [Linke et al., Phys. Rev. Lett., 2006, 96, 154502]. Moreover, the influences of the ratchet aspect ratio are investigated. For the considered ratchet surfaces, a critical value of the ratchet aspect ratio is approximately found, which corresponds to the maximum droplet mo...
Lattice Boltzmann methods for multiphase flow and phase-change heat transfer
Li, Qing; Kang, Q J; He, Y L; Chen, Q; Liu, Q
2016-01-01
Over the past few decades, tremendous progress has been made in the development of particle-based discrete simulation methods versus the conventional continuum-based methods. In particular, the lattice Boltzmann (LB) method has evolved from a theoretical novelty to a ubiquitous, versatile and powerful computational methodology for both fundamental research and engineering applications. It is a kinetic-based mesoscopic approach that bridges the microscales and macroscales, which offers distinctive advantages in simulation fidelity and computational efficiency. Applications of the LB method have been found in a wide range of disciplines including physics, chemistry, materials, biomedicine and various branches of engineering. The present work provides a comprehensive review of the LB method for thermofluids and energy applications, focusing on multiphase flows, thermal flows and thermal multiphase flows with phase change. The review first covers the theoretical framework of the LB method, revealing the existing ...
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...... forcing is used to explicitly represent individual ﬁbers in the ﬂuid. A novel variable time sub-stepping algorithm for dynamics of immersed rigid particles ensuring stability of simulations has been developed which, together with the IBM, provides an efﬁcient, yet accurate way to simulate ﬂow...... friction between ﬁbers and between ﬁbers and boundary conditions are introduced. Several simulation scenarios are presented and compared to experimental data to validate the proposed approach. Further an extension of the model to the structural scale is discussed and demonstrated on an example modeling...
Density fluctuations in lattice-Boltzmann simulations of multiphase fluids in a closed system
Energy Technology Data Exchange (ETDEWEB)
H. Basagaoglu; Paul Meakin
2007-02-01
A two-dimensional single component two-phase lattice Boltzmann model was used to simulate the Rayleigh-Taylor instability in a closed system. Spatiotemporally variable densities were generated by gravity acting on the fluid density. The density fluctuations were triggered by rapid changes in the fluid velocity induced by changes in the interface geometry and impact of the dense fluid on the rigid lower boundary of the computational domain. The ratio of the maximum density fluctuations to the maximum fluid velocity increased more rapidly at low velocities than at high velocities. The ratio of the maximum density fluctuations in the dense phase to its maximum velocity was on the order of the inverse of the sound speed. The solution became unstable when the density-based maximum local Knudsen number exceeded 0.13.
Lattice Boltzmann Method for Two-phase Flows on Unstructured Mesh
Lee, Taehun; Baroudi, Lina; Wardle, Kent
2013-11-01
A lattice Boltzmann method with Galerkin finite element discretization (FE-LBM) is proposed to simulate incompressible two-phase flows on unstructured mesh. Two-distribution functions are used to recover the transport equations for the order parameter, pressure, and momentum. Consistent treatment of streaming and intermolecular forcing terms in FE-LBM enables us to use small equilibrium interface thickness compared with the existing two-phase LBMs and thus to achieve numerical stability at higher Reynolds number and large material property contrast. Several benchmark test cases with non-trivial wall boundaries will be presented, which include turbulent free surface flow inside a concentric rotating cylinder, drop impact on patterned surfaces, and bubbly flows. This work is partially supported by the DOE's NEUP.
Simulation of non-ideal gases and liquid-gas phase transitions by lattice Boltzmann equation
Shan, X; Xiaowen Shan; Hudong Chen
1994-01-01
We describe in detail a recently proposed lattice-Boltzmann model for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey non-ideal gas equations of state and can undergo a liquid-gas type phase transition. The model is shown to be momentum-conserving. From the microscopic mechanical stability condition, the densities in bulk liquid and gas phases are obtained as functions of a temperature-like parameter. Comparisons with the thermodynamic theory of phase transition show that the LBE model can be made to correspond exactly to an isothermal process. The density profile in the liquid-gas interface is also obtained as function of the temperature-like parameter and is shown to be isotropic. The surface tension, which can be changed independently, is calculated. The analytical conclusions are verified by numerical simulations. (To appear in Phys. Rev. E)
Analysis of the absorbing layers for the weakly-compressible lattice Boltzmann schemes
Xu, Hui
2012-01-01
It has been demonstrated that Lattice Boltzmann schemes (LBSs) are very efficient for Computational AeroAcoustics (CAA). In order to handle the issue of absorbing acoustic boundary conditions for LBS, three kinds of damping terms are proposed and added into the right hand sides of the governing equations of LBS. From the classical theory, these terms play an important role to absorb and minimize the acoustic wave reflections from computational boundaries. Meanwhile, the corresponding macroscopic equations with the damping terms are recovered for analyzing the macroscopic behaviors of the these damping terms and determining the critical absorbing strength. Further, in order to detect the dissipation and dispersion behaviors, the linearized LBS with the damping terms is derived and analyzed. The dispersive and dissipative properties are explored in the wave-number spaces via the Von Neumann analysis. The related damping strength critical values and the optimal absorbing term are addressed. Finally, some benchma...
Multiscale Lattice Boltzmann method for flow simulations in highly heterogenous porous media
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.
Directory of Open Access Journals (Sweden)
G Boroni
2017-03-01
Full Text Available Lattice Boltzmann Method (LBM has shown great potential in fluid simulations, but performance issues and difficulties to manage complex boundary conditions have hindered a wider application. The upcoming of Graphic Processing Units (GPU Computing offered a possible solution for the performance issue, and methods like the Immersed Boundary (IB algorithm proved to be a flexible solution to boundaries. Unfortunately, the implicit IB algorithm makes the LBM implementation in GPU a non-trivial task. This work presents a fully parallel GPU implementation of LBM in combination with IB. The fluid-boundary interaction is implemented via GPU kernels, using execution configurations and data structures specifically designed to accelerate each code execution. Simulations were validated against experimental and analytical data showing good agreement and improving the computational time. Substantial reductions of calculation rates were achieved, lowering down the required time to execute the same model in a CPU to about two magnitude orders.
Flow and dispersion in anisotropic porous media: a Lattice-Boltzmann study
Maggiolo, Dario; Guarnieri, Massimo
2016-01-01
Given their capability of spreading active chemical species and collecting electricity, porous media made of carbon fibers are extensively used as diffusion layers in energy storage systems, such as redox flow batteries. In spite of this, the dispersion dynamics of species inside porous media is still not well understood and often lends itself to different interpretations. Actually, the microscopic design of efficient porous media which can potentially and effectively improve the performances of flow batteries, is a still open challenge. The present study aims to investigate the effect of fibrous media micro-structure on dispersion, in particular the effect of fiber orientation on drag and dispersion dynamics. Several Lattice-Boltzmann simulations of {flows through} differently-oriented fibrous media coupled with Lagrangian simulations of particle tracers have been performed. Results show that orienting fibers preferentially along the streamwise direction minimizes the drag and maximizes the dispersion, which...
Pradipto; Purqon, Acep
2017-07-01
Lattice Boltzmann Method (LBM) is the novel method for simulating fluid dynamics. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. The common collision model of LBM is the BGK with a constant single relaxation time τ. However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity. The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. The tests concluded that LBM with MRT are more stable than BGK, and have a similar accuracy. The maximum Reynolds number that converges for BGK is 3200 and 7500 for MRT respectively.
Lattice Boltzmann simulation of coalescence of multiple droplets on nonideal surfaces.
Zhou, Wenchao
2015-11-01
The interaction dynamics of droplets on a solid surface is a fundamental problem that is important to a wide variety of industrial applications, such as inkjet printing. Most previous research has focused on a single droplet and little research has been reported on the dynamics of multiple-droplet interactions on surfaces. Recently, Zhou et al. [W. Zhou, D. Loney, A. G. Fedorov, F. L. Degertekin, and D. W. Rosen, Lattice Boltzmann simulations of multiple-droplet interaction dynamics, Phys. Rev. E 89, 033311 (2014)] reported an efficient numerical solver based on the lattice Boltzmann method (LBM) that enabled the simulation of the multiple-droplet interaction dynamics on an ideal surface (i.e., smooth and homogeneous). In order to predict the interaction dynamics in the real world, it is necessary to take into consideration the contact angle hysteresis phenomenon on a nonideal surface, which is possibly caused by the surface roughness and chemical inhomogeneity of the surface. In this paper a dynamic contact angle boundary condition is developed to take into account the contact angle hysteresis effect based on the previously reported LBM. The improved LBM is validated with experimental data from the literature. The influence of the droplet impact conditions (e.g., fluid properties and impingement velocity), droplet spacing, and surface conditions on the two-droplet interaction dynamics is investigated with the validated LBM. Interesting phenomena are observed and discussed. The interaction of a line of six droplets on a nonideal surface is simulated to demonstrate the powerful capability of the developed numerical solver in simulating the multiple-droplet interaction dynamics in the real world.
Energy Technology Data Exchange (ETDEWEB)
Elton, A.B.H.
1990-09-24
A numerical theory for the massively parallel lattice gas and lattice Boltzmann methods for computing solutions to nonlinear advective-diffusive systems is introduced. The convergence theory is based on consistency and stability arguments that are supported by the discrete Chapman-Enskog expansion (for consistency) and conditions of monotonicity (in establishing stability). The theory is applied to four lattice methods: Two of the methods are for some two-dimensional nonlinear diffusion equations. One of the methods is for the one-dimensional lattice method for the one-dimensional viscous Burgers equation. And one of the methods is for a two-dimensional nonlinear advection-diffusion equation. Convergence is formally proven in the L{sub 1}-norm for the first three methods, revealing that they are second-order, conservative, conditionally monotone finite difference methods. Computational results which support the theory for lattice methods are presented. In addition, a domain decomposition strategy using mesh refinement techniques is presented for lattice gas and lattice Boltzmann methods. The strategy allows concentration of computational resources on regions of high activity. Computational evidence is reported for the strategy applied to the lattice gas method for the one-dimensional viscous Burgers equation. 72 refs., 19 figs., 28 tabs.
Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.
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.
Coclite, Alessandro; Pascazio, Giuseppe; Decuzzi, Paolo
2016-01-01
Modelling the vascular transport and adhesion of man-made particles is crucial for optimizing their efficacy in the detection and treatment of diseases. Here, a Lattice Boltzmann and Immersed Boundary methods are combined together for predicting the near wall dynamics of particles with different shapes in a laminar flow. For the lattice Boltzmann modelling, a Gauss-Hermite projection is used to derive the lattice equation, wall boundary conditions are imposed through the Zou-He framework, and a moving least squares algorithm accurately reconstructs the forcing term accounting for the immersed boundary. First, the computational code is validated against two well-known test cases: the sedimentation of circular and elliptical cylinders in a quiescent fluid. A very good agreement is observed between the present results and those available in the literature. Then, the transport of circular, elliptical, rectangular, square and triangular particles is analyzed in a Couette flow, at Re=20. All particles drifted later...
Conjugate heat and mass transfer in the lattice Boltzmann equation method.
Li, Like; Chen, Chen; Mei, Renwei; Klausner, James F
2014-04-01
An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer in porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved
Pore-scale simulation of miscible displacement in porous media using the lattice Boltzmann method
Xia, Ming
2016-03-01
A numerical model based on the lattice Boltzmann method is presented to investigate the viscous fingering phenomena of miscible displacement processes in porous media, which involves the fluid flow, heat transfer and mass transport. Especially, temperature- and concentration-dependent pore-fluid viscosity is considered. A complete list is derived and given for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled problems involving fluid flow, heat transfer and mass transport using the LBM. To demonstrate the proposed model capacity, two different complex geometry microstructures using high resolution micro-computed tomography (micro-CT) images of core sample have been obtained and incorporated as computation geometries for modeling miscible displacement processes in porous media. The viscous fingering phenomena of miscible displacement processes are simulated in two different cases, namely in a channel and a porous medium respectively. Some influencing factors on the miscible displacement process, such as the pore-scale microstructure, Le number and Re number, are studied in great detail. The related simulation results have demonstrated that: (1) the existence of the pore-scale microstructure can have a significant effect on the front morphologies and front propagation speed in the miscible displacement process; (2) as the Le number increases, the fluid front and thermal front evolve differently, with the thermal front being less unstable due to more diffusion; (3) a larger Re number can lead to an increase in the propagation speed of the front.
Quasiequilibrium lattice Boltzmann models with tunable bulk viscosity for enhancing stability.
Asinari, Pietro; Karlin, Ilya V
2010-01-01
Taking advantage of a closed-form generalized Maxwell distribution function [P. Asinari and I. V. Karlin, Phys. Rev. E 79, 036703 (2009)] and splitting the relaxation to the equilibrium in two steps, an entropic quasiequilibrium (EQE) kinetic model is proposed for the simulation of low Mach number flows, which enjoys both the H theorem and a free-tunable parameter for controlling the bulk viscosity in such a way as to enhance numerical stability in the incompressible flow limit. Moreover, the proposed model admits a simplification based on a proper expansion in the low Mach number limit (LQE model). The lattice Boltzmann implementation of both the EQE and LQE is as simple as that of the standard lattice Bhatnagar-Gross-Krook (LBGK) method, and practical details are reported. Extensive numerical testing with the lid driven cavity flow in two dimensions is presented in order to verify the enhancement of the stability region. The proposed models achieve the same accuracy as the LBGK method with much rougher meshes, leading to an effective computational speed-up of almost three times for EQE and of more than four times for the LQE. Three-dimensional extension of EQE and LQE is also discussed.
Performance Optimization of 3D Lattice Boltzmann Flow Solver on a GPU
Directory of Open Access Journals (Sweden)
Nhat-Phuong Tran
2017-01-01
Full Text Available Lattice Boltzmann Method (LBM is a powerful numerical simulation method of the fluid flow. With its data parallel nature, it is a promising candidate for a parallel implementation on a GPU. The LBM, however, is heavily data intensive and memory bound. In particular, moving the data to the adjacent cells in the streaming computation phase incurs a lot of uncoalesced accesses on the GPU which affects the overall performance. Furthermore, the main computation kernels of the LBM use a large number of registers per thread which limits the thread parallelism available at the run time due to the fixed number of registers on the GPU. In this paper, we develop high performance parallelization of the LBM on a GPU by minimizing the overheads associated with the uncoalesced memory accesses while improving the cache locality using the tiling optimization with the data layout change. Furthermore, we aggressively reduce the register uses for the LBM kernels in order to increase the run-time thread parallelism. Experimental results on the Nvidia Tesla K20 GPU show that our approach delivers impressive throughput performance: 1210.63 Million Lattice Updates Per Second (MLUPS.
Fritz, D. E.; Farmer, G. L.; Janecky, D. R.
2001-12-01
Lattice Boltzmann (LB) techniques are being applied to models of reactive transport processes in groundwaters with the purpose of modeling small scale (mm) interactions between water and rock in complex solid media. This method was used to create a simple porous media structure in which chemical reactions including sorption, dissolution and precipitation occur. A pre-existing lattice Boltzmann code developed at LANL for physical fluid flow was used as the basis for overlaying chemical exchange controls at each lattice node. Initially, Langmuir sorption isotherms were applied on open channel models varying from 10x4000 to 30x1000 nodes. The resulting breakthrough curves from these chemical slug models are compatible with analytical solutions that apply the isotherm equations on larger scales. The model was then further developed to include multiple solid compositions and dissolution and precipitation reactions to study the small scale spatial and temporal distributions of materials in porous media. Mineral nodes of varying composition which undergo specific chemical reactions can be created in the open channels or among evenly spaced blocks of solid nodes which simulate homogeneous porous media. This model structure is being used to investigate millimeter scale Sr isotopic variations observed in the K-metasomatized Lemitar Tuff from Southern New Mexico. Multiple samples of the adularia will provide an isochron age that may represent the time of K-metasomatism. Physical microsampling of this tuff has demonstrated the secondary adularia has a unique Sr isotopic characteristic (87}Sr/{86Sr near 0.727) relative to the fresh plagioclase and sanidine phenocrysts (0.709). The model is being used to discern between the possibilities of the Sr now present in the altered material originating from the surround matrix or alternatively from an outside source in the altering fluids. An outside source of Sr in the K-metasomatic groundwater would be likely with the failure of the
Hejranfar, Kazem; Saadat, Mohammad Hossein; Taheri, Sina
2017-02-01
In this work, a high-order weighted essentially nonoscillatory (WENO) finite-difference lattice Boltzmann method (WENOLBM) is developed and assessed for an accurate simulation of incompressible flows. To handle curved geometries with nonuniform grids, the incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation is transformed into the generalized curvilinear coordinates and the spatial derivatives of the resulting lattice Boltzmann equation in the computational plane are solved using the fifth-order WENO scheme. The first-order implicit-explicit Runge-Kutta scheme and also the fourth-order Runge-Kutta explicit time integrating scheme are adopted for the discretization of the temporal term. To examine the accuracy and performance of the present solution procedure based on the WENOLBM developed, different benchmark test cases are simulated as follows: unsteady Taylor-Green vortex, unsteady doubly periodic shear layer flow, steady flow in a two-dimensional (2D) cavity, steady cylindrical Couette flow, steady flow over a 2D circular cylinder, and steady and unsteady flows over a NACA0012 hydrofoil at different flow conditions. Results of the present solution are compared with the existing numerical and experimental results which show good agreement. To show the efficiency and accuracy of the solution methodology, the results are also compared with the developed second-order central-difference finite-volume lattice Boltzmann method and the compact finite-difference lattice Boltzmann method. It is shown that the present numerical scheme is robust, efficient, and accurate for solving steady and unsteady incompressible flows even at high Reynolds number flows.
Energy Technology Data Exchange (ETDEWEB)
Verschaeve, Joris C. G.
2011-07-01
The present thesis focuses on two distinct topics of computational fluid dynamics. The first one, treated in part I, focuses on the no-slip boundary conditions for the lattice Boltzmann method, whereas the second one, presented in part II, proposes a high order accurate description of the interface in two-phase flow computations for volume tracking in two dimensions.Part I of the present thesis presents an important issue in the framework of the lattice Boltzmann method, namely no-slip boundary conditions. Since the central object of the lattice Boltzmann method is the particle distribution function, the implementation of the no-slip boundary condition, although straightforward for continuum Navier Stokes solvers, is more involved. Additional physical arguments for the no-slip boundary condition at straight walls are presented. This leads to an alternative formulation of the no-slip boundary condition for the lattice Boltzmann method. This boundary condition is second order accurate with respect to the grid spacing and conserves mass. The origin of numerical instabilities observed for a variety of other boundary conditions is investigated, and it is shown how these can be removed leading to stable boundary conditions. Some arguments unifying different formulations of the no-slip boundary condition are presented. In addition to straight boundary conditions, the question of curved boundary conditions is treated. These represent an elevated level of complexity, since the lattice Boltzmann method is only defined for equidistant Cartesian grids. The curved boundary condition in the present thesis conserves the second order accuracy of the lattice Boltzmann method.Due to the complexity of two-phase flow problems, the majority of numerical methods in this field displays a rather low order of accuracy. In part II of the present thesis, a subproblem of the two-phase flow problem, namely the tracking of the interface is treated. Two different interface descriptions allowing
Sailfish: A flexible multi-GPU implementation of the lattice Boltzmann method
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
Large-scale parallel lattice Boltzmann-cellular automaton model of two-dimensional dendritic growth
Jelinek, Bohumir; Eshraghi, Mohsen; Felicelli, Sergio; Peters, John F.
2014-03-01
An extremely scalable lattice Boltzmann (LB)-cellular automaton (CA) model for simulations of two-dimensional (2D) dendritic solidification under forced convection is presented. The model incorporates effects of phase change, solute diffusion, melt convection, and heat transport. The LB model represents the diffusion, convection, and heat transfer phenomena. The dendrite growth is driven by a difference between actual and equilibrium liquid composition at the solid-liquid interface. The CA technique is deployed to track the new interface cells. The computer program was parallelized using the Message Passing Interface (MPI) technique. Parallel scaling of the algorithm was studied and major scalability bottlenecks were identified. Efficiency loss attributable to the high memory bandwidth requirement of the algorithm was observed when using multiple cores per processor. Parallel writing of the output variables of interest was implemented in the binary Hierarchical Data Format 5 (HDF5) to improve the output performance, and to simplify visualization. Calculations were carried out in single precision arithmetic without significant loss in accuracy, resulting in 50% reduction of memory and computational time requirements. The presented solidification model shows a very good scalability up to centimeter size domains, including more than ten million of dendrites. Catalogue identifier: AEQZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 29,767 No. of bytes in distributed program, including test data, etc.: 3131,367 Distribution format: tar.gz Programming language: Fortran 90. Computer: Linux PC and clusters. Operating system: Linux. Has the code been vectorized or parallelized?: Yes. Program is parallelized using MPI
Schaap, M. G.; Tuller, M.; Guber, A.; Martin, M. A.; Martinez, F. S.; Pachepsky, Y.
2007-12-01
Soil structure greatly affects the ability of soil to transmit and to retain water, chemicals, and colloidal particles that can carry contaminants or be contaminants themselves, e.g. pathogenic microorganisms. No theory or empirical relationships have been developed to date to quantitatively relate parameters of soil structure and parameters of the contaminant transport in soils. The absence of theoretical advances in this area seriously hampers the ability to address issues of public concern, e.g. spread of contaminants introduced in the environment by agricultural activities. Recently, computer tomography of soils has become available to generate detailed images of soil pore space with high resolution and density. Successful applications of computer tomography in medical and material sciences show the great potential of this technique to create an exhaustive characterization of soil structure heterogeneity. In this presentation we investigate saturated flow through twelve undisturbed macroporous soil columns (7.62- cm sample diameter and 18-cm length) with lattice Boltzmann simulations. Saturated flow was measured for the complete columns, as well as on 2 cm sections for selected columns. Computed X-Ray tomography was performed on each of the columns, using the 420 kV X-ray source of a HYTEC FlashCT high-speed industrial CT scanner. The resolution was 116 microns per voxel, yielding a final tomography image of 656x656x1482 (~ 6.3 10E8) voxels. X-Ray CT observations typically provide "gray-scale" representations of the imaged object that must be segmented to yield discrete pore and particle geometry. Many segmentation algorithms are available, each yielding different final pore geometries thus potentially creating uncertainties in subsequent flow analyses. Lattice Boltzmann (LB) simulations will be presented only for some of the columns as the simulations are extremely computationally intensive (each simulation requires ~ 60 GB of computer RAM at the observed
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.
Song, Wenyu; Zhang, Yaning; Li, Bingxi; Xu, Fei; Fu, Zhongbin
2017-06-01
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.
Study of the Dynamics of a Condensing Bubble Using Lattice Boltzmann Method
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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.
Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem.
Abas, Aizat; Mokhtar, N Hafizah; Ishak, M H H; Abdullah, M Z; Ho Tian, Ang
2016-01-01
This paper simulates and predicts the laminar flow inside the 3D aneurysm geometry, since the hemodynamic situation in the blood vessels is difficult to determine and visualize using standard imaging techniques, for example, magnetic resonance imaging (MRI). Three different types of Lattice Boltzmann (LB) models are computed, namely, single relaxation time (SRT), multiple relaxation time (MRT), and regularized BGK models. The results obtained using these different versions of the LB-based code will then be validated with ANSYS FLUENT, a commercially available finite volume- (FV-) based CFD solver. The simulated flow profiles that include velocity, pressure, and wall shear stress (WSS) are then compared between the two solvers. The predicted outcomes show that all the LB models are comparable and in good agreement with the FVM solver for complex blood flow simulation. The findings also show minor differences in their WSS profiles. The performance of the parallel implementation for each solver is also included and discussed in this paper. In terms of parallelization, it was shown that LBM-based code performed better in terms of the computation time required.
Lattice Boltzmann Model of 3D Multiphase Flow in Artery Bifurcation Aneurysm Problem
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Aizat Abas
2016-01-01
Full Text Available This paper simulates and predicts the laminar flow inside the 3D aneurysm geometry, since the hemodynamic situation in the blood vessels is difficult to determine and visualize using standard imaging techniques, for example, magnetic resonance imaging (MRI. Three different types of Lattice Boltzmann (LB models are computed, namely, single relaxation time (SRT, multiple relaxation time (MRT, and regularized BGK models. The results obtained using these different versions of the LB-based code will then be validated with ANSYS FLUENT, a commercially available finite volume- (FV- based CFD solver. The simulated flow profiles that include velocity, pressure, and wall shear stress (WSS are then compared between the two solvers. The predicted outcomes show that all the LB models are comparable and in good agreement with the FVM solver for complex blood flow simulation. The findings also show minor differences in their WSS profiles. The performance of the parallel implementation for each solver is also included and discussed in this paper. In terms of parallelization, it was shown that LBM-based code performed better in terms of the computation time required.
A lattice Boltzmann model for substrates with regularly structured surface roughness
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.
Energy Technology Data Exchange (ETDEWEB)
Kim, Hyung Min [Kyonggi Univ., Suwon (Korea, Republic of)
2016-11-15
The performance of proton exchange membrane fuel cells (PEMFC) is strongly related to the water flow and accumulation in the gas diffusion layer (GDL) and catalyst layer. Understanding the behavior of fluid from the characteristics of the media is crucial for the improvement of the performance and design of the GDL. In this paper, a numerical method is proposed to calculate the design parameters of the GDL, i.e., permeability, tortuosity, and effective diffusivity. The fluid flow in a channel filled with randomly packed hard spheres is simulated to validate the method. The flow simulation was performed by lattice Boltzmann method with bounce back condition for the solid volume fraction in the porous media, with different values of porosities. Permeability, which affects the flow, was calculated from the average pressure drop and the velocity in the porous media. Tortuosity, calculated by the ratio the average path length of the randomly injected massless particles to the thickness of the porous media, and the resultant effective diffusivity were in good agreement with the theoretical model. The suggested method can be used to calculate the parameters of real GDL accurately without any modification.
Li, Qing; Luo, K H
2013-11-01
In this paper, we aim to address an important issue about the pseudopotential lattice Boltzmann (LB) model, which has attracted much attention as a mesoscopic model for simulating interfacial dynamics of complex fluids, but suffers from the problem that the surface tension cannot be tuned independently of the density ratio. In the literature, a multirange potential was devised to adjust the surface tension [Sbragaglia et al., Phys. Rev. E 75, 026702 (2007)]. However, it was recently found that the density ratio of the system will be changed when the multirange potential is employed to adjust the surface tension. An alternative approach is therefore proposed in the present work. The basic strategy is to add a source term to the LB equation so as to tune the surface tension of the pseudopotential LB model. The proposed approach can guarantee that the adjustment of the surface tension does not affect the mechanical stability condition of the pseudopotential LB model, and thus provides a separate control of the surface tension and the density ratio. Meanwhile, it still retains the mesoscopic feature and the computational simplicity of the pseudopotential LB model. Numerical simulations are carried out for stationary droplets, capillary waves, and droplet splashing on a thin liquid film. The numerical results demonstrate that the proposed approach is capable of achieving a tunable surface tension over a very wide range and can keep the density ratio unchanged when adjusting the surface tension.
Simulation of regimes of convection and plume dynamics by the thermal Lattice Boltzmann Method
Mora, Peter; Yuen, David A.
2018-02-01
We present 2D simulations using the Lattice Boltzmann Method (LBM) of a fluid in a rectangular box being heated from below, and cooled from above. We observe plumes, hot narrow upwellings from the base, and down-going cold chutes from the top. We have varied both the Rayleigh numbers and the Prandtl numbers respectively from Ra = 1000 to Ra =1010 , and Pr = 1 through Pr = 5 ×104 , leading to Rayleigh-Bénard convection cells at low Rayleigh numbers through to vigorous convection and unstable plumes with pronounced vortices and eddies at high Rayleigh numbers. We conduct simulations with high Prandtl numbers up to Pr = 50, 000 to simulate in the inertial regime. We find for cases when Pr ⩾ 100 that we obtain a series of narrow plumes of upwelling fluid with mushroom heads and chutes of downwelling fluid. We also present simulations at a Prandtl number of 0.7 for Rayleigh numbers varying from Ra =104 through Ra =107.5 . We demonstrate that the Nusselt number follows power law scaling of form Nu ∼Raγ where γ = 0.279 ± 0.002 , which is consistent with published results of γ = 0.281 in the literature. These results show that the LBM is capable of reproducing results obtained with classical macroscopic methods such as spectral methods, and demonstrate the great potential of the LBM for studying thermal convection and plume dynamics relevant to geodynamics.
Pravinraj, T.; Patrikar, Rajendra
2017-07-01
Partial wetting surfaces and its influence on the droplet movement of micro and nano scale being contemplated for many useful applications. The dynamics of the droplet usually analyzed with a multiphase lattice Boltzmann method (LBM). In this paper, the influence of partial wetting surface on the dynamics of droplet is systematically analyzed for various cases. Splitting of droplets due to chemical gradient of the surface is studied and analyses of splitting time for various widths of the strips for different Weber numbers are computed. With the proposed model one can tune the splitting volume and time by carefully choosing a strip width and droplet position. The droplet spreading on chemically heterogeneous surfaces shows that the spreading can be controlled not only by parameters of Weber number but also by tuning strip width ratio. The transportation of the droplet from hydrophobic surface to hydrophilic surface due to chemical gradient is simulated and analyzed using our hybrid thermodynamic-image processing technique. The results prove that with the progress of time the surface free energy decreases with increase in spreading area. Finally, the transportation of a droplet on microstructure gradient is demonstrated. The model explains the temporal behaviour of droplet during the spreading, recoiling and translation along with tracking of contact angle hysteresis phenomenon.
Fei, K.; Chen, T. S.; Hong, C. W.
Carbon dioxide bubble removal at the anode of a direct methanol fuel cell (DMFC) is an important technique especially for applications in the portable power sources. This paper presents numerical investigations of the two-phase flow, CO 2 bubbles in a liquid methanol solution, in the anode microchannels from the aspect of microfluidics using a thermal lattice Boltzmann model (TLBM). The main purpose is to derive an efficient and effective computational scheme to deal with this technical problem. It is then examined by a commercially available software using Navier-Stokes plus volume of fluid (VOF) method. The latter approach is normally employed by most researchers. A simplified microchannel simulation domain with the dimension of 1.5 μm in height (or width) and 16.0 μm in length has been setup for both cases to mimic the actual flow path of a CO 2 bubble inside an anodic diffusion layer in the DMFC. This paper compares both numerical schemes and results under the same operation conditions from the viewpoint of fuel cell engineering.
Wissocq, Gauthier; Gourdain, Nicolas; Malaspinas, Orestis; Eyssartier, Alexandre
2017-02-01
This paper reports the investigations done to adapt the Characteristic Boundary Conditions (CBC) to the Lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM code: the baseline local one-dimension inviscid (BL-LODI) approach, its extension including the effects of the transverse terms (CBC-2D) and a local streamline approach in which the problem is reformulated in the incident wave framework (LS-LODI). Then all implementations of the CBC methods are tested for a variety of test cases, ranging from canonical problems (such as 2D plane and spherical waves and 2D vortices) to a 2D NACA profile at high Reynolds number (Re =105), representative of aeronautic applications. The LS-LODI approach provides the best results for pure acoustics waves (plane and spherical waves). However, it is not well suited to the outflow of a convected vortex for which the CBC-2D associated with a relaxation on density and transverse waves provides the best results. As regards numerical stability, a regularized adaptation is necessary to simulate high Reynolds number flows. The so-called regularized FD (Finite Difference) adaptation, a modified regularized approach where the off-equilibrium part of the stress tensor is computed thanks to a finite difference scheme, is the only tested adaptation that can handle the high Reynolds computation.
Simulation of phase separation with temperature-dependent viscosity using lattice Boltzmann method.
Wang, Heping; Zang, Duyang; Li, Xiaoguang; Geng, Xingguo
2017-12-27
This paper presents an exploration of the phase separation behavior and pattern formation in a binary fluid with temperature-dependent viscosity via a coupled lattice Boltzmann method (LBM). By introducing a viscosity-temperature relation into the LBM, the coupling effects of the viscosity-temperature coefficient [Formula: see text] , initial viscosity [Formula: see text] and thermal diffusion coefficient [Formula: see text] , on the phase separation were successfully described. The calculated results indicated that an increase in initial viscosity and viscosity-temperature coefficient, or a decrease in the thermal diffusion coefficient, can lead to the orientation of isotropic growth fronts over a wide range of viscosity. The results showed that droplet-type phase structures and lamellar phase structures with domain orientation parallel or perpendicular to the walls can be obtained in equilibrium by controlling the initial viscosity, thermal diffusivity, and the viscosity-temperature coefficient. Furthermore, the dataset was rearranged for growth kinetics of domain growth and thermal diffusion fronts in a plot by the spherically averaged structure factor and the ratio of separated and continuous phases. The analysis revealed two different temporal regimes: spinodal decomposition and domain growth stages, which further quantified the coupled effects of temperature and viscosity on the evolution of temperature-dependent phase separation. These numerical results provide guidance for setting optimum temperature ranges to obtain expected phase separation structures for systems with temperature-dependent viscosity.
Alapati, Suresh; Che, Woo Seong; Mannoor, Madhusoodanan; Suh, Yong Kweon
2016-06-01
In this paper, we present the results obtained from the simulation of particle motion induced by the fluid flow driven by an array of beating artificial cilia inside a micro-channel. A worm-like-chain model is used to simulate the elastic cilia, and the lattice Boltzmann equation is used to compute the fluid flow. We employ a harmonic force at the extreme tip of each cilium to actuate it. Our simulation methods are first validated by applying them to the motion of a single cilium and a freely falling sphere. After validation, we simulate the fluid flow generated by an array of beating cilia and find that a maximum flow rate is achieved at an optimum sperm number. Next, we simulate the motion of a neutrally buoyant spherical particle at this optimum sperm number by tracking the particle motion with a smoothed profile method. We address the effect of the following parameters on the particle velocity: the gap between cilia and particle, the particle size, the cilia density, and the presence of an array of intermediate particles.
Lattice Boltzmann method simulations of Stokes number effects on particle motion in a channel flow
Zhang, Lenan; Jebakumar, Anand Samuel; Abraham, John
2016-06-01
In a recent experimental study by Lau and Nathan ["Influence of Stokes number on the velocity and concentration distributions in particle-laden jets," J. Fluid Mech. 757, 432 (2014)], it was found that particles in a turbulent pipe flow tend to migrate preferentially toward the wall or the axis depending on their Stokes number (St). Particles with a higher St (>10) are concentrated near the axis while those with lower St (plane. They have explained this behavior in terms of the Saffman lift, Magnus lift, and wall repulsion forces acting on the particle. The present work extends the previous work done by Jebakumar et al. and aims to study the behavior of particles at intermediate St ranging from 10 to 20. It is in this range where the equilibrium position of the particle changes from near the wall to the axis and the particle starts oscillating about the axis. The Lattice Boltzmann method is employed to carry out this study. It is shown that the change in mean equilibrium position is related to increasing oscillations of the particle with mean position near the wall which results in the particle moving past the center plane to the opposite side. The responsible mechanisms are explained in detail.
Simulation of Fluid Flow and Heat Transfer in Porous Medium Using Lattice Boltzmann Method
Wijaya, Imam; Purqon, Acep
2017-07-01
Fluid flow and heat transfer in porous medium are an interesting phenomena to study. One kind example of porous medium is geothermal reservoir. By understanding the fluid flow and heat transfer in porous medium, it help us to understand the phenomena in geothermal reservoir, such as thermal change because of injection process. Thermal change in the reservoir is the most important physical property to known since it has correlation with performance of the reservoir, such as the electrical energy produced by reservoir. In this simulation, we investigate the fluid flow and heat transfer in geothermal reservoir as a simple flow in porous medium canal using Lattice Boltzmann Method. In this simulation, we worked on 2 dimension with nine vectors velocity (D2Q9). To understand the fluid flow and heat transfer in reservoir, we varied the fluid temperature that inject into the reservoir and set the heat source constant at 410°C. The first variation we set the fluid temperature 45°C, second 102.5°C, and the last 307.5°C. Furthermore, we also set the parameter of reservoir such as porosity, density, and injected fluid velocity are constant. Our results show that for the first temperature variation distribution between experiment and simulation is 92.86% match. From second variation shows that there is one pick of thermal distribution and one of turbulence zone, and from the last variation show that there are two pick of thermal distribution and two of turbulence zone.
A Unified Detail-Preserving Liquid Simulation by Two-Phase Lattice Boltzmann Modeling.
Guo, Yulong; Liu, Xiaopei; Xu, Xuemiao
2017-05-01
Traditional methods in graphics to simulate liquid-air dynamics under different scenarios usually employ separate approaches with sophisticated interface tracking/reconstruction techniques. In this paper, we propose a novel unified approach which is easy and effective to produce a variety of liquid-air interface phenomena. These phenomena, such as complex surface splashes, bubble interactions, as well as surface tension effects, can co-exist in one single simulation, and are created within the same computational framework. Such a framework is unique in that it is free from any complicated interface tracking/reconstruction procedures. Our approach is developed from the two-phase lattice Boltzmann method with the mean field model, which provides a unified framework for interface dynamics but is numerically unstable under turbulent conditions. Considering the drawbacks of the existing approaches, we propose techniques to suppress oscillations for significant stability enhancement, as well as derive a new subgrid-scale model to further improve stability, faithfully preserving liquid-air interface details without excessive diffusion by taking into account the density variation. The whole framework is highly parallel, enabling very efficient implementation. Comparisons with the related approaches show superiority on stable simulations with detail preservation and multiphase phenomena simultaneously involved. A set of animation results demonstrate the effectiveness of our method.
Coupling molecular dynamics with lattice Boltzmann method based on the immersed boundary method
Tan, Jifu; Sinno, Talid; Diamond, Scott
2017-11-01
The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable solids exposed to flow. The code was validated with the classic problem of rigid ellipsoid particle orbit in shear flow, blood cell stretching test and effective blood viscosity, and demonstrated essentially linear scaling over 16 cores. An example of the fluid-solid coupling was given for flexible filaments (drug carriers) transport in a flowing blood cell suspensions, highlighting the advantages and capabilities of the developed code. NIH 1U01HL131053-01A1.
Modeling of electrokinetic reactive transport in micropore using a coupled lattice Boltzmann method
Zhang, Li; Wang, Moran
2015-05-01
It is well known that a solid surface will be charged when it comes into contact with liquid, especially with electrolyte solutions. The surface charge influences ion distribution and transport and, therefore, affects the chemical reaction. Such an effect may become significant in micropores/nanopores when the electrical double layer thickness is comparable to the pore size, but this has never been well studied. This work investigates the coupled electrokinetic and reactive transport in micropores using mesoscopic modeling. We established a numerical framework by coupling multiple lattice Boltzmann models to combine all effects on ion transport from convection, diffusion and electrokinetics, and therefore, on heterogeneous reactions in micropore. After validations, the mechanism of surface charge effects on reactive transport is studied for an ion precipitation case and a solid dissolution case. The results show that two factors, transport and reaction, compete in such complicated processes based on their characteristic rates. When the transport rate, including diffusion and convection, is much lower than the reaction rate, i.e., the transport-dominated process, the surface charge significantly reduces the reaction. Otherwise for a reaction-dominated process, the surface charge effect may be negligible.
Safari, Hesameddin; Rahimian, Mohammad Hassan; Krafczyk, Manfred
2014-09-01
In the present article, we extend and generalize our previous article [H. Safari, M. H. Rahimian, and M. Krafczyk, Phys. Rev. E 88, 013304 (2013)] to include the gradient of the vapor concentration at the liquid-vapor interface as the driving force for vaporization allowing the evaporation from the phase interface to work for arbitrary temperatures. The lattice Boltzmann phase-field multiphase modeling approach with a suitable source term, accounting for the effect of the phase change on the velocity field, is used to solve the two-phase flow field. The modified convective Cahn-Hilliard equation is employed to reconstruct the dynamics of the interface topology. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius-Clapeyron correlation. Numerous validation tests including one-dimensional and two-dimensional cases are carried out to demonstrate the consistency of the presented model. Results show that the model is able to predict the flow features around and inside an evaporating droplet quantitatively in quiescent as well as convective environments.
Evaluation of outflow boundary conditions for two-phase lattice Boltzmann equation.
Lou, Qin; Guo, Zhaoli; Shi, Baochang
2013-06-01
Outflow boundary condition (OBC) is a critical issue in computational fluid dynamics. As a type of numerical method for fluid flows, the lattice Boltzmann equation (LBE) method has gained much success in a variety of complex flows, and certain OBCs have been suggested for the LBE in simulating simple single-phase flows. However, very few discussions on the OBCs have been made for the two-phase LBE method. In this work, three types of OBCs that are widely used in the LBE for single-phase flows, i.e., the Neumann boundary condition, the convective boundary condition, and the extrapolation boundary condition, are extended to a two-phase LBE method and their performances are investigated. The comprehensive results of several two-phase flows show that these boundary conditions behave quite differently in the simulations of two-phase flows. Specifically, it is found that the Neumann boundary condition and the extrapolation boundary condition give rather poor predictions, while the type of convective boundary conditions work well, although the choice of the convection velocity has some slight influences on the results. We also apply these OBC schemes to some other two-phase models, and similar observations are found.
A lattice Boltzmann method for axisymmetric multicomponent flows with high viscosity ratio
Liu, Haihu; Wu, Lei; Ba, Yan; Xi, Guang; Zhang, Yonghao
2016-12-01
A color-gradient lattice Boltzmann method (LBM) is proposed to simulate axisymmetric multicomponent flows. This method uses a collision operator that is a combination of three separate parts, namely single-component collision operator, perturbation operator, and recoloring operator. A source term is added into the single-component collision operator such that in each single-component region the axisymmetric continuity and momentum equations can be exactly recovered. The interfacial tension effect is realized by the perturbation operator, in which an interfacial force of axisymmetric form is derived using the concept of continuum surface force. A recoloring operator proposed by Latva-Kokko and Rothman is extended to the axisymmetric case for phase segregation and maintenance of the interface. To enhance the method's numerical stability for handling binary fluids with high viscosity ratio, a multiple-relaxation-time model is used for the collision operator. Several numerical examples, including static droplet test, oscillation of a viscous droplet, and breakup of a liquid thread, are presented to test the capability and accuracy of the proposed color-gradient LBM. It is found that the present method is able to accurately capture the phase interface and produce low spurious velocities. Also, the LBM results are all in good agreement with the analytical solutions and/or available experimental data for a very broad range of viscosity ratios.
Energy Technology Data Exchange (ETDEWEB)
Stewart, Mark L.; Rector, David R.; Muntean, George G.; Maupin, Gary D.
2004-08-01
Cordierite diesel particulate filters (DPFs) offer one of the most promising aftertreatment technologies to meet the quickly approaching EPA 2007 heavy-duty emissions regulations. A critical, yet poorly understood, component of particulate filter modeling is the representation of soot deposition. The structure and distribution of soot deposits upon and within the ceramic substrate directly influence many of the macroscopic phenomenon of interest, including filtration efficiency, back pressure, and filter regeneration. Intrinsic soot cake properties such as packing density and permeability coefficients remain inadequately characterized. The work reported in this paper involves subgrid modeling techniques which may prove useful in resolving these inadequacies. The technique involves the use of a lattice Boltzmann modeling approach. This approach resolves length scales which are orders of magnitude below those typical of a standard computational fluid dynamics (CFD) representation of an aftertreatment device. Individual soot particles are introduced and tracked as they move through the flow field and are deposited on the filter substrate or previously deposited particles. Electron micrographs of actual soot deposits were taken and compared to the model predictions. Descriptions of the modeling technique and the development of the computational domain are provided. Preliminary results are presented, along with some comparisons with experimental observations.
Entropic lattice Boltzmann method for multiphase flows: Fluid-solid interfaces.
Mazloomi M, Ali; Chikatamarla, Shyam S; Karlin, Iliya V
2015-08-01
The recently introduced entropic lattice Boltzmann model (ELBM) for multiphase flows [A. Mazloomi M., S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 114, 174502 (2015)] is extended to the simulation of dynamic fluid-solid interface problems. The thermodynamically consistent, nonlinearly stable ELBM together with a polynomial representation of the equation of state enables us to investigate the dynamics of the contact line in a wide range of applications, from capillary filling to liquid drop impact onto a flat surfaces with different wettability. The static interface behavior is tested by means of the liquid column in a channel to verify the Young-Laplace law. The numerical results of a capillary filling problem in a channel with wettability gradient show an excellent match with the existing analytical solution. Simulations of drop impact onto both wettable and nonwettable surfaces show that the ELBM reproduces the experimentally observed drop behavior in a quantitative manner. Results reported herein demonstrate that the present model is a promising alternative for studying the vapor-liquid-solid interface dynamics.
Phase-field lattice Boltzmann modeling of boiling using a sharp-interface energy solver
Mohammadi-Shad, Mahmood; Lee, Taehun
2017-07-01
The main objective of this paper is to extend an isothermal incompressible two-phase lattice Boltzmann equation method to model liquid-vapor phase change problems using a sharp-interface energy solver. Two discrete particle distribution functions, one for the continuity equation and the other for the pressure evolution and momentum equations, are considered in the current model. The sharp-interface macroscopic internal energy equation is discretized with an isotropic finite difference method to find temperature distribution in the system. The mass flow generated at liquid-vapor phase interface is embedded in the pressure evolution equation. The sharp-interface treatment of internal energy equation helps to find the interfacial mass flow rate accurately where no free parameter is needed in the calculations. The proposed model is verified against available theoretical solutions of the two-phase Stefan problem and the two-phase sucking interface problem, with which our simulation results are in good agreement. The liquid droplet evaporation in a superheated vapor, the vapor bubble growth in a superheated liquid, and the vapor bubble rising in a superheated liquid are analyzed and underlying physical characteristics are discussed in detail. The model is successfully tested for the liquid-vapor phase change with large density ratio up to 1000.
Lattice Boltzmann simulation of fluid flow in fracture networks with rough, self-affine surfaces.
Madadi, Mahyar; Sahimi, Muhammad
2003-02-01
Using the lattice Boltzmann method, we study fluid flow in a two-dimensional (2D) model of fracture network of rock. Each fracture in a square network is represented by a 2D channel with rough, self-affine internal surfaces. Various parameters of the model, such as the connectivity and the apertures of the fractures, the roughness profile of their surface, as well as the Reynolds number for flow of the fluid, are systematically varied in order to assess their effect on the effective permeability of the fracture network. The distribution of the fractures' apertures is approximated well by a log-normal distribution, which is consistent with experimental data. Due to the roughness of the fractures' surfaces, and the finite size of the networks that can be used in the simulations, the fracture network is anisotropic. The anisotropy increases as the connectivity of the network decreases and approaches the percolation threshold. The effective permeability K of the network follows the power law K approximately (beta), where is the average aperture of the fractures in the network and the exponent beta may depend on the roughness exponent. A crossover from linear to nonlinear flow regime is obtained at a Reynolds number Re approximately O(1), but the precise numerical value of the crossover Re depends on the roughness of the fractures' surfaces.
Lattice Boltzmann simulation of solute transport in a single rough fracture
Directory of Open Access Journals (Sweden)
Zhi DOU
2014-07-01
Full Text Available In this study, the lattice Boltzmann method (LBM was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves (BTCs for continuous injection sources in rough fractures were analyzed and discussed with different Reynolds numbers (Re. The results show that the rough fracture wall leads to a large fluid velocity gradient across the aperture. Consequently, there is a broad distribution of the immobile region along the rough fracture wall. This distribution of the immobile region is very sensitive to the Re and fracture geometry, and the immobile region is enlarged with the increase of Re and roughness. The concentration of the solute front in the mobile region increases with the Re. Furthermore, the Re and roughness have significant effects on BTCs, and the slow solute molecule exchange between the mobile and immobile regions results in a long breakthrough tail for the rough fracture. This study also demonstrates that the developed LBM can be effective in studying the solute transport in a rough fracture.
Modeling fluid flow and heat transfer in PEM fuel cell using lattice Boltzmann approach
Afsharpoya, Behnam
2005-11-01
The fluid flow and species transport in fuel cells are affected by diffusion, advection, thermal gradients, material properties, electrochemical effects, and interfacial forces. A consistent approach capable of modeling these processes has not yet been developed. There have been studies addressing transport of reactants and products in the gas phase, however, water management and convective / thermal effects are still poorly understood. While most modeling efforts in fuel-cell research adopt the traditional CFD approach based on the continuum governing equations, we are developing lattice- Boltzmann (LB) methods to model fluid and thermal transport inside flow channels and gas diffusion layers in proton exchange membrane fuel cells. Specifically, we have developed and tested a new method for implementing structured non-uniform mesh using Lagrangian interpolations. A three-dimensional LB code has been developed for thermal flows through a section of serpentine channel with a gas diffusion layer. The gas diffusion layer is modelled as a porous medium using a modified LB equation and a forcing term. A separate distribution is used to model thermal effects. Methods of validating the approach and preliminary results will be presented.
Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change
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.
Upscaled Lattice Boltzmann Method for Simulations of Flows in Heterogeneous Porous Media
Li, Jun
2017-02-16
An upscaled Lattice Boltzmann Method (LBM) for flow simulations in heterogeneous porous media at the Darcy scale is proposed in this paper. In the Darcy-scale simulations, the Shan-Chen force model is used to simplify the algorithm. The proposed upscaled LBM uses coarser grids to represent the average effects of the fine-grid simulations. In the upscaled LBM, each coarse grid represents a subdomain of the fine-grid discretization and the effective permeability with the reduced-order models is proposed as we coarsen the grid. The effective permeability is computed using solutions of local problems (e.g., by performing local LBM simulations on the fine grids using the original permeability distribution) and used on the coarse grids in the upscaled simulations. The upscaled LBM that can reduce the computational cost of existing LBM and transfer the information between different scales is implemented. The results of coarse-grid, reduced-order, simulations agree very well with averaged results obtained using a fine grid.
Lattice Boltzmann Explicit Schemes for 3D MHD on Non-Uniform Grids
Schleif, C.; Vahala, G.; Vahala, L.; Macnab, A.; Soe, M.; Carter, J.
2004-11-01
Lattice-Boltzmann Model (LBM) is a very promising alternative computational approach to MHD and to other nonlinear macroscopic systems because of its simplicity, ease of imposition of geometric boundary conditions and ideal parallelization on multi-PE (and especially vector) platforms. For example, on the Earth Simulator our 2D explicit LBM-MHD code has achieved over 3.6 TFlops/sec. The disparate length and time scales that appear in the solutions of dissipative MHD require careful treatment of ill-conditioned matrices in direct solvers. In LBM-MHD one introduces a scalar distribution function for the velocity field and a vector distribution function for the magnetic field. Since the magnetic evolution equation is obtained at the 1st moment closures, less speeds are needed than to recover the momentum equation. We are also investigating the least square LBM for non-uniform spatial grids. In one approach, the standard LBM is applied to the fine scales while the least square LBM is applied to the large scales. Since the least square algorithm involves matrices that are only grid-dependent, these matrices need only be calculated once leading to an efficient algorithm. Our algorithm will be applied to the 3D Orszag-Tang vortex and compare our results to the 3D pseudo-spectral results of Poquet et. al.
Lattice Boltzmann Method of Different BGA Orientations on I-Type Dispensing Method.
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Aizat Abas
Full Text Available This paper studies the three dimensional (3D simulation of fluid flows through the ball grid array (BGA to replicate the real underfill encapsulation process. The effect of different solder bump arrangements of BGA on the flow front, pressure and velocity of the fluid is investigated. The flow front, pressure and velocity for different time intervals are determined and analyzed for potential problems relating to solder bump damage. The simulation results from Lattice Boltzmann Method (LBM code will be validated with experimental findings as well as the conventional Finite Volume Method (FVM code to ensure highly accurate simulation setup. Based on the findings, good agreement can be seen between LBM and FVM simulations as well as the experimental observations. It was shown that only LBM is capable of capturing the micro-voids formation. This study also shows an increasing trend in fluid filling time for BGA with perimeter, middle empty and full orientations. The perimeter orientation has a higher pressure fluid at the middle region of BGA surface compared to middle empty and full orientation. This research would shed new light for a highly accurate simulation of encapsulation process using LBM and help to further increase the reliability of the package produced.
Optimization of a Lattice Boltzmann Computation on State-of-the-Art Multicore Platforms
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Williams, Samuel; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine
2009-04-10
We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Xeon E5345 (Clovertown), AMD Opteron 2214 (Santa Rosa), AMD Opteron 2356 (Barcelona), Sun T5140 T2+ (Victoria Falls), as well as a QS20 IBM Cell Blade. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us to identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned LBMHD application achieves up to a 15x improvement compared with the original code at a given concurrency. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.
Jiang, Di; Sun, Dongke; Xiang, Nan; Chen, Ke; Yi, Hong; Ni, Zhonghua
2013-01-01
This paper applies the lattice Boltzmann method (LBM) to a 3D simulation of micro flows in an expansion-contraction microchannel. We investigate the flow field under various inlet flow rates and cavity structures, and then systematically study the flow features of the vortex and Dean flow in this channel. Vortex formation analysis demonstrates that there is no observable vortex generated when the inlet flow rate is low enough. As the inlet flow rate increases, a small vortex first appears near the inlet, and then this vortex region will keep expanding until it fully occupies the cavity. A smaller cavity width may result in a larger vortex but the vortex is less influenced by cavity length. The Dean flow features at the outlet become more apparent with increasing inlet flow rate and more recirculation regions can be observed in the cross-section under over high inlet flow rate. In order to support the simulation results, some experimental processes are conducted successfully. It validates that the applied model can accurately characterize the flow in the microchannel. Results of simulations and experiments in this paper provide insights into the design and operation of microfluidic systems for particle/cell manipulation.
Lattice Boltzmann Method of a Flooding Accident at Gopeng, Perak, Malaysia
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Siti Habibah Shafiai
2017-01-01
Full Text Available The extraordinary flood had hit the residential area at Taman Raia Mesra, Gopeng, Perak, Malaysia, in November 2016. The event illustrated how the river basin had been fully inundated due to the heavy rainfall and caused the overflow to this affected area. It was reported that the occurrence became worst as the outlet of retention pond which connects to the river is unsuitable for the water outflow. Henceforth, this paper attempts to evaluate the causal factor of this recent disaster by using a model developed from Lattice Boltzmann Method (LBM. The model also incorporated with the rainfall and stormwater in LABSWE™. The simulation was commenced with the basic tests for model validation comprising turbulent and jet-forced flow in a circular channel, which resulted in a good agreement for both models. The simulation continued by using LABSWE model to reveal the water depth and velocity profile at the study site. These results had proven the incompatibility size of the outlet pond which is too small for the water to flow out to the river. The study is capable of providing the authorities with a sustainable design of proper drainage system, especially in Malaysia which is constantly receiving the outrageous heavy rainfall.
Simulation of Thermal Flow Problems via a Hybrid Immersed Boundary-Lattice Boltzmann Method
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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.
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Jiang Lei
2015-01-01
Full Text Available Direct numerical simulation (DNS of a round jet in crossflow based on lattice Boltzmann method (LBM is carried out on multi-GPU cluster. Data parallel SIMT (single instruction multiple thread characteristic of GPU matches the parallelism of LBM well, which leads to the high efficiency of GPU on the LBM solver. With present GPU settings (6 Nvidia Tesla K20M, the present DNS simulation can be completed in several hours. A grid system of 1.5 × 108 is adopted and largest jet Reynolds number reaches 3000. The jet-to-free-stream velocity ratio is set as 3.3. The jet is orthogonal to the mainstream flow direction. The validated code shows good agreement with experiments. Vortical structures of CRVP, shear-layer vortices and horseshoe vortices, are presented and analyzed based on velocity fields and vorticity distributions. Turbulent statistical quantities of Reynolds stress are also displayed. Coherent structures are revealed in a very fine resolution based on the second invariant of the velocity gradients.
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2016-04-01
The streaming potential phenomenon is produced by the flow of an electrolyte in a porous medium and is used for geophysical prospecting. It is quantified through an electrokinetic (EK) coefficient. The dependence of the EK coefficient on the conductivity of the electrolyte is described by the Helmholtz-Smoluchowski (HS) equation. This equation provides successful forecasts of the EK coefficient in the standard range of concentration. However, experimental measurements show deviations to this equation at extreme low and extreme high salinities. The aim of this study is to model the EK coefficient using Lattice Boltzmann simulations in a 2-D capillary channel, with a view to understanding these deviations. The effect of the constitutive parameters of the HS equation such as the permittivity and the viscosity is discussed. The validity of the HS equation using strong ζ potentials is assessed. Finally, a model of bulk fluid conductivity is derived. This model allows to take into account the change of local ionic distribution in the vicinity of the mineral. It appears to have a significant impact on the derivation of ζ potentials at low salinities and in the presence of polyvalent counterions.
Upscaled Lattice Boltzmann Method for Simulations of Flows in Heterogeneous Porous Media
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Jun Li
2017-01-01
Full Text Available An upscaled Lattice Boltzmann Method (LBM for flow simulations in heterogeneous porous media at the Darcy scale is proposed in this paper. In the Darcy-scale simulations, the Shan-Chen force model is used to simplify the algorithm. The proposed upscaled LBM uses coarser grids to represent the average effects of the fine-grid simulations. In the upscaled LBM, each coarse grid represents a subdomain of the fine-grid discretization and the effective permeability with the reduced-order models is proposed as we coarsen the grid. The effective permeability is computed using solutions of local problems (e.g., by performing local LBM simulations on the fine grids using the original permeability distribution and used on the coarse grids in the upscaled simulations. The upscaled LBM that can reduce the computational cost of existing LBM and transfer the information between different scales is implemented. The results of coarse-grid, reduced-order, simulations agree very well with averaged results obtained using a fine grid.
Lattice Boltzmann Simulation of Airflow and Mixed Convection in a General Ward of Hospital
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Taasnim Ahmed Himika
2016-01-01
Full Text Available In the present investigation the airflow and heat transfer for mixed convection have been simulated for a model general ward of hospital with six beds and partitions using the Lattice Boltzmann Method (LBM. Three different Reynolds numbers 100, 250, and 350 have been considered. Bounce-back condition has been applied at the wall. Results have been represented in three different case studies and the changes have been discussed in terms of streamlines and isotherms. Code validation has also been included before going through the simulation process and it shows good agreement with previously published papers when the comparison is made on average Nusselt number. Results show that the pattern of indoor airflow is varied in each and every case study due to the effect of mixed convection flow and placement of partition. In addition, the changes in average rate of heat transfer indicate that patients closer to inlet get the most air and feel better and if any patient does not need much air, he or she should be kept near the outlet to avoid temperature related complications.
Yan, Zhifeng; Yang, Xiaofan; Li, Siliang; Hilpert, Markus
2017-11-01
The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments. These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. The TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.
Study of heat transfer in an enclosure with a square cylinder using Lattice Boltzmann method
Moussaoui, Mohammed Amine; Mezrhab, Ahmed; Fontaine, Jean Pierre; Bouzidi, M.'hamed
2017-06-01
The purpose of this paper is to numerically examine the conjugate surface radiation-natural convection heat transfer in a 2D differentially heated enclosure with an inner square body, which generates heat. The numerical model is based on the coupling of the MRT-lattice Boltzmann model with finite difference method (FDM). The first one is used to compute the velocity field, while the second is adopted to obtain the temperature field. Various key parameters are studied, such as Rayleigh number (103 ≤ Ra ≤ 106), temperature-difference ratio ΔT*(0 ≤ ΔT* ≤ 50), body's thermal conductivity (0 < Ks < ∞) and locations. In this study, the air is considered as perfectly transparent to radiation. Among the salient findings, we can state that (i) the inner body location has a meaningful effect on isotherms, streamlines and total heat transfer through the enclosure, (ii) the heat transfer is affected considerably by increasing the body size and radiation exchange, specially at high Ra. Contribution to the topical issue "Materials for Energy harvesting, conversion and storage II (ICOME 2016)", edited by Jean-Michel Nunzi, Rachid Bennacer and Mohammed El Ganaoui
Ma, Qiang; Chen, Zhenqian; Liu, Hao
2017-07-01
In this paper, to predict the dynamics behaviors of flow and mass transfer with adsorption phenomena in porous media at the representative elementary volume (REV) scale, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for the convection-diffusion equation is developed to solve the transfer problem with an unsteady source term in porous media. Utilizing the Chapman-Enskog analysis, the modified MRT-LB model can recover the macroscopic governing equations at the REV scale. The coupled MRT-LB model for momentum and mass transfer is validated by comparing with the finite-difference method and the analytical solution. Moreover, using the MRT-LB method coupled with the linear driving force model, the fluid transfer and adsorption behaviors of the carbon dioxide in a porous fixed bed are explored. The breakthrough curve of adsorption from MRT-LB simulation is compared with the experimental data and the finite-element solution, and the transient concentration distributions of the carbon dioxide along the porous fixed bed are elaborated upon in detail. In addition, the MRT-LB simulation results show that the appearance time of the breakthrough point in the breakthrough curve is advanced as the mass transfer resistance in the linear driving force model increases; however, the saturation point is prolonged inversely.
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.
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.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding
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Pravinraj, T., E-mail: pravinraj1711@gmail.com; Patrikar, Rajendra
2017-07-01
Highlights: • A LBM model on partial wetting surface for droplet dynamics is presented by introducing a simple initial partial wetting boundary condition in SC model. • With our approach one can tune the splitting volume and time by carefully choosing strip width and position. • It is shown that the droplet spreading on chemically heterogeneous surfaces can be controlled not only by Weber number but also by tuning strip width ratio. • The directional transportation of a droplet due to chemical wetting gradient is simulated and analyzed using hybrid thermodynamic-image processing technique. • Microstructure surface and its influence on the directional wetting based transportation of droplet are demonstrated. - Abstract: Partial wetting surfaces and its influence on the droplet movement of micro and nano scale being contemplated for many useful applications. The dynamics of the droplet usually analyzed with a multiphase lattice Boltzmann method (LBM). In this paper, the influence of partial wetting surface on the dynamics of droplet is systematically analyzed for various cases. Splitting of droplets due to chemical gradient of the surface is studied and analyses of splitting time for various widths of the strips for different Weber numbers are computed. With the proposed model one can tune the splitting volume and time by carefully choosing a strip width and droplet position. The droplet spreading on chemically heterogeneous surfaces shows that the spreading can be controlled not only by parameters of Weber number but also by tuning strip width ratio. The transportation of the droplet from hydrophobic surface to hydrophilic surface due to chemical gradient is simulated and analyzed using our hybrid thermodynamic-image processing technique. The results prove that with the progress of time the surface free energy decreases with increase in spreading area. Finally, the transportation of a droplet on microstructure gradient is demonstrated. The model explains
Lattice Boltzmann simulation of water isotope fractionation during ice crystal growth in clouds
Lu, Guoping; DePaolo, Donald J.
2016-05-01
We describe a lattice Boltzmann (LB) method for simulating water isotope fractionation during diffusion-limited ice crystal growth by vapor deposition from water-oversaturated air. These conditions apply to the growth of snow crystals in clouds where the vapor composition is controlled by the presence of both ice crystals and water droplets. Modeling of water condensation with the LB method has the advantage of allowing concentration fields to evolve based on local conditions so that the controls on grain shapes of the condensed phase can be studied simultaneously with the controls on isotopic composition and growth rate. Water isotope fractionation during snow crystal growth involves kinetic effects due to diffusion of water vapor in air, which requires careful consideration of the boundary conditions at the ice-vapor interface. The boundary condition is relatively simple for water isotopes because the molecular exchange rate for water at the interface is large compared to the crystal growth rate. Our results for the bulk crystal isotopic composition are consistent with simpler models using analytical solutions for radial geometry. However, the model results are sufficiently different for oxygen isotopes that they could affect the interpretation of D-excess values of snow and ice. The extent of vapor oversaturation plays a major role in determining the water isotope fractionation as well as the degree of dendritic growth. Departures from isotopic equilibrium increase at colder temperatures as diffusivity decreases. Dendritic crystals are isotopically heterogeneous. Isotopic variations within individual snow crystals could yield information on the microphysics of ice condensation as well as on the accommodation or sticking coefficient of water associated with vapor deposition. Our results are ultimately a first step in implementing LB models for kinetically controlled condensation or precipitation reactions, but needs to be extended also to cases where the
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Ge Wen-Kai
2016-01-01
Full Text Available The spreading and permeation of droplets on porous substrates is a fundamental process in a variety of applications, such as coating, dyeing, and printing. The spreading and permeating usually occur synchronously but play different roles in the practical applications. The mechanisms of the competition between spreading and permeation is significant but still unclear. A lattice Boltzmann method is used to study the spreading and permeation of droplets on hybrid-wettability porous substrates, with different wettability on the surface and the inside pores. The competition between the spreading and the permeation processes is studied in this work from the effects of the substrate and the fluid properties, including the substrate wettability, the porous parameters, as well as the fluid surface tension and viscosity. The results show that increasing the surfacewettability and the porosity contact angle both inhibit the spreading and the permeation processes. When the inside porosity contact angle is larger than 90° (hydrophobic, the permeation process does not occur. The droplets suspend on substrates with Cassie state. The droplets are more easily to permeate into substrates with a small inside porosity contact angle (hydrophilic, as well as large pore sizes. Otherwise, the droplets are more easily to spread on substrate surfaces with small surface contact angle (hydrophilic and smaller pore sizes. The competition between droplet spreading and permeation is also related to the fluid properties. The permeation process is enhanced by increasing of surface tension, leading to a smaller droplet lifetime. The goals of this study are to provide methods to manipulate the spreading and permeation separately, which are of practical interest in many industrial applications.
Lattice Boltzmann flow simulations with applications of reduced order modeling techniques
Brown, Donald
2014-01-01
With the recent interest in shale gas, an understanding of the flow mechanisms at the pore scale and beyond is necessary, which has attracted a lot of interest from both industry and academia. One of the suggested algorithms to help understand flow in such reservoirs is the Lattice Boltzmann Method (LBM). The primary advantage of LBM is its ability to approximate complicated geometries with simple algorithmic modificatoins. In this work, we use LBM to simulate the flow in a porous medium. More specifically, we use LBM to simulate a Brinkman type flow. The Brinkman law allows us to integrate fast free-flow and slow-flow porous regions. However, due to the many scales involved and complex heterogeneities of the rock microstructure, the simulation times can be long, even with the speed advantage of using an explicit time stepping method. The problem is two-fold, the computational grid must be able to resolve all scales and the calculation requires a steady state solution implying a large number of timesteps. To help reduce the computational complexity and total simulation times, we use model reduction techniques to reduce the dimension of the system. In this approach, we are able to describe the dynamics of the flow by using a lower dimensional subspace. In this work, we utilize the Proper Orthogonal Decomposition (POD) technique, to compute the dominant modes of the flow and project the solution onto them (a lower dimensional subspace) to arrive at an approximation of the full system at a lowered computational cost. We present a few proof-of-concept examples of the flow field and the corresponding reduced model flow field.
Wang, Lei; Sun, Jianglong
2017-08-01
An axisymmetric two-phase lattice Boltzmann method is applied to simulate the dewetting dynamics of a thin liquid film on a substrate. Initially, a circular dry spot exists in the center of the liquid film. A contact line forms around the dry spot and expands outwards. The liquid films dewetting on smooth and rough substrates are investigated. For a smooth substrate, the effects of the contact angle (θeq), Ohnesorge number (Oh), and viscosity ratio (λμ) are studied. It is observed that the contact line recedes with a constant velocity V and that if θeq > 45°, V has a linear relationship with θeq, which has never been mentioned in previous literatures. For a rough substrate, well-distributed pillars are set up to represent the roughness. There are two states for the liquid film dewetting on a rough substrate: Cassie and Wenzel states. By comparison, it is found that the speed of the liquid film dewetting on the rough substrate of the Cassie state is slightly faster than that on the smooth substrate but much faster than that on the rough substrate of the Wenzel state, i.e., Wenzel state can obviously hold back the movement of the receding contact line. The corresponding mechanism is analyzed. The effect of the geometric factors of the pillars on the dewetting speed is discussed in detail. It is indicated that both the width and the depth of the grooves in roughness can significantly affect the dewetting speed. The results are helpful to design structured substrates for controlling the dewetting process of the liquid film.
Fully-resolved prolate spheroids in turbulent channel flows: A lattice Boltzmann study
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Amir Eshghinejadfard
2017-09-01
Full Text Available Particles are present in many natural and industrial multiphase flows. In most practical cases, particle shape is not spherical, leading to additional difficulties for numerical studies. In this paper, DNS of turbulent channel flows with finite-size prolate spheroids is performed. The geometry includes a straight wall-bounded channel at a frictional Reynolds number of 180 seeded with particles. Three different particle shapes are considered, either spheroidal (aspect ratio λ=2 or 4 or spherical (λ=1. Solid-phase volume fraction has been varied between 0.75% and 1.5%. Lattice Boltzmann method (LBM is used to model the fluid flow. The influence of the particles on the flow field is simulated by immersed boundary method (IBM. In this Eulerian-Lagrangian framework, the trajectory of each particle is computed individually. All particle-particle and particle-fluid interactions are considered (four-way coupling. Results show that, in the range of examined volume fractions, mean fluid velocity is reduced by addition of particles. However, velocity reduction by spheroids is much lower than that by spheres; 2% and 1.6%, compared to 4.6%. Maximum streamwise velocity fluctuations are reduced by addition of particle. By comparing particle and fluid velocities, it is seen that spheroids move faster than the fluid before reaching the same speed in the channel center. Spheres, on the other hand, move slower than the fluid in the buffer layer. Close to the wall, all particle types move faster than the fluid. Moreover, prolate spheroids show a preferential orientation in the streamwise direction, which is stronger close to the wall. Far from the wall, the orientation of spheroidal particles tends to isotropy.
Lattice Boltzmann model for high-order nonlinear partial differential equations
Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang
2018-01-01
In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.
Lattice Boltzmann Study on Seawall-Break Flows under the Influence of Breach and Buildings
Mei, Qiu-Ying; Zhang, Wen-Huan; Wang, Yi-Hang; Chen, Wen-Wen
2017-10-01
In the process of storm surge, the seawater often overflows and even destroys the seawall. The buildings near the shore are usually inundated by the seawater through the breach. However, at present, there is little study focusing on the effects of buildings and breach on the seawall-break flows. In this paper, the lattice Boltzmann (LB) model with nine velocities in two dimensions (D2Q9) for the shallow water equations is adopted to simulate the seawall-break flows. The flow patterns and water depth distributions for the seawall-break flows under various densities, layouts and shapes of buildings and different breach discharges, sizes and locations are investigated. It is found that when buildings with a high enough density are perpendicular to the main flow direction, an obvious backwater phenomenon appears near buildings while this phenomenon does not occur when buildings with the same density are parallel to the main flow direction. Moreover, it is observed that the occurrence of backwater phenomenon is independent of the building shape. As to the effects of breach on the seawall-break flows, it is found that only when the breach discharge is large enough or the breach size is small enough, the effects of asymmetric distribution of buildings on the seawall-break flows become important. The breach location only changes the flow pattern in the upstream area of the first building that seawater meets, but has little impact on the global water depth distribution. Supported by the National Natural Science Foundation of China under Grant No. 11502124, the Natural Science Foundation of Zhejiang Province under Grant No. LQ16A020001, the Scientific Research Fund of Zhejiang Provincial Education Department under Grant No. Y201533808, the Natural Science Foundation of Ningbo under Grant No. 2016A610075, and is sponsored by K.C. Wong Magna Fund in Ningbo University.
Brogi, F.; Malaspinas, O.; Bonadonna, C.; Chopard, B.; Ripepe, M.
2015-12-01
Low frequency (< 20Hz) acoustic measurements have a great potential for the real time characterization of volcanic plume source parameters. Using the classical source theory, acoustic data can be related to the exit velocity of the volcanic jet and to mass eruption rate, based on the geometric constrain of the vent and the mixture density. However, the application of the classical acoustic source models to volcanic explosive eruptions has shown to be challenging and a better knowledge of the link between the acoustic radiation and actual volcanic fluid dynamics processes is required. New insights into this subject could be given by the study of realistic aeroacoustic numerical simulations of a volcanic jet. Lattice Boltzmann strategies (LBS) provide the opportunity to develop an accurate, computationally fast, 3D physical model for a volcanic jet. In the field of aeroacoustic applications, dedicated LBS has been proven to have the low dissipative properties needed for capturing the weak acoustic pressure fluctuations. However, due to the big disparity in magnitude between the flow and the acoustic disturbances, even weak spurious noise sources in simulations can ruin the accuracy of the acoustic predictions. Reflected waves from artificial boundaries defined around the flow region can have significant influence on the flow field and overwhelm the acoustic field of interest. In addition, for highly multiscale turbulent flows, such as volcanic plumes, the number of grid points needed to represent the smallest scales might become intractable and the most complicated physics happen only in small portions of the computational domain. The implementation of the grid refinement, in our model allow us to insert local finer grids only where is actually needed and to increase the size of the computational domain for running more realistic simulations. 3D LBS model simulations for turbulent jet aeroacoustics have been accurately validated. Both mean flow and acoustic results
Lattice-Boltzmann simulation of multi-phase phenomena related to fuel cells
Akhgar, A.; Khalili, B.; Moa, B.; Rahnama, M.; Djilali, N.
2017-07-01
Fuel cells are devices that allow conversion of the chemical potential of a fuel and oxidant to produce electricity. A key component of a fuel cell is the catalyst layer, which facilitates the electrochemical reaction and where transport of reactants, charge, and byproduct heat and water take place. The structure and morphology of the catalyst layer determine its effectiveness and, in turn, strongly impact the overall performance and cost of a fuel cell. This paper discusses two central issue related to catalyst layers involving two-phase flow: liquid water transport in the catalyst layer during fuel cell operation, and fabrication of the catalyst layer from colloidal inks where a process of particle agglomeration takes place and eventually determines the final catalyst layer structure. Insight into these two issues are obtained using lattice-Botzmann based multi-phase simulations with formulations tailored to deal with features including high density ratio gas-liquid flow in complex porous media, and particle-particle and particle-hydrodynamic interactions.
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.
Energy Technology Data Exchange (ETDEWEB)
Escobar, Rodrigo A.; Amon, Cristina H. [Department of Mechanical Engineering and Institute for Complex Engineered Systems, Carnegie Mellon University, Pittsburgh, PA 15213 (United States); Ghai, Sartaj S.; Jhon, Myung S. [Department of Chemical Engineering and Institute for Complex Engineered Systems, Carnegie Mellon University, Pittsburgh, PA 15213 (United States)
2006-01-15
The lattice Boltzmann method (LBM) is used to investigate one-dimensional, multi-length and -time scale transient heat conduction in crystalline semiconductor solids, in which sub-continuum effects are important. The implementation of this method and its application to electronic devices are described. A silicon-on-insulator transistor subject to Joule heating conditions is used as a case study to illustrate the essence of the LBM. We compare our LBM results, for the diffusive to the ballistic transport regimes, with various hierarchical methodologies of heat transport such as the Fourier, Cattaneo, and ballistic-diffusive transport equations. (author)
2017-07-01
Boundary Conditions D2Q9 2-dimentional lattice (D2) with nine discrete velocities (Q9) model IMB Immersed Moving Boundary Kn Knudsen number LBE...Lattice Boltzmann Equation LBM Lattice Boltzzmann Method NS Navier-Stokes method Nu Nusselt number Pr Prandtl number Ra Reynolds number ...kinetic theory was introduced. The LBM includes no continuum assumption with regard to the flow; rather the fluid is described by individual
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.
Fakhari, Abbas; Bolster, Diogo; Luo, Li-Shi
2017-07-01
We present a lattice Boltzmann method (LBM) with a weighted multiple-relaxation-time (WMRT) collision model and an adaptive mesh refinement (AMR) algorithm for direct numerical simulation of two-phase flows in three dimensions. The proposed WMRT model enhances the numerical stability of the LBM for immiscible fluids at high density ratios, particularly on the D3Q27 lattice. The effectiveness and efficiency of the proposed WMRT-LBM-AMR is validated through simulations of (a) buoyancy-driven motion and deformation of a gas bubble rising in a viscous liquid; (b) the bag-breakup mechanism of a falling drop; (c) crown splashing of a droplet on a wet surface; and (d) the partial coalescence mechanism of a liquid drop at a liquid-liquid interface. The numerical simulations agree well with available experimental data and theoretical approximations where applicable.
Qiu, Ruo-Fan; You, Yan-Cheng; Zhu, Cheng-Xiang; Chen, Rong-Qian; Zhu, Jian-Feng
2017-12-01
Two three-dimensional (3D) lattice Boltzmann models in the framework of coupled double-distribution-function approach for compressible flows, in which specific-heat ratio and Prandtl number can be adjustable, are developed in this paper. The main differences between the two models are discrete equilibrium density and total energy distribution function. One is the D3Q25 model obtained from spherical function, and the other is the D3Q27 standard lattice model obtained from Hermite expansions of the corresponding continuous equilibrium distribution functions. The two models are tested by numerical simulations of some typical compressible flows, and their numerical stability and precision are also analysed. The results indicate that the two models are capable for supersonic flows, while the one from Hermite expansions is not suitable for compressible flows with shock waves.
Yoshida, Hiroaki; Kobayashi, Takayuki; Hayashi, Hidemitsu; Kinjo, Tomoyuki; Washizu, Hitoshi; Fukuzawa, Kenji
2014-07-01
A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.
Hejranfar, Kazem; Ezzatneshan, Eslam
2014-06-01
In this work, the implementation of a high-order compact finite-difference lattice Boltzmann method (CFDLBM) is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non-uniform grids. The incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates. Herein, the spatial derivatives in the resulting lattice Boltzmann (LB) equation in the computational plane are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient incompressible flow solver. A high-order spectral-type low-pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions, flow non-linearities and grid non-uniformity. All boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates. The accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems. A sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution. Four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are: unsteady Couette flow and steady flow in a 2-D cavity with non-uniform grid and steady and unsteady flows over a circular cylinder and the NACA0012 hydrofoil at different flow conditions. Results obtained for the above test cases are in good agreement with the existing numerical and experimental results. The study shows the present solution methodology based on the
Alizadeh, A; Wang, J K; Pooyan, S; Mirbozorgi, S A; Wang, M
2013-10-01
In this paper, the effect of temperature difference between inlet flow and walls on the electro-osmotic flow through a two-dimensional microchannel is investigated. The main objective is to study the effect of temperature variations on the distribution of ions and consequently internal electric potential field, electric body force, and velocity fields in an electro-osmotic flow. We assume constant temperature and zeta potential on walls and use the mean temperature of each cross section to characterize the Boltzmann ion distribution across the channel. Based on these assumptions, the multiphysical transports are still able to be described by the classical Poisson-Boltzmann model. In this work, the Navier-Stokes equation for fluid flow, the Poisson-Boltzmann equation for ion distribution, and the energy equation for heat transfer are solved by a couple lattice Boltzmann method. The modeling results indicate that the temperature difference between walls and the inlet solution may lead to two symmetrical vortices at the entrance region of the microchannel which is appropriate for mixing enhancements. The advantage of this phenomenon for active control of mixing in electro-osmotic flow is the manageability of the vortex scale without extra efforts. For instance, the effective domain of this pattern could broaden by the following modulations: decreasing the external electric potential field, decreasing the electric double layer thickness, or increasing the temperature difference between inlet flow and walls. This work may provide a novel strategy for design or optimization of microsystems. Copyright © 2013 Elsevier Inc. All rights reserved.
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.
Hussein, M A; Esterl, S; Pörtner, R; Wiegandt, K; Becker, T
2008-12-05
Owing to the growing demand of cartilage tissue repair and transplants, engineered cartilage cells have emerged as a prospective solution. Several bioreactors were built for artificially grown cartilage cells. In this work, a recently designed flow bed bioreactor is numerically investigated and compared with experimental results. The flow field inside the bioreactor was modelled using the lattice Boltzmann method. The flow consists of two phases which are the liquid component (nutrition supply) and gas component (oxygen supply). The flow field is simulated using the multi-phase lattice Boltzmann method, whilst the cell activity is modelled using Michaelis-Menten kinetics. The oxygen diffusion level at the exit of the nutrition phase is used as an evaluation process between the numerical and experimental results reporting the possibility of using the proposed model to fully simulate such bioreactors, though greatly saving time and money. Shear stress and pressure distributions are as well compared with published human cartilage load measurements to estimate the dynamic similarity between the bioreactor and the human knee. The predicted oxygen levels proved consistent trends with the experimental work with a 7% difference after 1h measuring time. The shear stress levels recorded 10-11 orders of magnitude lower than in humans and also one order of magnitude lower in the pressure distribution.
Nemati, Maedeh; Shateri Najaf Abady, Ali Reza; Toghraie, Davood; Karimipour, Arash
2018-01-01
The incorporation of different equations of state into single-component multiphase lattice Boltzmann model is considered in this paper. The original pseudopotential model is first detailed, and several cubic equations of state, the Redlich-Kwong, Redlich-Kwong-Soave, and Peng-Robinson are then incorporated into the lattice Boltzmann model. A comparison of the numerical simulation achievements on the basis of density ratios and spurious currents is used for presentation of the details of phase separation in these non-ideal single-component systems. The paper demonstrates that the scheme for the inter-particle interaction force term as well as the force term incorporation method matters to achieve more accurate and stable results. The velocity shifting method is demonstrated as the force term incorporation method, among many, with accuracy and stability results. Kupershtokh scheme also makes it possible to achieve large density ratio (up to 104) and to reproduce the coexistence curve with high accuracy. Significant reduction of the spurious currents at vapor-liquid interface is another observation. High-density ratio and spurious current reduction resulted from the Redlich-Kwong-Soave and Peng-Robinson EOSs, in higher accordance with the Maxwell construction results.
Chen, Sheng; Tölke, Jonas; Krafczyk, Manfred
2009-07-01
A simple lattice Boltzmann model for numerical simulation of fluid flow and heat transfer inside a rotating disk-cylinder configuration, which is of fundamental interest and practical importance in science as well as in engineering, is proposed in this paper. Unlike existing lattice Boltzmann models for such flows, which were based on “primitive-variable” Navier-Stokes equations, the target macroscopic equations of the present model for the flow field are vorticity-stream function equations, inspired by our recent work designed for nonrotating flows [S. Chen, J. Tölke, and M. Krafczyk, Phys. Rev. E 79, 016704 (2009); S. Chen, J. Tölke, S. Geller, and M. Krafczyk, Phys. Rev. E 78, 046703 (2008)]. The flow field and the temperature field both are solved by the D2Q5 model. Compared with the previous models, the present model is more efficient, more stable, and much simpler. It was found that, even though with a relatively low grid resolution, the present model can still work well when the Grashof number is very high. The advantages of the present model are validated by numerical experiments.
Lattice Boltzmann Simulation of Kinetic Isotope Effect During Snow Crystal Formation
Lu, G.; Depaolo, D. J.; Kang, Q.; Zhang, D.
2007-12-01
The isotopic composition of precipitation, especially that of snow, plays a special role in the global hydrological cycle and in reconstruction of past climates using polar ice cores. The fractionation of the major water isotope species (HHO, HDO, HHO-18) during ice crystal formation is critical to understanding the global distribution of isotopes in precipitation. Ice crystal growth in clouds is traditionally treated with a spherically-symmetric steady state diffusion model, with semi-empirical modifications added to account for ventilation and for complex crystal morphology. Although it is known that crystal growth rate, which depends largely on the degree of vapor over- saturation, determines crystal morphology, there are no quantitative models that relate morphology to the vapor saturation factor. Since kinetic (vapor phase diffusion-controlled) isotopic fractionation also depends on growth rate, there should be direct relationships between vapor saturation, crystal morphology, and crystal isotopic composition. We use a 2D lattice Boltzmann model to simulate diffusion-controlled ice crystal growth from vapor- oversaturated air. In the model, crystals grow solely according to the diffusive fluxes just above the crystal surfaces, and hence crystal morphology arises from the initial and boundary conditions in the model and does not need to be specified a priori. Crystal growth patterns can be varied between random growth and deterministic growth (along the maximum concentration gradient for example). The input parameters needed are the isotope- dependent vapor deposition rate constant (k) and the water vapor diffusivity in air (D). The values of both k and D can be computed from kinetic theory, and there are also experimentally determined values of D. The deduced values of k are uncertain to the extent that the condensation coefficient for ice is uncertain. The ratio D/k is a length (order 1 micron) that determines the minimum scale of dendritic growth features
Lattice Boltzmann Simulation of Water Isotope Fractionation During Growth of Ice Crystals in Clouds
Lu, G.; Depaolo, D.; Kang, Q.; Zhang, D.
2006-12-01
The isotopic composition of precipitation, especially that of snow, plays a special role in the global hydrological cycle and in reconstruction of past climates using polar ice cores. The fractionation of the major water isotope species (HHO, HDO, HHO-18) during ice crystal formation is critical to understanding the global distribution of isotopes in precipitation. Ice crystal growth in clouds is traditionally treated with a spherically- symmetric steady state diffusion model, with semi-empirical modifications added to account for ventilation and for complex crystal morphology. Although it is known that crystal growth rate, which depends largely on the degree of vapor over-saturation, determines crystal morphology, there are no existing quantitative models that directly relate morphology to the vapor saturation factor. Since kinetic (vapor phase diffusion-controlled) isotopic fractionation also depends on growth rate, there should be a direct relationship between vapor saturation, crystal morphology, and crystal isotopic composition. We use a 2D Lattice-Boltzmann model to simulate diffusion-controlled ice crystal growth from vapor- oversaturated air. In the model, crystals grow solely according to the diffusive fluxes just above the crystal surfaces, and hence crystal morphology arises from the initial and boundary conditions in the model and does not need to be specified a priori. The input parameters needed are the isotope-dependent vapor deposition rate constant (k) and the water vapor diffusivity in air (D). The values of both k and D can be computed from kinetic theory, and there are also experimentally determined values of D. The deduced values of k are uncertain to the extent that the sticking coefficient (or accommodation coefficient) for ice is uncertain. The ratio D/k is a length that determines the minimum scale of dendritic growth features and allows us to scale the numerical calculations to atmospheric conditions using a dimensionless Damkohler number
Puglisi, Andrea
2015-01-01
This brief offers a concise presentation of granular fluids from the point of view of non-equilibrium statistical physics. The emphasis is on fluctuations, which can be large in granular fluids due to the small system size (the number of grains is many orders of magnitude smaller than in molecular fluids). Firstly, readers will be introduced to the most intriguing experiments on fluidized granular fluids. Then granular fluid theory, which goes through increasing levels of coarse-graining and emerging collective phenomena, is described. Problems and questions are initially posed at the level of kinetic theory, which describes particle densities in full or reduced phase-space. Some answers become clear through hydrodynamics, which describes the evolution of slowly evolving fields. Granular fluctuating hydrodynamics, which builds a bridge to the most recent results in non-equilibrium statistical mechanics, is also introduced. Further and more interesting answers come when the dynamics of a massive intruder are...
Amiri Delouei, A.; Nazari, M.; Kayhani, M. H.; Succi, S.
2014-05-01
In this study, the immersed boundary-thermal lattice Boltzmann method has been used to simulate non-Newtonian fluid flow over a heated circular cylinder. The direct-forcing algorithm has been employed to couple the off-lattice obstacles and on-lattice fluid nodes. To investigate the effect of boundary sharpness, two different diffuse interface schemes are considered to interpolate the velocity and temperature between the boundary and computational grid points. The lattice Boltzmann equation with split-forcing term is applied to consider the effects of the discrete lattice and the body force to the momentum flux, simultaneously. A method for calculating the Nusselt number based on diffuse interface schemes is developed. The rheological and thermal properties of non-Newtonian fluids are investigated under the different power-law indices and Reynolds numbers. The effect of numerical parameters on the accuracy of the proposed method has been investigated in detail. Results show that the rheological and thermal properties of non-Newtonian fluids in the presence of a heated immersed body can be suitably captured using the immersed boundary thermal lattice Boltzmann method.
Fiorentino, Eve-Agnès; Toussaint, Renaud; Jouniaux, Laurence
2017-02-01
The streaming potential phenomenon is an electrokinetic effect that occurs in porous media. It is characterized by an electrokinetic (EK) coefficient. The aim of this paper is to simulate the EK coefficient in unsaturated conditions using the Lattice Boltzmann method in a 2-D capillary channel. The multiphase flow is simulated with the model of Shan & Chen. The Poisson-Boltzmann equation is solved by implementing the model of Chai & Shi. The streaming potential response shows a non-monotonous behaviour due to the combination of the increase of charge density and decrease of flow velocity with decreasing water saturation. Using a ζ potential of -20 mV at the air-water interface, an enhancement of a factor 5-30 of the EK coefficient, compared to the saturated state, can be observed due to the positive charge excess at this interface which is magnified by the fluid velocity away from the rock surface. This enhancement is correlated to the fractioning of the bubbles, and to the dynamic state of these bubbles, moving or entrapped in the crevices of the channel.
Boyd, J.; Buick, J. M.
2008-10-01
Numerical modelling is a powerful tool in the investigation of human blood flow and arterial diseases such as atherosclerosis. It is known that near wall velocity and shear are important in the pathogenesis and progression of atherosclerosis. In this paper results for a simulation of blood flow in a three-dimensional carotid artery geometry using the lattice Boltzmann method are presented. The velocity fields in the body of the fluid are analysed at six times of interest during a physiologically accurate velocity waveform. It is found that the three-dimensional model agrees well with previous literature results for carotid artery flow. Regions of low near wall velocity and circulatory flow are observed near the outer wall of the bifurcation and in the lower regions of the external carotid artery, which are regions that are typically prone to atherosclerosis.
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.
Yi, Hou-Hui; Yang, Xiao-Feng; Wang, Cai-Feng; Li, Hua-Bing
2009-07-01
The rolling massage is one of the most important manipulations in Chinese massage, which is expected to eliminate many diseases. Here, the effect of the rolling massage on a pair of particles moving in blood vessels under rolling massage manipulation is studied by the lattice Boltzmann simulation. The simulated results show that the motion of each particle is considerably modified by the rolling massage, and it depends on the relative rolling velocity, the rolling depth, and the distance between particle position and rolling position. Both particles' translational average velocities increase almost linearly as the rolling velocity increases, and obey the same law. The increment of the average relative angular velocity for the leading particle is smaller than that of the trailing one. The result is helpful for understanding the mechanism of the massage and to further develop the rolling techniques.
Schmieschek, S.; Shamardin, L.; Frijters, S.; Krüger, T.; Schiller, U. D.; Harting, J.; Coveney, P. V.
2017-08-01
We introduce the lattice-Boltzmann code LB3D, version 7.1. Building on a parallel program and supporting tools which have enabled research utilising high performance computing resources for nearly two decades, LB3D version 7 provides a subset of the research code functionality as an open source project. Here, we describe the theoretical basis of the algorithm as well as computational aspects of the implementation. The software package is validated against simulations of meso-phases resulting from self-assembly in ternary fluid mixtures comprising immiscible and amphiphilic components such as water-oil-surfactant systems. The impact of the surfactant species on the dynamics of spinodal decomposition are tested and quantitative measurement of the permeability of a body centred cubic (BCC) model porous medium for a simple binary mixture is described. Single-core performance and scaling behaviour of the code are reported for simulations on current supercomputer architectures.
Directory of Open Access Journals (Sweden)
A. R. Rahmati
2016-12-01
Full Text Available Because of its kinetic nature and computational advantages, the Lattice Boltzmann method (LBM has been well accepted as a useful tool to simulate micro-scale flows. The slip boundary model plays a crucial role in the accuracy of solutions for micro-channel flow simulations. The most used slip boundary condition is the Maxwell slip model. The results of Maxwell slip model are affected by the accommodation coefficient significantly, but there is not an explicitly relationship between properties at wall and accommodation coefficient. In the present wok, Langmuir slip model is used beside LBM to simulate micro-channel and micro-orifice flows. Slip velocity and nonlinear pressure drop profiles are presented as two major effects in such flows. The results are in good agreement with existing results in the literature.
Ambruş, Victor Eugen; Sofonea, Victor
2012-07-01
We use the spherical coordinate system in the momentum space and an appropriate discretization procedure to derive a hierarchy of lattice Boltzmann (LB) models with variable temperature. The separation of the integrals in the momentum space into angular and radial parts allows us to compute the moments of the equilibrium distribution function by means of Gauss-Legendre and Gauss-Laguerre quadratures, as well as to find the elements of the discrete momentum set for each LB model in the hierarchy. The capability of the high-order models in this hierarchy to capture specific effects in microfluidics is investigated through a computer simulation of Couette flow by using the Shakhov collision term to get the right value of the Prandtl number.
Directory of Open Access Journals (Sweden)
Bouchmel Mliki
2015-09-01
Full Text Available In the present paper, fluid flow and heat transfer inside L-shaped enclosure filled with Cu/water nanofluid has been investigated numerically using the Lattice Boltzmann Method. The validity of the numerical code used is ascertained and good agreement was found with published results. The effects of different parameters such as Rayleigh number (103–106, aspect ratio of the L-shaped enclosure (0.2–0.6 and nanoparticle volume concentration (0–0.05 on the flow and temperature fields are studied. The obtained results show that nanofluid enhances the heat transfer amount and reducing the aspect ratio improves this effect. Also it was found that the mean Nusselt number increased with increase in Rayleigh number.
Yuan, H. Z.; Wang, Y.; Shu, C.
2017-12-01
This paper presents an adaptive mesh refinement-multiphase lattice Boltzmann flux solver (AMR-MLBFS) for effective simulation of complex binary fluid flows at large density ratios. In this method, an AMR algorithm is proposed by introducing a simple indicator on the root block for grid refinement and two possible statuses for each block. Unlike available block-structured AMR methods, which refine their mesh by spawning or removing four child blocks simultaneously, the present method is able to refine its mesh locally by spawning or removing one to four child blocks independently when the refinement indicator is triggered. As a result, the AMR mesh used in this work can be more focused on the flow region near the phase interface and its size is further reduced. In each block of mesh, the recently proposed MLBFS is applied for the solution of the flow field and the level-set method is used for capturing the fluid interface. As compared with existing AMR-lattice Boltzmann models, the present method avoids both spatial and temporal interpolations of density distribution functions so that converged solutions on different AMR meshes and uniform grids can be obtained. The proposed method has been successfully validated by simulating a static bubble immersed in another fluid, a falling droplet, instabilities of two-layered fluids, a bubble rising in a box, and a droplet splashing on a thin film with large density ratios and high Reynolds numbers. Good agreement with the theoretical solution, the uniform-grid result, and/or the published data has been achieved. Numerical results also show its effectiveness in saving computational time and virtual memory as compared with computations on uniform meshes.
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.
Maslo, Aljaž; Panjan, Jože; Žagar, Dušan
2014-07-15
This paper tests the adequacy of using the lattice Boltzmann method in large-scale oil spill modelling, such as the Lebanon oil spill. Several numerical experiments were performed in order to select the most appropriate lattice and to decide between the single- and two-relaxation time models. Large-scale oil spills require simulations with short computational times. In order to speed up the computation and preserve adequate accuracy of the model, five different flux limiting interpolation techniques were compared and evaluated. The model was validated on the Lebanon oil spill with regard to the oil-slick position and concentrations in the sea, and the beaching area on the coast. Good agreement with satellite images of the slick and field data on beaching was achieved. The main advantages of the applied method are the capability of simulating very low oil concentrations and computational times that are by an order of magnitude shorter compared to similar models. Copyright © 2014 Elsevier Ltd. All rights reserved.
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.
Nash, Rupert W.; Carver, Hywel B.; Bernabeu, Miguel O.; Hetherington, James; Groen, Derek; Krüger, Timm; Coveney, Peter V.
2014-02-01
Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002), 10.1063/1.1471914; Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001), 10.1063/1.1399290; Junk and Yang, Phys. Rev. E 72, 066701 (2005), 10.1103/PhysRevE.72.066701] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.
Wang, Ying; Krafczyk, Manfred; Geier, Martin; Schönherr, Martin
2014-05-01
The quantification of soil evaporation and of soil water content dynamics near the soil surface are critical in the physics of land-surface processes on many scales and are dominated by multi-component and multi-phase mass and energy fluxes between the ground and the atmosphere. Although it is widely recognized that both liquid and gaseous water movement are fundamental factors in the quantification of soil heat flux and surface evaporation, their computation has only started to be taken into account using simplified macroscopic models. As the flow field over the soil can be safely considered as turbulent, it would be natural to study the detailed transient flow dynamics by means of Large Eddy Simulation (LES [1]) where the three-dimensional flow field is resolved down to the laminar sub-layer. Yet this requires very fine resolved meshes allowing a grid resolution of at least one order of magnitude below the typical grain diameter of the soil under consideration. In order to gain reliable turbulence statistics, up to several hundred eddy turnover times have to be simulated which adds up to several seconds of real time. Yet, the time scale of the receding saturated water front dynamics in the soil is on the order of hours. Thus we are faced with the task of solving a transient turbulent flow problem including the advection-diffusion of water vapour over the soil-atmospheric interface represented by a realistic tomographic reconstruction of a real porous medium taken from laboratory probes. Our flow solver is based on the Lattice Boltzmann method (LBM) [2] which has been extended by a Cumulant approach similar to the one described in [3,4] to minimize the spurious coupling between the degrees of freedom in previous LBM approaches and can be used as an implicit LES turbulence model due to its low numerical dissipation and increased stability at high Reynolds numbers. The kernel has been integrated into the research code Virtualfluids [5] and delivers up to 30% of the
Khali, S.; Nebbali, R.; Ameziani, D. E.; Bouhadef, K.
2013-05-01
In this work the instability of the Taylor-Couette flow for Newtonian and non-Newtonian fluids (dilatant and pseudoplastic fluids) is investigated for cases of finite aspect ratios. The study is conducted numerically using the lattice Boltzmann method (LBM). In many industrial applications, the apparatuses and installations drift away from the idealized case of an annulus of infinite length, and thus the end caps effect can no longer be ignored. The inner cylinder is rotating while the outer one and the end walls are maintained at rest. The lattice two-dimensional nine-velocity (D2Q9) Boltzmann model developed from the Bhatnagar-Gross-Krook approximation is used to obtain the flow field for fluids obeying the power-law model. The combined effects of the Reynolds number, the radius ratio, and the power-law index n on the flow characteristics are analyzed for an annular space of finite aspect ratio. Two flow modes are obtained: a primary Couette flow (CF) mode and a secondary Taylor vortex flow (TVF) mode. The flow structures so obtained are different from one mode to another. The critical Reynolds number Rec for the passage from the primary to the secondary mode exhibits the lowest value for the pseudoplastic fluids and the highest value for the dilatant fluids. The findings are useful for studies of the swirling flow of non-Newtonians fluids in axisymmetric geometries using LBM. The flow changes from the CF to TVF and its structure switches from the two-cells to four-cells regime for both Newtonian and dilatant fluids. Contrariwise for pseudoplastic fluids, the flow exhibits 2-4-2 structure passing from two-cells to four cells and switches again to the two-cells configuration. Furthermore, the critical Reynolds number presents a monotonic increase with the power-law index n of the non-Newtonian fluid, and as the radius ratio grows, the transition flow regimes tend to appear for higher critical Reynolds numbers.
Zhuo, Congshan; Sagaut, Pierre
2017-06-01
In this paper, a variant of the acoustic multipole source (AMS) method is proposed within the framework of the lattice Boltzmann method. A quadrupole term is directly included in the stress system (equilibrium momentum flux), and the dependency of the quadrupole source in the inviscid limit upon the fortuitous discretization error reported in the works of E. M. Viggen [Phys. Rev. E 87, 023306 (2013), 10.1103/PhysRevE.87.023306] is removed. The regularized lattice Boltzmann (RLB) method with this variant AMS method is presented for the 2D and 3D acoustic problems in the inviscid limit, and without loss of generality, the D3Q19 model is considered in this work. To assess the accuracy and the advantage of the RLB scheme with this AMS for acoustic point sources, the numerical investigations and comparisons with the multiple-relaxation-time (MRT) models and the analytical solutions are performed on the 2D and 3D acoustic multipole point sources in the inviscid limit, including monopoles, x dipoles, and x x quadrupoles. From the present results, the good precision of this AMS method is validated, and the RLB scheme exhibits some superconvergence properties for the monopole sources compared with the MRT models, and both the RLB and MRT models have the same accuracy for the simulations of acoustic dipole and quadrupole sources. To further validate the capability of the RLB scheme with AMS, another basic acoustic problem, the acoustic scattering from a solid cylinder presented at the Second Computational Aeroacoustics Workshop on Benchmark Problems, is numerically considered. The directivity pattern of the acoustic field is computed at r =7.5 ; the present results agree well with the exact solutions. Also, the effects of slip and no-slip wall treatments within the regularized boundary condition on this pure acoustic scattering problem are tested, and compared with the exact solution, the slip wall treatment can present a better result. All simulations demonstrate that the
Silva, Goncalo; Semiao, Viriato
2017-07-01
The first nonequilibrium effect experienced by gaseous flows in contact with solid surfaces is the slip-flow regime. While the classical hydrodynamic description holds valid in bulk, at boundaries the fluid-wall interactions must consider slip. In comparison to the standard no-slip Dirichlet condition, the case of slip formulates as a Robin-type condition for the fluid tangential velocity. This makes its numerical modeling a challenging task, particularly in complex geometries. In this work, this issue is handled with the lattice Boltzmann method (LBM), motivated by the similarities between the closure relations of the reflection-type boundary schemes equipping the LBM equation and the slip velocity condition established by slip-flow theory. Based on this analogy, we derive, as central result, the structure of the LBM boundary closure relation that is consistent with the second-order slip velocity condition, applicable to planar walls. Subsequently, three tasks are performed. First, we clarify the limitations of existing slip velocity LBM schemes, based on discrete analogs of kinetic theory fluid-wall interaction models. Second, we present improved slip velocity LBM boundary schemes, constructed directly at discrete level, by extending the multireflection framework to the slip-flow regime. Here, two classes of slip velocity LBM boundary schemes are considered: (i) linear slip schemes, which are local but retain some calibration requirements and/or operation limitations, (ii) parabolic slip schemes, which use a two-point implementation but guarantee the consistent prescription of the intended slip velocity condition, at arbitrary plane wall discretizations, further dispensing any numerical calibration procedure. Third and final, we verify the improvements of our proposed slip velocity LBM boundary schemes against existing ones. The numerical tests evaluate the ability of the slip schemes to exactly accommodate the steady Poiseuille channel flow solution, over
Ripesi, P; Schifano, S F; Tripiccione, R
2014-01-01
We study the turbulent evolution originated from a system subjected to a Rayleigh-Taylor instability with a double density at high resolution in a 2 dimensional geometry using a highly optimized thermal Lattice Boltzmann code for GPUs. The novelty of our investigation stems from the initial condition, given by the superposition of three layers with three different densities, leading to the development of two Rayleigh-Taylor fronts that expand upward and downward and collide in the middle of the cell. By using high resolution numerical data we highlight the effects induced by the collision of the two turbulent fronts in the long time asymptotic regime. We also provide details on the optimized Lattice-Boltzmann code that we have run on a cluster of GPUs
Safari, Hesameddin; Rahimian, Mohammad Hassan; Krafczyk, Manfred
2013-07-01
In this article, a method based on the multiphase lattice Boltzmann framework is presented which is applicable to liquid-vapor phase-change phenomena. Both liquid and vapor phases are assumed to be incompressible. For phase changes occurring at the phase interface, the divergence-free condition of the velocity field is no longer satisfied due to the gas volume generated by vaporization or fluid volume generated by condensation. Thus, we extend a previous model by a suitable equation to account for the finite divergence of the velocity field within the interface region. Furthermore, the convective Cahn-Hilliard equation is extended to take into account vaporization effects. In a first step, a D1Q3 LB model is constructed and validated against the analytical solution of a one-dimensional Stefan problem for different density ratios. Finally the model is extended to two dimensions (D2Q9) to simulate droplet evaporation. We demonstrate that the results obtained by this approach are in good agreement with theory.
Hilpert, Markus
2007-05-15
Theoretical considerations and experiments in capillary tubes suggest that blobs exhibit resonance in porous media when they are trapped because of interfacial tension. Here, we investigate the hypothesis that such blobs can be mobilized by exploiting a phenomenon entitled capillarity-induced resonance, that is, by exciting the blobs at their resonant frequency. We used Lattice-Boltzmann (LB) modeling to perform numerical experiments, and we validated the LB model using analytical solutions that approximate the linear response of blobs with pinned menisci in straight and polygonal pore channels to an oscillatory body force. The LB simulations agree well with the quasistatic response, which the analytical solutions describe correctly. Furthermore, the frequency response, particularly the resonant frequency, agrees well, even though the analytical solutions do not accurately estimate viscous pressure drops. Numerical experiments in polygonal and sinusoidal pore channels, as well as disc packings, show that blobs, which are trapped even though a constant body force is applied, can indeed be mobilized by exploiting capillarity-induced resonance. Moreover, the resonant frequency can be estimated in numerical experiments by determining the dominant frequency in the blob amplitude in response to a force pulse. This is of great practical relevance for complex geometries, for which the resonant frequency cannot be easily predicted theoretically.
Deiterding, Ralf; Fragner, Moritz M.
2015-11-01
Numerical investigations in order to determine the forces induced by side wind onto a train geometry are generally not sufficiently accurate to be used as a predictive tool for regulatory safety assessment. Especially for larger yaw angles, the turbulent cross-wind flow is characterized by highly instationary behavior, driven primarily by vortex shedding on the roof and underside geometric details, i.e., the bogie and wheel systems. While industry-typical Reynolds-averaged turbulence models are not well suited for this scenario, better results are obtained when large eddy simulation (LES) techniques are applied. Here, we employ a recently self-developed weakly compressible lattice Boltzmann method (LBM) with Smagorinsky LES model on hierarchically adaptive block-structured Cartesian meshes. Using a train front-car of 1:25 scale at yaw angle 30° and Re = 250 , 000 as main test case, we compare the LBM results with incompressible large eddy and detached eddy simulations on unstructured boundary-layer type meshes using the OpenFOAM package. It is found that time averaged force and moment predictions from our LBM code compare better to available wind tunnel data, while mesh adaptation and explicit nature of the LBM approach reduce the computational costs considerably.
Chai, Zhenhua; Zhao, T S
2014-07-01
In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.
Yamabe, Hirotatsu; Tsuji, Takeshi; Liang, Yunfeng; Matsuoka, Toshifumi
2015-01-06
CO2 geosequestration in deep aquifers requires the displacement of water (wetting phase) from the porous media by supercritical CO2 (nonwetting phase). However, the interfacial instabilities, such as viscous and capillary fingerings, develop during the drainage displacement. Moreover, the burstlike Haines jump often occurs under conditions of low capillary number. To study these interfacial instabilities, we performed lattice Boltzmann simulations of CO2-water drainage displacement in a 3D synthetic granular rock model at a fixed viscosity ratio and at various capillary numbers. The capillary numbers are varied by changing injection pressure, which induces changes in flow velocity. It was observed that the viscous fingering was dominant at high injection pressures, whereas the crossover of viscous and capillary fingerings was observed, accompanied by Haines jumps, at low injection pressures. The Haines jumps flowing forward caused a significant drop of CO2 saturation, whereas Haines jumps flowing backward caused an increase of CO2 saturation (per injection depth). We demonstrated that the pore-scale Haines jumps remarkably influenced the flow path and therefore equilibrium CO2 saturation in crossover domain, which is in turn related to the storage efficiency in the field-scale geosequestration. The results can improve our understandings of the storage efficiency by the effects of pore-scale displacement phenomena.
Fortunato, V A; Caneppele, F L; Ribeiro, R; Rabi, J A
2018-02-01
While computational modelling has increasingly supported wastewater bioreactor engineering, novel numerical techniques have been developed such as the lattice-Boltzmann method (LBM). With vinasse treatment as case study, this work is a first step towards a comprehensive LBM simulator of a continuous-flow anaerobic packed-bed reactor. Extensions from typical models comprise one-dimensional (besides time) dependence, species transport via convection and diffusion, and imposition of either Dirichlet or Danckwerts condition at inlet. The LBM simulator proved to be operational when simulating the bioreactor at different hydraulic retention times (HRTs). Simulated profiles show that stepwise feeding concentrations are smoothed as they are transported towards the bioreactor exit while concentrations increase or decrease in response to generation or degradation kinetics. Good fitting was observed for concentrations of acetic acid (2.1 kg-COD/m 3 for HRT = 24 h) and butyric acid (1.3 kg-COD/m 3 for HRT = 16 h) at the exit whereas other concentrations were numerically simulated at proper order of magnitude.
Jinuntuya, Fontip; Whiteley, Michael; Chen, Rui; Fly, Ashley
2018-02-01
The Gas Diffusion Layer (GDL) of a Polymer Electrolyte Membrane Fuel Cell (PEMFC) plays a crucial role in overall cell performance. It is responsible for the dissemination of reactant gasses from the gas supply channels to the reactant sites at the Catalyst Layer (CL), and the adequate removal of product water from reactant sites back to the gas channels. Existing research into water transport in GDLs has been simplified to 2D estimations of GDL structures or use virtual stochastic models. This work uses X-ray computed tomography (XCT) to reconstruct three types of GDL in a model. These models are then analysed via Lattice Boltzmann methods to understand the water transport behaviours under differing contact angles and pressure differences. In this study, the three GDL samples were tested over the contact angles of 60°, 80°, 90°, 100°, 120° and 140° under applied pressure differences of 5 kPa, 10 kPa and 15 kPa. By varying the contact angle and pressure difference, it was found that the transition between stable displacement and capillary fingering is not a gradual process. Hydrophilic contact angles in the region of 60°<θ < 90° showed stable displacement properties, whereas contact angles in the region of 100°<θ < 140° displayed capillary fingering characteristics.
Fu, Yu-Hang; Bai, Lin; Luo, Kai-Hong; Jin, Yong; Cheng, Yi
2017-04-01
In this work, we propose a general approach for modeling mass transfer and reaction of dilute solute(s) in incompressible three-phase flows by introducing a collision operator in lattice Boltzmann (LB) method. An LB equation was used to simulate the solute dynamics among three different fluids, in which the newly expanded collision operator was used to depict the interface behavior of dilute solute(s). The multiscale analysis showed that the presented model can recover the macroscopic transport equations derived from the Maxwell-Stefan equation for dilute solutes in three-phase systems. Compared with the analytical equation of state of solute and dynamic behavior, these results are proven to constitute a generalized framework to simulate solute distributions in three-phase flows, including compound soluble in one phase, compound adsorbed on single-interface, compound in two phases, and solute soluble in three phases. Moreover, numerical simulations of benchmark cases, such as phase decomposition, multilayered planar interfaces, and liquid lens, were performed to test the stability and efficiency of the model. Finally, the multiphase mass transfer and reaction in Janus droplet transport in a straight microchannel were well reproduced.
Directory of Open Access Journals (Sweden)
Ahmad Reza Rahmati
2016-12-01
Full Text Available In this study, mixed convection heat transfer of water-Cu nanofluid in a double lid-driven cavity has been analyzed by lattice Boltzmann method. The double lid-driven are insulated and the side walls have sinusoidal temperature distribution. Simulations have been carried out at constant Grashof number 100, the Richardson numbers of 0.01, 0.1,1,10 and 100, temperature phase deviation of 0, π/4, π/2, 3π/4 and π, the solid volume fraction from zero to 0.06 and the Prandtl number of 6.57. The thermal modeling of passive scalar is applied and two separate distribution functions for the flow and temperature fields are considered. In order to calculate the thermal conductivity coefficient of nanofluid, constant and variable properties models are used. The results showed that in high Richardson numbers, the effect of the thermal phase deviation changes on the flow pattern is evident and in low Richardson numbers, the phase deviation changes do not affect the flow pattern. In all thermal phase deviations by reducing the Richardson number, the Nusselt number increases and thus the heat transfer increases. Also the average Nusselt number obtained for the constant properties model is higher compared with that of variable properties model.
Directory of Open Access Journals (Sweden)
Arshia Merdasi
2016-11-01
Full Text Available In this study, the Lattice Boltzmann Method (LBM is used to investigate the deformation of two droplets within microfluidic T-junctions (MFTD. In order to increase the accuracy the two immiscible fluids are modeled using the He-Chen-Zhang model. First, this model is applied to ensure that the surface tension effect existing between the droplets and the continuous fluid is properly implemented in the model. Then the collision and merging of the two droplets within the intersection of a T-shaped microchannel is investigated. For generating droplet formation the effects of relevant dimensionless parameters such as the Reynolds, the Weber numbers as well as a collision parameter affecting the two droplets during their motion and deformation are studied. It is found that by increasing the relative velocities of the inlet flows and droplet sizes, the deformation of the two droplets increases significantly. Our results also show that when the surface tension increases, it takes less time for the droplets to collide each other. Therefore, the droplet formation in MFTD depends significantly on the droplet size, inlet velocity as well as surface tension. Finally, we successfully investigated a two-phase flow streaming energy conversion system associated with droplet coalescence. The apprehension of fundamental physics of the droplet formation is useful for many applications including, stem cell phenotypes, cell transplantation and drug delivery in biomedical applications.
Molaeimanesh, G. R.; Nazemian, M.
2017-08-01
Proton exchange membrane (PEM) fuel cells with a great potential for application in vehicle propulsion systems will have a promising future. However, to overcome the exiting challenges against their wider commercialization further fundamental research is inevitable. The effects of gas diffusion layer (GDL) compression on the performance of a PEM fuel cell is not well-recognized; especially, via pore-scale simulation technique capturing the fibrous microstructure of the GDL. In the current investigation, a stochastic microstructure reconstruction method is proposed which can capture GDL microstructure changes by compression. Afterwards, lattice Boltzmann pore-scale simulation technique is adopted to simulate the reactive gas flow through 10 different cathode electrodes with dissimilar carbon paper GDLs produced from five different compression levels and two different carbon fiber diameters. The distributions of oxygen mole fraction, water vapor mole fraction and current density for the simulated cases are presented and analyzed. The results of simulations demonstrate that when the fiber diameter is 9 μm adding compression leads to lower average current density while when the fiber diameter is 7 μm the compression effect is not monotonic.
Xie, Jian.-Fei.; He, S.; Zu, Y. Q.; Lamy-Chappuis, B.; Yardley, B. W. D.
2017-08-01
In this paper, the migration of supercritical carbon dioxide (CO2) in realistic sandstone rocks under conditions of saline aquifers, with applications to the carbon geological storage, has been investigated by a two-phase lattice Boltzmann method (LBM). Firstly the digital images of sandstone rocks were reproduced utilizing the X-ray computed microtomography (micro-CT), and high resolutions (up to 2.5 μm) were applied to the pore-scale LBM simulations. For the sake of numerical stability, the digital images were "cleaned" by closing the dead holes and removing the suspended particles in sandstone rocks. In addition, the effect of chemical reactions occurred in the carbonation process on the permeability was taken into account. For the wetting brine and non-wetting supercritical CO2 flows, they were treated as the immiscible fluids and were driven by pressure gradients in sandstone rocks. Relative permeabilities of brine and supercritical CO2 in sandstone rocks were estimated. Particularly the dynamic saturation was applied to improve the reliability of the calculations of the relative permeabilities. Moreover, the effects of the viscosity ratio of the two immiscible fluids and the resolution of digital images on the relative permeability were systematically investigated.
Shan, Feng; Tu, Juan; Cheng, Jianchun; Zhang, Dong; Li, Faqi; Wang, Zhibiao
2017-03-01
High-intensity focused ultrasound (HIFU) has become an attractive therapeutic tool for noninvasive tumor treatment. The key component of HIFU systems is the acoustic transducer, which generates a focal region of high-intensity focused ultrasonic energy. A key determinant of safety in HIFU treatment is the size of the focal region. To achieve subwavelength focusing, we previously investigated the feasibility of an ultrasonic spherical cavity resonator (USCR) with two open ends. To further investigate the properties of the USCR, experiments and simulations were performed to comprehensively characterize the acoustic field generated. The emphasis was on the field formation process, the pressure distribution, the frequency dependence, and the acoustic nonlinearity. As a novel simulation approach, an axisymmetric isothermal multi-relaxation-time lattice Boltzmann method (MRT-LBM) model was used to numerically analyze the acoustic field. The reliability of this model was verified by comparing the results generated with those from experiments. The MRT-LBM model gave new insight into conventional acoustic numerical simulations and provided significant indications for USCR parameter optimization. The USCR demonstrated its feasibility for application in HIFU treatment or in other fields that demand high-precision focusing.
Ammar, Sami; Pernaudat, Guillaume; Trépanier, Jean-Yves
2017-08-01
The interdependence of surface tension and density ratio is a weakness of pseudo-potential based lattice Boltzmann models (LB). In this paper, we propose a 3D multi-relaxation time (MRT) model for multiphase flows at large density ratios. The proposed model is capable of adjusting the surface tension independently of the density ratio. We also present the 3D macroscopic equations recovered by the proposed forcing scheme. A high order of isotropy for the interaction force is used to reduce the amplitude of spurious currents. The proposed 3D-MRT model is validated by verifying Laplace's law and by analyzing its thermodynamic consistency and the oscillation period of a deformed droplet. The model is then applied to the simulation of the impact of a droplet on a dry surface. Impact dynamics are determined and the maximum spread factor calculated for different Reynolds and Weber numbers. The numerical results are in agreement with data published in the literature. The influence of surface wettability on the spread factor is also investigated. Finally, our 3D-MRT model is applied to the simulation of the impact of a droplet on a wet surface. The propagation of transverse waves is observed on the liquid surface.
Kang, Q.; Chen, L.
2014-12-01
Although short-term production of unconventional gas depends on the area of contact created by hydraulic fracturing and connections with pre-existing natural fracture networks, sustainable recovery is limited by transfer of gas from nanoporous matrix into the fractures, because the permeability of hydraulic fractures is orders of magnitude higher than that of the shale matrix. Therefore, a fundamental understanding of hydrocarbon mobility in shale matrix is urgently needed for improving recovery efficiencies. Shale transport properties (diffusivity, permeability, and electronic conductivity), which are critical for understanding the fundamental transport mechanisms, are still poorly understood. There have been some studies using experimental techniques such as scanning electron microscopy (SEM) to visualize the nanoscale structures of shale. Due to the ultra-low porosity and permeability, it is difficult to experimentally investigate the fundamental transport processes inside the shale or accurately measure the transport properties. Advanced pore-scale numerical methods, e.g., the lattice Boltzman method (LBM) may provide an alternative approach. In the present study, three-dimensional nanoscale porous structures of shale are reconstructed based on SEM images of shale samples. Characterization analysis of the nanoscale reconstructed shale is performed, including determination of porosity, pore size distribution, specific surface area, and pore connectivity. The LBM flow model and diffusion model are adopted to simulate fluid flow and Knudsen diffusion in the reconstructed shale, respectively. Tortuosity, intrinsic permeability, and effective Knudsen diffusivity are numerically predicted. The tortuosity is much higher than what is commonly employed in Bruggeman equation. Correction of the intrinsic permeability by taking into consideration the contribution of Knudsen diffusion, which leads to the apparent permeability, is performed. The correction factor under
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Kwon, Kyung [Tuskegee Univ., Tuskegee, AL (United States); Fan, Liang-Shih [The Ohio State Univ., Columbus, OH (United States); Zhou, Qiang [The Ohio State Univ., Columbus, OH (United States); Yang, Hui [The Ohio State Univ., Columbus, OH (United States)
2014-09-30
A new and efficient direct numerical method with second-order convergence accuracy was developed for fully resolved simulations of incompressible viscous flows laden with rigid particles. The method combines the state-of-the-art immersed boundary method (IBM), the multi-direct forcing method, and the lattice Boltzmann method (LBM). First, the multi-direct forcing method is adopted in the improved IBM to better approximate the no-slip/no-penetration (ns/np) condition on the surface of particles. Second, a slight retraction of the Lagrangian grid from the surface towards the interior of particles with a fraction of the Eulerian grid spacing helps increase the convergence accuracy of the method. An over-relaxation technique in the procedure of multi-direct forcing method and the classical fourth order Runge-Kutta scheme in the coupled fluid-particle interaction were applied. The use of the classical fourth order Runge-Kutta scheme helps the overall IB-LBM achieve the second order accuracy and provides more accurate predictions of the translational and rotational motion of particles. The preexistent code with the first-order convergence rate is updated so that the updated new code can resolve the translational and rotational motion of particles with the second-order convergence rate. The updated code has been validated with several benchmark applications. The efficiency of IBM and thus the efficiency of IB-LBM were improved by reducing the number of the Lagragian markers on particles by using a new formula for the number of Lagrangian markers on particle surfaces. The immersed boundary-lattice Boltzmann method (IBLBM) has been shown to predict correctly the angular velocity of a particle. Prior to examining drag force exerted on a cluster of particles, the updated IB-LBM code along with the new formula for the number of Lagrangian markers has been further validated by solving several theoretical problems. Moreover, the unsteadiness of the drag force is examined when a
Electro-osmosis of non-Newtonian fluids in porous media using lattice Poisson-Boltzmann method.
Chen, Simeng; He, Xinting; Bertola, Volfango; Wang, Moran
2014-12-15
Electro-osmosis in porous media has many important applications in various areas such as oil and gas exploitation and biomedical detection. Very often, fluids relevant to these applications are non-Newtonian because of the shear-rate dependent viscosity. The purpose of this study was to investigate the behaviors and physical mechanism of electro-osmosis of non-Newtonian fluids in porous media. Model porous microstructures (granular, fibrous, and network) were created by a random generation-growth method. The nonlinear governing equations of electro-kinetic transport for a power-law fluid were solved by the lattice Poisson-Boltzmann method (LPBM). The model results indicate that: (i) the electro-osmosis of non-Newtonian fluids exhibits distinct nonlinear behaviors compared to that of Newtonian fluids; (ii) when the bulk ion concentration or zeta potential is high enough, shear-thinning fluids exhibit higher electro-osmotic permeability, while shear-thickening fluids lead to the higher electro-osmotic permeability for very low bulk ion concentration or zeta potential; (iii) the effect of the porous medium structure depends significantly on the constitutive parameters: for fluids with large constitutive coefficients strongly dependent on the power-law index, the network structure shows the highest electro-osmotic permeability while the granular structure exhibits the lowest permeability on the entire range of power law indices considered; when the dependence of the constitutive coefficient on the power law index is weaker, different behaviors can be observed especially in case of strong shear thinning. Copyright © 2014 Elsevier Inc. All rights reserved.
Gupta, Anupam; Sbragaglia, Mauro
2016-01-01
The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number (Ca), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to Ca ≈ 3×10(-2). A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P model). We present the results of three-dimensional simulations in a range of Ca which is broad enough to characterize all the three characteristic mechanisms of break-up in the confined T-junction, i.e. squeezing, dripping and jetting regimes. The various model parameters of the FENE-P constitutive equations, including the polymer relaxation time τP and the finite extensibility parameter L2, are changed to provide quantitative details on how the dynamics and break-up properties are affected by viscoelasticity. We will analyze cases with Droplet Viscoelasticity (DV), where viscoelastic properties are confined in the dispersed (d) phase, as well as cases with Matrix Viscoelasticity (MV), where viscoelastic properties are confined in the continuous (c) phase. Moderate flow-rate ratios Q ≈ O(1) of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, as the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by the polymer stresses.
Chen, Sheng; Tölke, Jonas; Krafczyk, Manfred
2009-08-01
Natural convection within an enclosed circular annular cavity formed by two concentric vertical cylinders is of fundamental interest and practical importance. Generally, the assumption of axisymmetric thermal flow is adopted for simulating such natural convections and the validity of the assumption of axisymmetric thermal flow is still held even for some turbulent convection. Usually the Rayleigh numbers (Ra) of realistic flows are very high. However, the work to design suitable and efficient lattice Boltzmann (LB) models on such flows is quite rare. To bridge the gap, in this paper a simple LB subgrid-scale (SGS) model, which is based on our recent work [S. Chen, J. Tölke, and M. Krafczyk, Phys. Rev. E 79, 016704 (2009); S. Chen, J. Tölke, S. Geller, and M. Krafczyk, Phys. Rev. E 78, 046703 (2008)], is proposed for simulating convectional flow with high Ra within an enclosed circular annular cavity. The key parameter for the SGS model can be quite easily and efficiently evaluated by the present model. The numerical experiments demonstrate that the present model works well for a large range of Ra and Prandtl number (Pr). Though in the present study a popularly used static Smagorinsky turbulence model is adopted to demonstrate how to develop a LB SGS model for simulating axisymmetric thermal flows with high Ra, other state-of-the-art turbulence models can be incorporated into the present model in the same way. In addition, the present model can be extended straightforwardly to simulate other axisymmetric convectional flows with high Ra, for example, turbulent convection with internal volumetric heat generation in a vertical cylinder, which is an important simplified representation of a nuclear reactor.
Munk, David J.; Kipouros, Timoleon; Vio, Gareth A.; Steven, Grant P.; Parks, Geoffrey T.
2017-11-01
Recently, the study of micro fluidic devices has gained much interest in various fields from biology to engineering. In the constant development cycle, the need to optimise the topology of the interior of these devices, where there are two or more optimality criteria, is always present. In this work, twin physical situations, whereby optimal fluid mixing in the form of vorticity maximisation is accompanied by the requirement that the casing in which the mixing takes place has the best structural performance in terms of the greatest specific stiffness, are considered. In the steady state of mixing this also means that the stresses in the casing are as uniform as possible, thus giving a desired operating life with minimum weight. The ultimate aim of this research is to couple two key disciplines, fluids and structures, into a topology optimisation framework, which shows fast convergence for multidisciplinary optimisation problems. This is achieved by developing a bi-directional evolutionary structural optimisation algorithm that is directly coupled to the Lattice Boltzmann method, used for simulating the flow in the micro fluidic device, for the objectives of minimum compliance and maximum vorticity. The needs for the exploration of larger design spaces and to produce innovative designs make meta-heuristic algorithms, such as genetic algorithms, particle swarms and Tabu Searches, less efficient for this task. The multidisciplinary topology optimisation framework presented in this article is shown to increase the stiffness of the structure from the datum case and produce physically acceptable designs. Furthermore, the topology optimisation method outperforms a Tabu Search algorithm in designing the baffle to maximise the mixing of the two fluids.
Wang, Min; Chen, Yi-Feng; Ma, Guo-Wei; Zhou, Jia-Qing; Zhou, Chuang-Bing
2016-10-01
This study investigates the impacts of surface roughness on the nonlinear fluid flow through three-dimensional (3D) self-affine rock fractures, whose original surface roughness is decomposed into primary roughness (i.e. the large-scale waviness of the fracture morphology) and secondary roughness (i.e. the small-scale unevenness) with a wavelet analysis technique. A 3D Lattice Boltzmann method (LBM) is adopted to predict the flow physics in rock fractures numerically created with and without consideration of the secondary roughness, respectively. The simulation results show that the primary roughness mostly controls the pressure distribution and fracture flow paths at a large scale, whereas the secondary roughness determines the nonlinear properties of the fluid flow at a local scale. As the pressure gradient increases, the secondary roughness enhances the local complexity of velocity distribution by generating and expanding the eddy flow and back flow regions in the vicinity of asperities. It was found that the Forchheimer's law characterizes well the nonlinear flow behavior in fractures of varying roughness. The inertial effects induced by the primary roughness differ only marginally in fractures with the roughness exponent varying from 0.5 to 0.8, and it is the secondary roughness that significantly enhances the nonlinear flow and leads to earlier onset of nonlinearity. Further examined were the effects of surface roughness on the transmissivity, hydraulic aperture and the tortuosity of flow paths, demonstrating again the dominant role of the secondary roughness, especially for the apparent transmissivity and the equivalent hydraulic aperture at high pressure gradient or high Reynolds number. The results may enhance our understanding of the role of surface roughness in the nonlinear flow behaviors in natural rock fractures.
Talon, L.; Bauer, D.; Gland, N.; Youssef, S.; Auradou, H.; Ginzburg, I.
2012-04-01
The recent advances in 3-D imaging of porous structures have generated a tremendous interest in the simulation of complex single and two-phase flows. Lattice-Boltzmann (LB) schemes present a powerful tool to solve the flow field directly from the binarized 3-D images. However, as viscosity often plays an important role, the LB scheme should correctly treat viscosity effects. This is the case using a LB scheme with two relaxation times (TRT) unlike the broadly used, the single-relaxation rate, BGK, where the velocity of the modeled fluid does not vary as the inverse of the viscosity applying the bounce-back (no-slip) boundary rule. The aim of this work is to apply the LB-TRT approach to different types of porous media (straight channels, 2-D model porous media, sandstone) to solve for the flow field and to evaluate the approach in terms of parameter dependence, error and convergence time on the basis of permeability. We show that the variation of permeability with the free relaxation parameter Λ of the TRT scheme depends on the heterogeneity of the sample and on the numerical resolution. The convergence time depends on the applied viscosity and the parameter standing for the speed of sound, thus the computation time can be reduced by choosing appropriate values of those parameters. Two approaches to calculate permeability (Darcy's law and viscous energy dissipation) are proposed and investigated. We recommend to use Darcy's law, as dependence on Λ is less important. Periodic (in the presence of a driving body force) and pressure boundary conditions are evaluated in terms of the results.
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
Lattice hydrodynamic modeling of two-lane traffic flow with timid and aggressive driving behavior
Sharma, Sapna
2015-03-01
In this paper, a new two-lane lattice hydrodynamic traffic flow model is proposed by considering the aggressive or timid characteristics of driver's behavior. The effect of driver's characteristic on the stability of traffic flow is examined through linear stability analysis. It is shown that for both the cases of lane changing or without lane changing the stability region significantly enlarges (reduces) as the proportion of aggressive (timid) drivers increases. To describe the propagation behavior of a density wave near the critical point, nonlinear analysis is conducted and mKdV equation representing kink-antikink soliton is derived. The effect of anticipation parameter with more aggressive (timid) drivers is also investigated and found that it has a positive (negative) effect on the stability of two-lane traffic flow dynamics. Simulation results are found consistent with the theoretical findings which confirm that the driver's characteristics play a significant role in a two-lane traffic system.
Cui, Shuqi; Hong, Ning; Shi, Baochang; Chai, Zhenhua
2016-04-01
In this paper, we will focus on the multiple-relaxation-time (MRT) lattice Boltzmann model for two-dimensional convection-diffusion equations (CDEs), and analyze the discrete effect on the halfway bounce-back (HBB) boundary condition (or sometimes called bounce-back boundary condition) of the MRT model where three different discrete velocity models are considered. We first present a theoretical analysis on the discrete effect of the HBB boundary condition for the simple problems with a parabolic distribution in the x or y direction, and a numerical slip proportional to the second-order of lattice spacing is observed at the boundary, which means that the MRT model has a second-order convergence rate in space. The theoretical analysis also shows that the numerical slip can be eliminated in the MRT model through tuning the free relaxation parameter corresponding to the second-order moment, while it cannot be removed in the single-relaxation-time model or the Bhatnagar-Gross-Krook model unless the relaxation parameter related to the diffusion coefficient is set to be a special value. We then perform some simulations to confirm our theoretical results, and find that the numerical results are consistent with our theoretical analysis. Finally, we would also like to point out the present analysis can be extended to other boundary conditions of lattice Boltzmann models for CDEs.
Directory of Open Access Journals (Sweden)
Wang Ye-Long
2012-01-01
Full Text Available A direct forcing method for the simulation of particulate flows based on immersed boundary-lattice Boltzmann method is used to study the flow of power-law fluid through an infinite array of circular cylinders with cylinder separations of 20a (a is the cylinder radius with laminar shedding behind cylinders. Time averaged drag coefficient, maximum of lift coefficient and Strouhal number are given out with the power-law index in the range of 0.4 ≤ n ≤ 1.8 and Re in the range of 50 ≤ Re ≤ 140.
Extensão do framework waLBerla para uso de GPU em simulações do Método de Lattice Boltzmann
Sepka Junior, José Aurimar
2015-01-01
Orientador : Prof. Dr. Daniel Weingaertner Dissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa: Curitiba, 27/08/2015 Inclui referências : f. 86-90 Resumo: Este trabalho apresenta uma proposta de paralelização do Método de Lattice Boltzmann em três dimensões para o framework waLBerla utilizando a plataforma de computação paralela Compute Unified Device Architecture (CUDA). Com esse propósito, foi desenvolv...
Gao, Jinfang; Xing, Huilin; Tian, Zhiwei; Pearce, Julie K.; Sedek, Mohamed; Golding, Suzanne D.; Rudolph, Victor
2017-01-01
Injection of CO2 subsurface may lead to chemical reactivity of rock where CO2 is dissolved in groundwater. This process can modify pore networks to increase or decrease porosity through mineral dissolution and precipitation. A lattice Boltzmann (LB) based computational model study on the pore scale reactive transport in three dimensional heterogeneous porous media (sandstone consisting of both reactive and non-reactive minerals) is described. This study examines how fluid transport in porous materials subject to reactive conditions is affected by unsteady state local reactions and unstable dissolution fronts. The reaction of a calcite cemented core sub-plug from the Hutton Sandstone of the Surat Basin, Australia, is used as a study case. In particular, the work studies the interaction of acidic fluid (an aqueous solution with an elevated concentration of carbonic acid) with reactive (e.g. calcite) and assumed non-reactive (e.g. quartz) mineral surfaces, mineral dissolution and mass transfer, and resultant porosity change. The proposed model is implemented in our custom LBM code and suitable for studies of multiple mineral reactions with disparate reaction rates. A model for carbonic acid reaction with calcite cemented sandstone in the CO2-water-rock system is verified through laboratory experimental data including micro-CT characterization before and after core reaction at reservoir conditions. The experimentally validated model shows: (1) the dissolution of calcite cement forms conductive channels at the pore scale, and enables the generation of pore throats and connectivity; (2) the model is able to simulate the reaction process until the reaction equilibrium status is achieved (around 1440 days); (3) calcite constituting a volume of around 9.6% of the whole core volume is dissolved and porosity is consequently increased from 1.1% to 10.7% on reaching equilibrium; (4) more than a third of the calcite (constituting 7.4% of the total core volume) is unaffected
Chun, Byoungjin; Kwon, Ilyoung; Jung, Hyun Wook; Hyun, Jae Chun
2017-12-01
The shear-induced migration of concentrated non-Brownian monodisperse suspensions in combined plane Couette-Poiseuille (C-P) flows is studied using a lattice Boltzmann simulation. The simulations are mainly performed for a particle volume fraction of ϕbulk = 0.4 and H/a = 44.3, 23.3, where H and a denote the channel height and radius of suspended particles, respectively. The simulation method is validated in two simple flows, plane Poiseuille and plane Couette flows. In the Poiseuille flow, particles migrate to the mid-plane of the channel where the local concentration is close to the limit of random-close-packing, and a random structure is also observed at the plane. In the Couette flow, the particle distribution remains in the initial uniform distribution. In the combined C-P flows, the behaviors of migration are categorized into three groups, namely, Poiseuille-dominant, Couette-dominant, and intermediate regimes, based on the value of a characteristic force, G, where G denotes the relative magnitude of the body force (P) against the wall-driving force (C). With respect to the Poiseuille-dominant regime, the location of the maximum concentration is shifted from the mid-plane to the lower wall moving in the same direction as the external body force, when G decreases. With respect to the Couette-dominant regime, the behavior is similar to that of a simple shear flow with the exception that a slightly higher concentration of particles is observed near the lower wall. However, with respect to the intermediate value of G, several layers of highly ordered particles are unexpectedly observed near the lower wall where the plane of maximum concentration is located. The locally ordered structure is mainly due to the lateral migration of particles and wall confinement. The suspended particles migrate toward a vanishingly small shear rate at the wall, and they are consequently layered into highly ordered two-dimensional structures at the high local volume fraction.
Large-Eddy Simulation of the Gust Index in an Urban Area Using the Lattice Boltzmann Method
Ahmad, Nurul Huda; Inagaki, Atsushi; Kanda, Manabu; Onodera, Naoyuki; Aoki, Takayuki
2017-06-01
We used numerical simulations to investigate the general relationship between urban morphology and the intensity of wind gusts in built-up areas at the pedestrian level. The simulated urban boundary layer developed over a 19.2 km (length) × 4.8 km (width) × 1.0 km (height) simulation domain, with 2-m resolution in all directions, to explicitly resolve the detailed shapes of buildings and the flow at the pedestrian level. This complex computation was accomplished using the lattice Boltzmann method and by implementing a large-eddy simulation model. To generalize the results, a new parameter that expresses the intensity of gusts (the gust index, {\\tilde{U}}_{ max}) was defined as the local maximum wind speed divided by the freestream velocity. In addition, this parameter was decomposed into the mean wind-speed ratio, {\\tilde{U}} and turbulent gust ratio, {\\tilde{U}}^' }} to evaluate the qualities of gusts. These parameters were useful for quantitatively comparing the gust intensities within urban canopies at different locations or even among different experiments. In addition, the entire horizontal domain was subdivided into homogeneous square patches, in which both the simulated gust parameters and the morphological characteristics of building geometries were averaged. This procedure masked the detailed structure of individual buildings but retained the bulk characteristics of the urban morphology. At the pedestrian level, the gust index decreased with increasing building cover. Compared to {\\tilde{U}} , the quantity {\\tilde{U}}^' }} notably contributed to the index throughout the range of plan area index (λ _p) values. The dependences of all normalized wind-speed ratios transiently changed at λ _p = 0.28. In cases where λ _p 0.28, {\\tilde{U}} was almost constant and {\\tilde{U}}^' }} decreased with increasing λ _p . This was explained by the change in flow regimes within the building canyon. At a higher elevation above the canopy layer, λ _p becomes
Lycett-Brown, Daniel; Luo, Kai H
2016-11-01
A recently developed forcing scheme has allowed the pseudopotential multiphase lattice Boltzmann method to correctly reproduce coexistence curves, while expanding its range to lower surface tensions and arbitrarily high density ratios [Lycett-Brown and Luo, Phys. Rev. E 91, 023305 (2015)PLEEE81539-375510.1103/PhysRevE.91.023305]. Here, a third-order Chapman-Enskog analysis is used to extend this result from the single-relaxation-time collision operator, to a multiple-relaxation-time cascaded collision operator, whose additional relaxation rates allow a significant increase in stability. Numerical results confirm that the proposed scheme enables almost independent control of density ratio, surface tension, interface width, viscosity, and the additional relaxation rates of the cascaded collision operator. This allows simulation of large density ratio flows at simultaneously high Reynolds and Weber numbers, which is demonstrated through binary collisions of water droplets in air (with density ratio up to 1000, Reynolds number 6200 and Weber number 440). This model represents a significant improvement in multiphase flow simulation by the pseudopotential lattice Boltzmann method in which real-world parameters are finally achievable.
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Roberto Rojas
2013-03-01
Full Text Available The applicability of the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM to high Reynolds number flows about a circular cylinder is examined. Two-dimensional simulations of flows past a stationary circular cylinder are carried out for a wide range of the Reynolds number, Re, i.e., 1 ≤ Re ≤ 1×105. An immersed boundary-lattice Boltzmann method (IB-LBM is also used for comparison. Then free-falling circular cylinders are simulated to demonstrate the feasibility of predicting moving particles at high Reynolds numbers. The main conclusions obtained are as follows: (1 steady and unsteady flows about a stationary cylinder are well predicted with IB-LBM and IB-FDLBM, provided that the spatial resolution is high enough to satisfy the conditions of numerical stability, (2 high spatial resolution is required for stable IB-LBM simulation of high Reynolds number flows, (3 IB-FDLBM can stably simulate flows at very high Reynolds numbers without increasing the spatial resolution, (4 IB-FDLBM gives reasonable predictions of the drag coefficient for 1 ≤ Re ≤ 1×105, and (5 IB-FDLBM gives accurate predictions for the motion of free-falling cylinders at intermediate Reynolds numbers.
Liu, Q
2016-01-01
In this paper, a three-dimensional (3D) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is presented for convection heat transfer in porous media at the representative elementary volume (REV) scale. The model is developed in the framework of the double-distribution-function (DDF) approach: an MRT-LB model of the density distribution function with the D3Q19 lattice (or D3Q15 lattice) is proposed to simulate the flow field based on the generalized non-Darcy model, while an MRT-LB model of the temperature distribution function with the D3Q7 lattice is proposed to simulate the temperature filed. The present model is employed to simulate mixed convection flow in a porous channel and natural convection in a cubical porous cavity. The numerical results demonstrate the effectiveness and accuracy of the present model in solving 3D convection heat transfer problems in porous media. The numerical results also demonstrate that the present model is approximately second-order accuracy in space. In addition, an ...
Ginzburg, Irina
2017-01-01
The effect of the heterogeneity in the soil structure or the nonuniformity of the velocity field on the modeled resident time distribution (RTD) and breakthrough curves is quantified by their moments. While the first moment provides the effective velocity, the second moment is related to the longitudinal dispersion coefficient (kT) in the developed Taylor regime; the third and fourth moments are characterized by their normalized values skewness (Sk) and kurtosis (Ku), respectively. The purpose of this investigation is to examine the role of the truncation corrections of the numerical scheme in kT, Sk, and Ku because of their interference with the second moment, in the form of the numerical dispersion, and in the higher-order moments, by their definition. Our symbolic procedure is based on the recently proposed extended method of moments (EMM). Originally, the EMM restores any-order physical moments of the RTD or averaged distributions assuming that the solute concentration obeys the advection-diffusion equation in multidimensional steady-state velocity field, in streamwise-periodic heterogeneous structure. In our work, the EMM is generalized to the fourth-order-accurate apparent mass-conservation equation in two- and three-dimensional duct flows. The method looks for the solution of the transport equation as the product of a long harmonic wave and a spatially periodic oscillating component; the moments of the given numerical scheme are derived from a chain of the steady-state fourth-order equations at a single cell. This mathematical technique is exemplified for the truncation terms of the two-relaxation-time lattice Boltzmann scheme, using plug and parabolic flow in straight channel and cylindrical capillary with the d2Q9 and d3Q15 discrete velocity sets as simple but illustrative examples. The derived symbolic dependencies can be readily extended for advection by another, Newtonian or non-Newtonian, flow profile in any-shape open-tabular conduits. It is
Boghosian, B M; Alexander, F J; Margolus, N H; Boghosian, Bruce M.; Yepez, Jeffrey; Alexander, Francis J.; Margolus, Norman H.
1996-01-01
We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term that arises from the breaking of galilean invariance in these models. We show that this prefactor can be set to unity in the generalized model, therby effectively restoring galilean invariance. Moreover, we derive an expression for the kinematic viscosity, and show that it tends to decrease with the maximum number of particles allowed in each direction, so that higher Reynolds numbers may be achieved. Finally, we derive expressions for the statistical noise and the Boltzmann entropy of these models.
Peters, Amanda; Melchionna, Simone; Latt, Jonas; Succi, Sauro; Kaxiras, Efthimios
2010-11-01
We present a computational method for the simulation of cardiovascular flows in realistic human geometries derived from computed tomography angiography (CTA) data. The simulation is based on the Lattice Boltzmann method to model the blood flow in large-scale arterial systems and extends previously published studies using static geometries to include the effect of the pulsating heart on the coronary arteries. We provide here the derivation for introducing the deformational forces exerted on the arterial flows from the movement of the heart by borrowing concepts from cosmodynamics. The deformational forces are then cast into the kinetic formalism by using a Gauss-Hermite projection procedure. In this presentation, we will discuss this method as well as provide an analysis of the impact of these additional forces on the endothelial shear stress, a quantity associated with the localization and progression of heart diseases like atherosclerosis.
Shahmardan, M. M.; Sedaghat, M. H.; Norouzi, M.; Nazari, M.
2015-12-01
Numerical simulation based on immersed boundary-lattice Boltzmann method has been employed to study 2D muco-ciliary transport problem. The periciliary liquid (PCL) and mucus layers in this study are considered as the Newtonian and viscoelastic fluid respectively. An Oldroyd-B model is used as the constitutive equations of mucus layer. To simulate accurate effects of the cilia and PCL-mucus interface on the fluid, immersed boundary method is used. Numerical simulations have been performed to investigate the effects of mucus depth on the muco-ciliary clearance at various values of cilia beat frequencies. Our results show that, by increasing mucus depth, which results from air pollution and smoking, mean mucus velocity decreases. But it can be completely modified by increasing cilia beat frequency and the cilia beat frequency has great effect on the muco-ciliary clearance.
Geier, Martin; Pasquali, Andrea; Schönherr, Martin
2017-11-01
The optimized cumulant lattice Boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to Reynolds number 106. The drag crisis is well captured by the method. We demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions. The intermediate values of drag in a small range of Reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions. Around the critical Reynolds number, the time spent in the low drag condition increases with the Reynolds number such that the average drag curve has a finite steepness.
Long, Wei; Hilpert, Markus
2009-06-15
In this paper, we develop a new correlation for the clean-bed filter coefficient (lambda0) for Brownian particles, for which diffusion is the main deposition mechanism. The correlation is based on numerical Lattice-Boltzmann (LB) simulations in random packings of spheres of uniform diameter. We use LB methods to solve the Navier-Stokes equation for flow and then the advection-diffusion equation for particle transport. We determine a correlation for an "equivalent" single-collector diffusion efficiency, etaD, so that we can compare our predictions to "true" single-collector correlations stemming from unit-cell modeling approaches. We compared our new correlation to experiments on the filtration of latex particles. For small particle diameters, 50 nm etaG and nI terms from unit-cell correlations to our etaD model. The resulting correlation predicts experiments with latex particles of dp > 300 nm well.
Rabhi, R.; Amami, B.; Dhahri, H.; Mhimid, A.
2017-11-01
This paper deals with heat transfer and fluid flow in a porous micro duct under local thermal non equilibrium conditions subjected to an external oriented magnetic field. The considered sample is a micro duct filled with porous media assumed to be homogenous, isotropic and saturated. The slip velocity and the temperature jump were uniformly imposed to the wall. In modeling the flow, the Brinkmann-Forchheimer extended Darcy model was incorporated into the momentum equations. In the energy equation, the local thermal non equilibrium between the two phases was adopted. A modified axisymmetric lattice Boltzmann method was used to solve the obtained governing equation system. Attention was focused on the influence of the emerging parameters such as Knudsen number, Kn, Hartmann number, Ha, Eckert number, Ec, Biot number, Bi and the magnetic field inclination γ on flow and heat transfer throughout this paper.
Yang, PeiPei; Wen, Zhi; Dou, RuiFeng; Liu, Xunliang
2016-08-01
Flow and heat transfer through a 2D random porous medium are studied by using the lattice Boltzmann method (LBM). For the random porous medium, the influence of disordered cylinder arrangement on permeability and Nusselt number are investigated. Results indicate that the permeability and Nusselt number for different cylinder locations are unequal even with the same number and size of cylinders. New correlations for the permeability and coefficient b‧Den of the Forchheimer equation are proposed for random porous medium composed of Gaussian distributed circular cylinders. Furthermore, a general set of heat transfer correlations is proposed and compared with existing experimental data and empirical correlations. Our results show that the Nu number increases with the increase of the porosity, hence heat transfer is found to be accurate considering the effect of porosity.
Qin, Shunda; Ge, Hongxia; Cheng, Rongjun
2018-02-01
In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model.
Pelliccioni, O.; Cerrolaza, Miguel; Herrera, M.
2006-01-01
Se presenta un modelo para la simulación del flujo tridimensional que pasa a través de una válvula artificial de corazón en posición aórtica utilizando la ecuación generalizada de lattice Boltzmann bajo un modelo de multi-relajación. Se presentan resultados gráficos de velocidades, líneas de corriente, vorticidad y esfuerzos de corte a lo largo del flujo por la arteria. La simulación combina la aplicación del modelo de lattice Boltzmann con un método de multi-reflexión para el con...
Pelliccioni, O.; Cerrolaza, M.; Herrera, M.
2006-01-01
Se presenta un modelo para la simulación del flujo tridimensional que pasa a través de una válvula artificial de corazón en posición aórtica utilizando la ecuación generalizada de lattice Boltzmann bajo un modelo de multi-relajación. Se presentan resultados gráficos de velocidades, líneas de corriente, vorticidad y esfuerzos de corte a lo largo del flujo por la arteria. La simulación combina la aplicación del modelo de lattice Boltzmann con un método de multi-reflexión para el condicionamient...
Résumé : La méthode Lattice Boltzmann (LBM)et la celle des ...
African Journals Online (AJOL)
JOSLIN
méthodes précédentes et la méthode des Eléments finis (EF) sont utilisées afin de simuler la convection ..... distribution de l'énergie sur une paroi adiabatique est égale à celle sur le lattice immédiatement voisin. .... courbes montrent que les résultats sont très proches les uns des autres quelle que soit la méthode utilisée.
Böttger, B.; Haberstroh, C.; Giesselmann, N.
2016-01-01
Based on the results of microstructure simulations, fluid flow through the semisolid region during directional solidification of the technical Ni-base alloy 718 has been studied. Three-dimensional microstructures at different positions in the semisolid region were obtained by using a multicomponent multiphase-field model that was online coupled to a commercial thermodynamic database. For the range of five different primary dendrite distances λ 1 between 50 µm and 250 µm, the flow velocity and the permeability perpendicular to the dendrite growth direction was evaluated by using a proprietary Lattice-Boltzmann model. The commercial CFD software ANSYS FLUENT was alternatively applied for reference. Consistent values of the average flow velocity along the dendrites were obtained for both methods. From the results of the fluid flow simulations, the cross-permeability was evaluated as a function of temperature and fraction liquid for each of the five different primary dendrite distances λ 1. The obtained permeability values can be approximated by a single analytical function of the fraction liquid and λ 1 and are discussed and compared with known relations from the literature.
Zhu, Lianhua; Guo, Zhaoli
2015-01-01
The general characteristics based off-lattice Boltzmann scheme (BKG) proposed by Bardow et~al.(2006), and the discrete unified gas kinetic scheme (DUGKS) are two methods that successfully overcome the time step restriction by the collision time, which is commonly seen in many other kinetic schemes. Basically, the BKG scheme is a time splitting scheme, while the DUGKS is an un-split finite volume scheme. In this work, we first perform a theoretical analysis of the two schemes in the finite volume framework by comparing their numerical flux evaluations. It is found that the effects of collision term are considered in the reconstructions of the cell-interface distribution function in both schemes, which explains why they can overcome the time step restriction and can give accurate results even as the time step is much larger than the collision time. The difference between the two schemes lies in the treatment of the integral of the collision term, in which the Bardow's scheme uses the rectangular rule while the ...
Wang, Peng; Wang, Lian-Ping; Guo, Zhaoli
2016-10-01
The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter k_{max}η>3, where k_{max} is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of k_{max}η>1 for the pseudospectral method and k_{max}η>2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.
Hirohashi, Kensuke; Inamuro, Takaji
2017-08-01
Hovering and targeting flights of the dragonfly-like flapping wing-body model are numerically investigated by using the immersed boundary-lattice Boltzmann method. The governing parameters of the problem are the Reynolds number Re, the Froude number Fr, and the non-dimensional mass m. We set the parameters at Re = 200, Fr = 15 and m = 51. First, we simulate free flights of the model for various values of the phase difference angle ϕ between the forewing and the hindwing motions and for various values of the stroke angle β between the stroke plane and the horizontal plane. We find that the vertical motion of the model depends on the phase difference angle ϕ, and the horizontal motion of the model depends on the stroke angle β. Secondly, using the above results we try to simulate the hovering flight by dynamically changing the phase difference angle ϕ and the stroke angle β. The hovering flight can be successfully simulated by a simple proportional controller of the phase difference angle and the stroke angle. Finally, we simulate a targeting flight by dynamically changing the stroke angle β.
Sakaida, Satoshi; Tabe, Yutaka; Chikahisa, Takemi
2017-09-01
A method for the large-scale simulation with the lattice Boltzmann method (LBM) is proposed for liquid water movement in a gas diffusion layer (GDL) of polymer electrolyte membrane fuel cells. The LBM is able to analyze two-phase flows in complex structures, however the simulation domain is limited due to heavy computational loads. This study investigates a variety means to reduce computational loads and increase the simulation areas. One is applying an LBM treating two-phases as having the same density, together with keeping numerical stability with large time steps. The applicability of this approach is confirmed by comparing the results with rigorous simulations using actual density. The second is establishing the maximum limit of the Capillary number that maintains flow patterns similar to the precise simulation; this is attempted as the computational load is inversely proportional to the Capillary number. The results show that the Capillary number can be increased to 3.0 × 10-3, where the actual operation corresponds to Ca = 10-5∼10-8. The limit is also investigated experimentally using an enlarged scale model satisfying similarity conditions for the flow. Finally, a demonstration is made of the effects of pore uniformity in GDL as an example of a large-scale simulation covering a channel.
Başağaoğlu, Hakan; Harwell, John R.; Nguyen, Hoa; Succi, Sauro
2017-04-01
Significant improvements in the computational performance of the lattice-Boltzmann (LB) model, coded in FORTRAN90, were achieved through application of enhancement techniques. Applied techniques include optimization of array memory layouts, data structure simplification, random number generation outside the simulation thread(s), code parallelization via OpenMP, and intra- and inter-timestep task pipelining. Effectiveness of these optimization techniques was measured on three benchmark problems: (i) transient flow of multiple particles in a Newtonian fluid in a heterogeneous fractured porous domain, (ii) thermal fluctuation of the fluid at the sub-micron scale and the resultant Brownian motion of a particle, and (iii) non-Newtonian fluid flow in a smooth-walled channel. Application of the aforementioned optimization techniques resulted in an average 21 × performance improvement, which could significantly enhance practical uses of the LB models in diverse applications, focusing on the fate and transport of nano-size or micron-size particles in non-Newtonian fluids.
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Y. Bakhshan
2015-01-01
Full Text Available Micro scale gas flows has attracted significant research interest in the last two decades. In this research, the fluid flow of gases in the stepped micro-channel at a wide range of Knudsen number has been analyzed with using the Lattice Boltzmann (MRT method. In the model, a modified second-order slip boundary condition and a Bosanquet-type effective viscosity are used to consider the velocity slip at the boundaries and to cover the slip and transition regimes of flow and to gain an accurate simulation of rarefied gases. It includes the slip and transition regimes of flow. The flow specifications such as pressure loss, velocity profile, streamline and friction coefficient at different conditions have been presented. The results show good agreement with available experimental data. The calculation shows that the friction coefficient decreases with increasing the Knudsen number and stepping the micro-channel has an inverse effect on the friction coefficient. Furthermore, a new correlation is suggested for calculation of the friction coefficient in the stepped micro-channel as below: C_f Re = 3.113+2.915/(1 +2 Kn+ 0.641 exp(3.203/(1 + 2 Kn
Bakhshan, Younes; Omidvar, Alireza
2015-12-01
Micro scale gas flows have attracted significant research interest in the last two decades. In this research, the fluid flow of gases in a stepped micro-channel has been conducted. Wide range of Knudsen number has been implemented using the Lattice Boltzmann (MRT) method in this study. A modified second-order slip boundary condition and a Bosanquet-type effective viscosity are used to consider the velocity slip at the boundaries and to cover the slip and transition regimes of flow to obtain an accurate simulation of rarefied gases. The flow specifications such as pressure loss, velocity profile, stream lines and friction coefficient at different conditions have been presented. The results show, good agreement with available experimental data. The calculation shows, that the friction coefficient decreases with increasing the Knudsen number and stepping the micro-channel has an inverse effect on the friction coefficient value. Furthermore, a new correlation is suggested for calculation of the friction coefficient in the stepped micro-channel flows as below;
Leclaire, Sébastien; Parmigiani, Andrea; Malaspinas, Orestis; Chopard, Bastien; Latt, Jonas
2017-03-01
This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this
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Frank Rodolfo Fonseca-Fonseca
2014-01-01
Full Text Available Hemos simulado la formación de patrones en superficies de silic io. Para este propósito, se utilizó el método de Lattice-Boltzm ann suponiendo dos fluidos no ideales, que interactúan, utilizando una rejilla de velocidades D2Q9 . El experimento se llevó a cabo con un láser de pulsos multilínea (1064, 532 y 355 nm de Nd: YAG, qu e emplea un rango de energía 310 a 3.100 J, en una superficie d e silicio monocristalino , tipo p, orientado en la dirección [111]. Todo el sistema se som etió a soplado de gas de argón que es clave en la formación de los patrones. La simulación computacional reproduc e bastante bien, el comportamiento global de los patrones geomé tricos experimentales, expresados en ondulaciones paralelas oblicuas.
Kohanpur, A. H.; Chen, Y.; Valocchi, A. J.; Tudek, J.; Crandall, D.
2016-12-01
CO2-brine flow in deep natural rocks is the focus of attention in geological storage of CO2. Understanding rock/flow properties at pore-scale is a vital component in field-scale modeling and prediction of fate of injected CO2. There are many challenges in working at the pore scale, such as size and selection of representative elementary volume (REV), particularly for material with complex geometry and heterogeneity, and the high computational costs. These issues factor into trade-offs that need to be made in choosing and applying pore-scale models. On one hand, pore-network modeling (PNM) simplifies the geometry and flow equations but can provide characteristic curves on fairly large samples. On the other hand, the lattice Boltzmann method (LBM) solves Navier-Stokes equations on the real geometry but is limited to small samples due to its high computational costs. Thus, both methods have some advantages but also face some challenges, which warrants a more detailed comparison and evaluation. In this study, we used industrial and micro-CT scans of actual reservoir rock samples to characterize pore structure at different resolutions. We ran LBM models directly on the characterized geometry and PNM on the equivalent 3D extracted network to determine single/two-phase flow properties during drainage and imbibition processes. Specifically, connectivity, absolute permeability, relative permeability curve, capillary pressure curve, and interface location are compared between models. We also did simulations on several subsamples from different locations including different domain sizes and orientations to encompass analysis of heterogeneity and isotropy. This work is primarily supported as part of the Center for Geologic Storage of CO2, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science and partially supported by the International Institute for Carbon-Neutral Energy Research (WPI-I2CNER) based at Kyushu University, Japan.
Liu, Qing; He, Ya-Ling; Li, Qing
2017-08-01
In this paper, an enthalpy-based multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed for solid-liquid phase-change heat transfer in metal foams under the local thermal nonequilibrium (LTNE) condition. The enthalpy-based MRT-LB method consists of three different MRT-LB models: one for flow field based on the generalized non-Darcy model, and the other two for phase-change material (PCM) and metal-foam temperature fields described by the LTNE model. The moving solid-liquid phase interface is implicitly tracked through the liquid fraction, which is simultaneously obtained when the energy equations of PCM and metal foam are solved. The present method has several distinctive features. First, as compared with previous studies, the present method avoids the iteration procedure; thus it retains the inherent merits of the standard LB method and is superior to the iteration method in terms of accuracy and computational efficiency. Second, a volumetric LB scheme instead of the bounce-back scheme is employed to realize the no-slip velocity condition in the interface and solid phase regions, which is consistent with the actual situation. Last but not least, the MRT collision model is employed, and with additional degrees of freedom, it has the ability to reduce the numerical diffusion across the phase interface induced by solid-liquid phase change. Numerical tests demonstrate that the present method can serve as an accurate and efficient numerical tool for studying metal-foam enhanced solid-liquid phase-change heat transfer in latent heat storage. Finally, comparisons and discussions are made to offer useful information for practical applications of the present method.
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Soyoun Son
2016-02-01
Full Text Available In porous media, pore geometry and wettability are determinant factors for capillary flow in drainage or imbibition. Pores are often considered as cylindrical tubes in analytical or computational studies. Such simplification prevents the capture of phenomena occurring in pore corners. Considering the corners of pores is crucial to realistically study capillary flow and to accurately estimate liquid distribution, degree of saturation and dynamic liquid behavior in pores and in porous media. In this study, capillary flow in polygonal tubes is studied with the Shan-Chen pseudopotential multiphase lattice Boltzmann model (LBM. The LB model is first validated through a contact angle test and a capillary intrusion test. Then capillary rise in square and triangular tubes is simulated and the pore meniscus height is investigated as a function of contact angle θ. Also, the occurrence of fluid in the tube corners, referred to as corner arc menisci, is studied in terms of curvature versus degree of saturation. In polygonal capillary tubes, the number of sides leads to a critical contact angle θc which is known as a key parameter for the existence of the two configurations. LBM succeeds in simulating the formation of a pore meniscus at θ > θc or the occurrence of corner arc menisci at θ < θc. The curvature of corner arc menisci is known to decrease with increasing saturation and decreasing contact angle as described by the Mayer and Stoewe-Princen (MS-P theory. We obtain simulation results that are in good qualitative and quantitative agreement with the analytical solutions in terms of height of pore meniscus versus contact angle and curvature of corner arc menisci versus saturation degree. LBM is a suitable and promising tool for a better understanding of the complicated phenomena of multiphase flow in porous media.
Jain, Kartik; Jiang, Jingfeng; Strother, Charles; Mardal, Kent-André
2016-11-01
Blood flow in intracranial aneurysms has, until recently, been considered to be disturbed but still laminar. Recent high resolution computational studies have demonstrated, in some situations, however, that the flow may exhibit high frequency fluctuations that resemble weakly turbulent or transitional flow. Due to numerous assumptions required for simplification in computational fluid dynamics (CFD) studies, the occurrence of these events, in vivo, remains unsettled. The detection of these fluctuations in aneurysmal blood flow, i.e., hemodynamics by CFD, poses additional challenges as such phenomena cannot be captured in clinical data acquisition with magnetic resonance (MR) due to inadequate temporal and spatial resolutions. The authors' purpose was to address this issue by comparing results from highly resolved simulations, conventional resolution laminar simulations, and MR measurements, identify the differences, and identify their causes. Two aneurysms in the basilar artery, one with disturbed yet laminar flow and the other with transitional flow, were chosen. One set of highly resolved direct numerical simulations using the lattice Boltzmann method (LBM) and another with adequate resolutions under laminar flow assumption were conducted using a commercially available ANSYS Fluent solver. The velocity fields obtained from simulation results were qualitatively and statistically compared against each other and with MR acquisition. Results from LBM, ANSYS Fluent, and MR agree well qualitatively and quantitatively for one of the aneurysms with laminar flow in which fluctuations were ∼ 600 Hz showed vivid differences between LBM, ANSYS Fluent, and magnetic resonance imaging. After ensemble averaging and down-sampling to coarser space and time scales, these differences became minimal. A combination of MR derived data and CFD can be helpful in estimating the hemodynamic environment of intracranial aneurysms. Adequately resolved CFD would suffice gross assessment of
Liu, Qing; He, Ya-Ling; Li, Qing
2017-08-01
In this paper, an enthalpy-based multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed for solid-liquid phase-change heat transfer in metal foams under the local thermal nonequilibrium (LTNE) condition. The enthalpy-based MRT-LB method consists of three different MRT-LB models: one for flow field based on the generalized non-Darcy model, and the other two for phase-change material (PCM) and metal-foam temperature fields described by the LTNE model. The moving solid-liquid phase interface is implicitly tracked through the liquid fraction, which is simultaneously obtained when the energy equations of PCM and metal foam are solved. The present method has several distinctive features. First, as compared with previous studies, the present method avoids the iteration procedure; thus it retains the inherent merits of the standard LB method and is superior to the iteration method in terms of accuracy and computational efficiency. Second, a volumetric LB scheme instead of the bounce-back scheme is employed to realize the no-slip velocity condition in the interface and solid phase regions, which is consistent with the actual situation. Last but not least, the MRT collision model is employed, and with additional degrees of freedom, it has the ability to reduce the numerical diffusion across the phase interface induced by solid-liquid phase change. Numerical tests demonstrate that the present method can serve as an accurate and efficient numerical tool for studying metal-foam enhanced solid-liquid phase-change heat transfer in latent heat storage. Finally, comparisons and discussions are made to offer useful information for practical applications of the present method.
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D S Ayala
2013-11-01
Full Text Available This article presents an analysis of blood flow patterns in intracranial saccular aneurysm and the effects of the shape and porosity of the stents used in endovascular treatments. In this study will be used the flow reduction criteria for characterizing the efficiency of the stent. The hemodynamic properties of a newtonian blood flow into the aneurysm will be evaluated using the Lattice Boltzmann method (LBM. Porosity values and stent forms are proposed for analysis. In all stent cases analyzed is observed a reduction of velocity and pressure and an increase in viscosity. It is further noted that the rectangular contour stent is the optimal case and reduces the magnitude of the flow velocity inside the aneurysm much as 76%. The results help to understand the role of porosity in the form and design of a stent.En este artículo se presenta un analísis de los patrones de flujo sanguíneo en un aneurisma sacular intracraneal y los efectos de la forma y la porosidad de los stents empleados en tratamientos endovasculares. En este estudio se empleará el criterio de reducción del flujo para caracterizar la eficiencia del stent. Se evaluarán las propiedades hemodinámicas de un flujo sanguíneo newtoniano dentro del aneurisma a partir del método de Lattice Boltzmann (LBM. Se proponen algunos valores de porosidad y forma de stent para el análisis. En todos los casos de stent analizados se observa una reducción de velocidades y presiones y un aumento de viscosidad. Se observa además que el stent de contorno rectangular es el caso óptimo y reduce la magnitud de la velocidad del flujo en el interior del aneurisma hasta en un 76 %. Los resultados obtenidos ayudan a entender el papel de la forma y porosidad en el diseño de un stent.
Silva, Goncalo; Talon, Laurent; Ginzburg, Irina
2017-04-01
The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes-Brinkman-Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes-Brinkman-Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM
Energy Technology Data Exchange (ETDEWEB)
Silva, Goncalo, E-mail: goncalo.nuno.silva@gmail.com [Irstea, Antony Regional Centre, HBAN, 1 rue Pierre-Gilles de Gennes CS 10030, 92761 Antony cedex (France); Talon, Laurent, E-mail: talon@fast.u-psud.fr [CNRS (UMR 7608), Laboratoire FAST, Batiment 502, Campus University, 91405 Orsay (France); Ginzburg, Irina, E-mail: irina.ginzburg@irstea.fr [Irstea, Antony Regional Centre, HBAN, 1 rue Pierre-Gilles de Gennes CS 10030, 92761 Antony cedex (France)
2017-04-15
The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM
Ginzburg, Irina; Silva, Goncalo; Talon, Laurent
2015-02-01
This work focuses on the numerical solution of the Stokes-Brinkman equation for a voxel-type porous-media grid, resolved by one to eight spacings per permeability contrast of 1 to 10 orders in magnitude. It is first analytically demonstrated that the lattice Boltzmann method (LBM) and the linear-finite-element method (FEM) both suffer from the viscosity correction induced by the linear variation of the resistance with the velocity. This numerical artefact may lead to an apparent negative viscosity in low-permeable blocks, inducing spurious velocity oscillations. The two-relaxation-times (TRT) LBM may control this effect thanks to free-tunable two-rates combination Λ. Moreover, the Brinkman-force-based BF-TRT schemes may maintain the nondimensional Darcy group and produce viscosity-independent permeability provided that the spatial distribution of Λ is fixed independently of the kinematic viscosity. Such a property is lost not only in the BF-BGK scheme but also by "partial bounce-back" TRT gray models, as shown in this work. Further, we propose a consistent and improved IBF-TRT model which vanishes viscosity correction via simple specific adjusting of the viscous-mode relaxation rate to local permeability value. This prevents the model from velocity fluctuations and, in parallel, improves for effective permeability measurements, from porous channel to multidimensions. The framework of our exact analysis employs a symbolic approach developed for both LBM and FEM in single and stratified, unconfined, and bounded channels. It shows that even with similar bulk discretization, BF, IBF, and FEM may manifest quite different velocity profiles on the coarse grids due to their intrinsic contrasts in the setting of interface continuity and no-slip conditions. While FEM enforces them on the grid vertexes, the LBM prescribes them implicitly. We derive effective LBM continuity conditions and show that the heterogeneous viscosity correction impacts them, a property also shared
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.
A multi-component discrete Boltzmann model for nonequilibrium reactive flows.
Lin, Chuandong; Luo, Kai Hong; Fei, Linlin; Succi, Sauro
2017-11-06
We propose a multi-component discrete Boltzmann model (DBM) for premixed, nonpremixed, or partially premixed nonequilibrium reactive flows. This model is suitable for both subsonic and supersonic flows with or without chemical reaction and/or external force. A two-dimensional sixteen-velocity model is constructed for the DBM. In the hydrodynamic limit, the DBM recovers the modified Navier-Stokes equations for reacting species in a force field. Compared to standard lattice Boltzmann models, the DBM presents not only more accurate hydrodynamic quantities, but also detailed nonequilibrium effects that are essential yet long-neglected by traditional fluid dynamics. Apart from nonequilibrium terms (viscous stress and heat flux) in conventional models, specific hydrodynamic and thermodynamic nonequilibrium quantities (high order kinetic moments and their departure from equilibrium) are dynamically obtained from the DBM in a straightforward way. Due to its generality, the developed methodology is applicable to a wide range of phenomena across many energy technologies, emissions reduction, environmental protection, mining accident prevention, chemical and process industry.
Hydrodynamic repulsion of spheroidal microparticles from micro-rough surfaces.
Belyaev, Aleksey V
2017-01-01
Isolation of microparticles and biological cells from mixtures and suspensions is a central problem in a variety of biomedical applications. This problem, for instance, is of an immense importance for microfluidic devices manipulating with whole blood samples. It is instructive to know how the mobility and dynamics of rigid microparticles is altered by the presence of micrometer-size roughness on walls. The presented theoretical study addresses this issue via computer simulations. The approach is based on a combination of the Lattice Boltzmann method for calculating hydrodynamics and the Lagrangian Particle dynamics method to describe the dynamics of cell membranes. The effect of the roughness on the mobility of spheroidal microparticles in a shear fluid flow was quantified. We conclude that mechanical and hydrodynamic interactions lift the particles from the surface and change their mobility. The effect is sensitive to the shape of particles.
Lattice gas with molecular dynamics collision operator
Parsa, M. Reza; Wagner, Alexander J.
2017-07-01
We introduce a lattice gas implementation that is based on coarse-graining a molecular dynamics (MD) simulation. Such a lattice gas is similar to standard lattice gases, but its collision operator is informed by an underlying MD simulation. This can be considered an optimal lattice gas implementation because it allows for the representation of any system that can be simulated with MD. We show here that equilibrium behavior of the popular lattice Boltzmann algorithm is consistent with this optimal lattice gas. This comparison allows us to make a more accurate identification of the expressions for temperature and pressure in lattice Boltzmann simulations, which turn out to be related not only to the physical temperature and pressure but also to the lattice discretization. We show that for any spatial discretization, we need to choose a particular temporal discretization to recover the lattice Boltzmann equilibrium.
Ren, Qinlong
2018-02-10
Efficient pumping of blood flow in a microfluidic device is essential for rapid detection of bacterial bloodstream infections (BSI) using alternating current (AC) electrokinetics. Compared with AC electroosmosis (ACEO) phenomenon, the advantage of AC electrothermal (ACET) mechanism is its capability of pumping biofluids with high electrical conductivities at a relatively high AC voltage frequency. In the current work, the microfluidic pumping of non-Newtonian blood flow using ACET forces is investigated in detail by modeling its multi-physics process with hybrid boundary element method (BEM) and immersed boundary-lattice Boltzmann method (IB-LBM). The Carreau-Yasuda model is used to simulate the realistic rheological behavior of blood flow. The ACET pumping efficiency of blood flow is studied in terms of different AC voltage magnitudes and frequencies, thermal boundary conditions of electrodes, electrode configurations, channel height, and the channel length per electrode pair. Besides, the effect of rheological behavior on the blood flow velocity is theoretically analyzed by comparing with the Newtonian fluid flow using scaling law analysis under the same physical conditions. The results indicate that the rheological behavior of blood flow and its frequency-dependent dielectric property make the pumping phenomenon of blood flow different from that of the common Newtonian aqueous solutions. It is also demonstrated that using a thermally insulated electrode could enhance the pumping efficiency dramatically. Besides, the results conclude that increasing the AC voltage magnitude is a more economical pumping approach than adding the number of electrodes with the same energy consumption when the Joule heating effect is acceptable. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.
The Boltzmann equation in the difference formulation
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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.
Lattice Boltzmann Methods for Fluid Structure Interaction
2012-09-01
Approved By: Knox T. Millsaps, Professor & Chair, Dept. of Mechanical & Aerospace Engineering Approved By: Doug Moses, Vice Provost for Academic Affairs...similar procedure including the Burgers Equation [10], the Korteweg-de Vries equation [11], the Brinkman equation [12] and the Schrödinger equation [13...method for a two-dimensional viscous Burgers equation: Computational results.,” in Supercomputing, pp. 242–252, 1991. [11] G. Yan and J. Zhang, “A higher
Hydrodynamics of unitary Fermi gases
Young, Ryan E.
Unitary fermi gases have been widely studied as they provide a tabletop archetype for re- search on strongly coupled many body systems and perfect fluids. Research into unitary fermi gases can provide insight into may other strongly interacting systems including high temperature superconductor, quark-gluon plasmas, and neutron stars. Within the unitary regime, the equilib- rium transport coefficients and thermodynamic properties are universal functions of density and temperature. Thus, unitary fermi gases provide a archetype to study nonperturbative many-body physics, which is of fundamental significance and crosses several fields. This thesis reports on two topics regarding unitary fermi gases. A recent string theory conjecture gives a lower bound for the dimensionless ratio of shear viscosity of entropy, η/s ≥ 4pi /kb . Unitary fermi gases are a candidate for prefect fluids, yet η/s is well above the string theory bound. Using a stochastic formulation of hydrodynamics, we calculate a lower bound for this ratio accounting for the momentum dissipation from fluctuations. This lower bound is in good agreement with both theoretical and experimental results. The second question addressed is the simulation of elliptic flow. Elliptic flow, first observed in 2002, is a characteristic of strongly coupled systems and has been studied in both quark-gluon plasmas and unitary fermi gases. As such, simulations of these systems are of interest. We test a variety of lattice Boltzmann models and compare the simulation results to the theoretical and experimental findings.
Foundations of radiation hydrodynamics
Mihalas, D.; Mihalas, B. W.
This book is the result of an attempt, over the past few years, to gather the basic tools required to do research on radiating flows in astrophysics. The microphysics of gases is discussed, taking into account the equation of state of a perfect gas, the first and second law of thermodynamics, the thermal properties of a perfect gas, the distribution function and Boltzmann's equation, the collision integral, the Maxwellian velocity distribution, Boltzmann's H-theorem, the time of relaxation, and aspects of classical statistical mechanics. Other subjects explored are related to the dynamics of ideal fluids, the dynamics of viscous and heat-conducting fluids, relativistic fluid flow, waves, shocks, winds, radiation and radiative transfer, the equations of radiation hydrodynamics, and radiating flows. Attention is given to small-amplitude disturbances, nonlinear flows, the interaction of radiation and matter, the solution of the transfer equation, acoustic waves, acoustic-gravity waves, basic concepts of special relativity, and equations of motion and energy.
Ludwig Boltzmann: Atomic genius
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Cercignani, C. [Department of Mathematics, Politecnico di Milano (Italy)]. E-mail: carcer@mate.polimi.it
2006-09-15
On the centenary of the death of Ludwig Boltzmann, Carlo Cercignani examines the immense contributions of the man who pioneered our understanding of the atomic nature of matter. The man who first gave a convincing explanation of the irreversibility of the macroscopic world and the symmetry of the laws of physics was the Austrian physicist Ludwig Boltzmann, who tragically committed suicide 100 years ago this month. One of the key figures in the development of the atomic theory of matter, Boltzmann's fame will be forever linked to two fundamental contributions to science. The first was his interpretation of 'entropy' as a mathematically well-defined measure of the disorder of atoms. The second was his derivation of what is now known as the Boltzmann equation, which describes the statistical properties of a gas as made up of molecules. The equation, which described for the first time how a probability can evolve with time, allowed Boltzmann to explain why macroscopic phenomena are irreversible. The key point is that while microscopic objects like atoms can behave reversibly, we never see broken coffee cups reforming because it would involve a long series of highly improbable interactions - and not because it is forbidden by the laws of physics. (U.K.)
Lindley, David
2002-01-01
Ludwig Boltzmann (1844-1906) è il fisico e matematico austriaco che negli ultimi decenni dell'Ottocento e ancora ai primi del Novecento lottò contro l'opinione dominante tra gli scienziati dell'epoca per affermare la teoria atomica della materia. È noto come con Albert Einstein e fino a oggi la fisica si sia sviluppata e abbia celebrato i propri trionfi lungo le linee anticipate da Boltzmann. La controversia con Mach non riguardava soltanto l'esistenza degli atomi, ma l'intero modo di fare fisica che Boltzmann non riteneva di dover limitare allo studio di quantità misurabili, introducendo invece spiegazioni più elaborate basate su ipotesi più ampie.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034. Author Affiliations.
Indian Academy of Sciences (India)
Page 1. CPMGlKAlBGE-340/2001. Licenced to post WPP(E) No.6. Resonance - September 2001. Ludluig Eduard Boltzmann. (1844 - 19(6). Registered with Registrar of Newspapers in India vide Regn. No. 66273196. ISSN 0971-8044.
Generalized Boltzmann formalism for oscillating neutrinos
Strack, P.; Burrows, A.
2005-05-01
In the standard approaches to neutrino transport in the simulation of core-collapse supernovas, one will often start from the classical Boltzmann equation for the neutrino’s spatial, temporal, and spectral evolution. For each neutrino species, and its antiparticle, the classical density in phase space, or the associated specific intensity, will be calculated as a function of time. The neutrino radiation is coupled to matter by source and sink terms on the “right-hand side” of the transport equation and together with the equations of hydrodynamics this set of coupled partial differential equations for classical densities describes, in principle, the evolution of core collapse and explosion. However, with the possibility of neutrino oscillations between species, a purely quantum-physical effect, how to generalize this set of Boltzmann equations for classical quantities to reflect oscillation physics has not been clear. To date, the formalisms developed have retained the character of quantum operator physics involving complex quantities and have not been suitable for easy incorporation into standard supernova codes. In this paper, we derive generalized Boltzmann equations for quasiclassical, real-valued phase-space densities that retain all the standard oscillation phenomenology, including the matter-enhanced resonant flavor conversion (Mikheev-Smirnov-Wolfenstein effect), neutrino self-interactions, and the interplay between decohering matter coupling and flavor oscillations. With this formalism, any code(s) that can now handle the solution of the classical Boltzmann or transport equation can easily be generalized to include neutrino oscillations in a quantum-physically consistent fashion.
On the dispute between Boltzmann and Gibbs entropy
Energy Technology Data Exchange (ETDEWEB)
Buonsante, Pierfrancesco; Franzosi, Roberto, E-mail: roberto.franzosi@ino.it; Smerzi, Augusto
2016-12-15
The validity of the concept of negative temperature has been recently challenged by arguing that the Boltzmann entropy (that allows negative temperatures) is inconsistent from a mathematical and statistical point of view, whereas the Gibbs entropy (that does not admit negative temperatures) provides the correct definition for the microcanonical entropy. Here we prove that the Boltzmann entropy is thermodynamically and mathematically consistent. Analytical results on two systems supporting negative temperatures illustrate the scenario we propose. In addition we numerically study a lattice system to show that negative temperature equilibrium states are accessible and obey standard statistical mechanics prediction.
Rajasekar, S.; Athavan, N.
2006-01-01
In this manuscript we present a brief life history of Ludwig Edward Boltzmann and his achivements. Particularly, we discuss his H-theorem, his work on entropy and statistical interpretation of second-law of thermodynamics. We point out his some other contributions in physics, characteristics of his work, his strong support on atomism, character of his personality and relationship with his students and final part of his life.
Direct numerical simulation of a fluid flow in core samples based on quasi-hydrodynamic equations
Balashov, V. A.; Savenkov, E. B.; Kuleshov, A. A.
2016-12-01
Direct numerical modeling techniques for the evaluation of a macroscopic permeability coefficient of samples of naturally occurring geological media using their micro-computer tomography (micro-CT) images is considered. The basic mathematical model of a flow is based on quasi-hydrodynamic (QHD) equations for viscous heat-conducting compressible gas flows. The evaluation of a permeability coefficient of artificial and real porous media is discussed. Free available micro-CT images are used. Results of computations for artificial porous media are compared with the analytic ones, for real porous media — with the results obtained by the Lattice Boltzmann method and results obtained by other researchers. It is shown that the approach based on QHD equations is highly competitive with other approaches.
Lattice Kinetic Theory in a Comoving Galilean Reference Frame.
Frapolli, N; Chikatamarla, S S; Karlin, I V
2016-07-01
We prove that the fully discrete lattice Boltzmann method is invariant with respect to Galilean transformation. Based on this finding, a novel class of shifted lattices is proposed which dramatically increases the operating range of lattice Boltzmann simulations, in particular, for gas dynamics applications. A simulation of vortex-shock interaction is used to demonstrate the accuracy and efficiency of the proposed lattices. With one single algorithm it is now possible to simulate a broad range of applications, from low Mach number flows to transonic and supersonic flow regimes.
Restricted Boltzmann machine learning for solving strongly correlated quantum systems
Nomura, Yusuke; Darmawan, Andrew S.; Yamaji, Youhei; Imada, Masatoshi
2017-11-01
We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an artificial neural network is combined with a conventional variational Monte Carlo method with pair product (geminal) wave functions and quantum number projections. The combination allows an application of the machine learning scheme to interacting fermionic systems. The combined method substantially improves the accuracy beyond that ever achieved by each method separately, in the Heisenberg as well as Hubbard models on square lattices, thus proving its power as a highly accurate quantum many-body solver.
Training Restricted Boltzmann Machines
DEFF Research Database (Denmark)
Fischer, Asja
Restricted Boltzmann machines (RBMs) are probabilistic graphical models that can also be interpreted as stochastic neural networks. Training RBMs is known to be challenging. Computing the likelihood of the model parameters or its gradient is in general computationally intensive. Thus, training re...... of the applied sampling procedure and I will introduce a transition operator that leads to faster mixing. Finally, a different parametrisation of RBMs will be discussed that leads to better learning results and more robustness against changes in the data representation....... relies on sampling based approximations of the log-likelihood gradient. I will present an empirical and theoretical analysis of the bias of these approximations and show that the approximation error can lead to a distortion of the learning process. The bias decreases with increasing mixing rate...
On higher order and anisotropic hydrodynamics for Bjorken and Gubser flows
2018-01-01
We study the evolution of hydrodynamic and non-hydrodynamic moments of the distribution function using anisotropic and third-order Chapman-Enskog hydrodynamics for systems undergoing Bjorken and Gubser flows. The hydrodynamic results are compared with the exact solution of the Boltzmann equation with a collision term in relaxation time approximation. While the evolution of the hydrodynamic moments of the distribution function (i.e. of the energy momentum tensor) can be described with high accuracy by both hydrodynamic approximation schemes, their description of the evolution of the entropy of the system is much less precise. We attribute this to large contributions from non-hydrodynamic modes coupling into the entropy evolution which are not well captured by the hydrodynamic approximations. The differences between the exact solution and the hydrodynamic approximations are larger for the third-order Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which effectively resums some of the dissipati...
Hydrodynamics beyond Navier-Stokes: The slip flow model
Yudistiawan, Wahyu P.; Ansumali, Santosh; Karlin, Iliya V.
2008-07-01
Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali , Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation—the nine-bit model in two dimensions—in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.
Jashnsaz, Hossein; Al Juboori, Mohammed; Weistuch, Corey; Miller, Nicholas; Nguyen, Tyler; Meyerhoff, Viktoria; McCoy, Bryan; Perkins, Stephanie; Wallgren, Ross; Ray, Bruce D; Tsekouras, Konstantinos; Anderson, Gregory G; Pressé, Steve
2017-03-28
The Gram-negative Bdellovibrio bacteriovorus (BV) is a model bacterial predator that hunts other bacteria and may serve as a living antibiotic. Despite over 50 years since its discovery, it is suggested that BV probably collides into its prey at random. It remains unclear to what degree, if any, BV uses chemical cues to target its prey. The targeted search problem by the predator for its prey in three dimensions is a difficult problem: it requires the predator to sensitively detect prey and forecast its mobile prey's future position on the basis of previously detected signal. Here instead we find that rather than chemically detecting prey, hydrodynamics forces BV into regions high in prey density, thereby improving its odds of a chance collision with prey and ultimately reducing BV's search space for prey. We do so by showing that BV's dynamics are strongly influenced by self-generated hydrodynamic flow fields forcing BV onto surfaces and, for large enough defects on surfaces, forcing BV in orbital motion around these defects. Key experimental controls and calculations recapitulate the hydrodynamic origin of these behaviors. While BV's prey (Escherichia coli) are too small to trap BV in hydrodynamic orbit, the prey are also susceptible to their own hydrodynamic fields, substantially confining them to surfaces and defects where mobile predator and prey density is now dramatically enhanced. Colocalization, driven by hydrodynamics, ultimately reduces BV's search space for prey from three to two dimensions (on surfaces) even down to a single dimension (around defects). We conclude that BV's search for individual prey remains random, as suggested in the literature, but confined, however-by generic hydrodynamic forces-to reduced dimensionality. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Temperature based Restricted Boltzmann Machines
Li, Guoqi; Deng, Lei; Xu, Yi; Wen, Changyun; Wang, Wei; Pei, Jing; Shi, Luping
2016-01-01
Restricted Boltzmann machines (RBMs), which apply graphical models to learning probability distribution over a set of inputs, have attracted much attention recently since being proposed as building blocks of multi-layer learning systems called deep belief networks (DBNs). Note that temperature is a key factor of the Boltzmann distribution that RBMs originate from. However, none of existing schemes have considered the impact of temperature in the graphical model of DBNs. In this work, we propose temperature based restricted Boltzmann machines (TRBMs) which reveals that temperature is an essential parameter controlling the selectivity of the firing neurons in the hidden layers. We theoretically prove that the effect of temperature can be adjusted by setting the parameter of the sharpness of the logistic function in the proposed TRBMs. The performance of RBMs can be improved by adjusting the temperature parameter of TRBMs. This work provides a comprehensive insights into the deep belief networks and deep learning architectures from a physical point of view.
Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions
Alqahtani, Mubarak; Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael
2017-10-01
We compare phenomenological results from 3 +1 D quasiparticle anisotropic hydrodynamics (aHydroQP) with experimental data collected in the CERN Large Hadron Collider 2.76 TeV Pb-Pb collisions. In particular, we present comparisons of particle spectra, average transverse momentum, elliptic flow, and Hanbury Brown-Twiss radii. The aHydroQP model relies on the introduction of a single temperature-dependent quasiparticle mass which is fit to lattice QCD data. By taking moments of the resulting Boltzmann equation, we obtain the dynamical equations used in the hydrodynamic stage which include the effects of both shear and bulk viscosities. At freeze-out, we use anisotropic Cooper-Frye freeze-out performed on a fixed-energy-density hypersurface to convert to hadrons. To model the production and decays of the hadrons we use therminator2 which is customized to sample from ellipsoidal momentum-space distribution functions. Using smooth Glauber initial conditions, we find very good agreement with many heavy-ion collision observables.
Immiscible multicomponent lattice Boltzmann model for fluids with ...
Indian Academy of Sciences (India)
It finds good applications in both static and dynamic ... liquid systems and they are widely used in industry for various purposes. For example, gas is released into liquid phase to form small bubbles in boling-water reactors for cooling ... Laplace's law and next, we compare the static features of SC model and the improved LB.
Lattice Boltzmann Method for 3-D Flows with Curved Boundary
2002-06-01
Page at http://www.sti.nasa.gov • Email your question via the Internet to help@sti.nasa.gov • Fax your question to the NASA STI Help Desk at (301) 621...Decomposition Tech- niques and Experimental Validation, Ph.D. Dissertation, Universitat Politecnica de Catalunya , Spain, 1999. [27] W. Shyy, Computational
Lattice Boltzmann Simulation of Particle Laden Flows in Microfluidic Systems
Energy Technology Data Exchange (ETDEWEB)
Clague, D S; Weisgraber, T; Wheeler, E; Hon, G; Radford, J; Gascoyne, P; Smity, R; Liepmann, D; Meinhart, C; Santiago, J; Krulevitch, P
2003-07-22
The goal of this effort was to develop dynamic simulation tools to study and characterize particulate transport in Microfluidic devices. This includes the effects of external fields and near-field particle-particle, particle-surface interactions. The unique aspect of this effort is that we focused on the particles in suspension and rigorously accounted for all of the interactions that they experienced in solution. In contrast, other numerical methods within the program, finite element and finite volume approaches, typically treat the suspended species as non-interacting point particles. Later in the program, some of these approaches incorporated approximations to begin to account for particle-particle interactions. Through the programs (BioFlips and SIMBIOSYS), we developed collaborative relationships with device-oriented efforts. More specifically and at the request of the SIMBIOSYS program manager, we allowed our efforts/milestones to be more guided by the needs of our BioFlips colleagues; therefore, our efforts were focused on the needs of the MD Anderson Cancer Center (Peter Gascoyne), UCDavis (Rosemary Smith), and UC Berkeley (Dorian Liepmann). The first two collaborations involved the development of Dielectrophoresis analysis tools and the later involved the development of suspension and fluid modeling tools for microneedles.
Automatic grid refinement criterion for lattice Boltzmann method
Lagrava, Daniel; Malaspinas, Orestis; Latt, Jonas; Chopard, Bastien
2015-01-01
In all kinds of engineering problems, and in particular in methods for computational fluid dynamics based on regular grids, local grid refinement is of crucial importance. To save on computational expense, many applications require to resolve a wide range of scales present in a numerical simulation by locally adding more mesh points. In general, the need for a higher (or a lower) resolution is not known a priori, and it is therefore difficult to locate areas for which local grid refinement is...
Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation Project
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...
Milne-Thomson, L M
2011-01-01
This classic exposition of the mathematical theory of fluid motion is applicable to both hydrodynamics and aerodynamics. Based on vector methods and notation with their natural consequence in two dimensions - the complex variable - it offers more than 600 exercises and nearly 400 diagrams. Prerequisites include a knowledge of elementary calculus. 1968 edition.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 9. Hydrodynamic Lubrication Experiment with 'Floating' Drops. Jaywant H Arakeri K R Sreenivas. General Article Volume 1 Issue 9 September 1996 pp 51-58. Fulltext. Click here to view fulltext PDF. Permanent link:
Bonneau, Dominique; Souchet, Dominique
2014-01-01
This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the rheological models and the equations of lubrication. It also presents the numerical approaches used to solve the above equations by finite differences, finite volumes and finite elements methods.
Phonon hydrodynamics for nanoscale heat transport at ordinary temperatures
Guo, Yangyu; Wang, Moran
2018-01-01
The classical Fourier's law fails in extremely small and ultrafast heat conduction even at ordinary temperatures due to strong thermodynamic nonequilibrium effects. In this work, a macroscopic phonon hydrodynamic equation beyond Fourier's law with a relaxation term and nonlocal terms is derived through a perturbation expansion to the phonon Boltzmann equation around a four-moment nonequilibrium solution. The temperature jump and heat flux tangential retardant boundary conditions are developed based on the Maxwell model of the phonon-boundary interaction. Extensive steady-state and transient nanoscale heat transport cases are modeled by the phonon hydrodynamic model, which produces quantitative predictions in good agreement with available phonon Boltzmann equation solutions and experimental results. The phonon hydrodynamic model provides a simple and elegant mathematical description of non-Fourier heat conduction with a clear and intuitive physical picture. The present work will promote deeper understanding and macroscopic modeling of heat transport in extreme states.
Energy Technology Data Exchange (ETDEWEB)
Castor, J I
2003-10-16
The discipline of radiation hydrodynamics is the branch of hydrodynamics in which the moving fluid absorbs and emits electromagnetic radiation, and in so doing modifies its dynamical behavior. That is, the net gain or loss of energy by parcels of the fluid material through absorption or emission of radiation are sufficient to change the pressure of the material, and therefore change its motion; alternatively, the net momentum exchange between radiation and matter may alter the motion of the matter directly. Ignoring the radiation contributions to energy and momentum will give a wrong prediction of the hydrodynamic motion when the correct description is radiation hydrodynamics. Of course, there are circumstances when a large quantity of radiation is present, yet can be ignored without causing the model to be in error. This happens when radiation from an exterior source streams through the problem, but the latter is so transparent that the energy and momentum coupling is negligible. Everything we say about radiation hydrodynamics applies equally well to neutrinos and photons (apart from the Einstein relations, specific to bosons), but in almost every area of astrophysics neutrino hydrodynamics is ignored, simply because the systems are exceedingly transparent to neutrinos, even though the energy flux in neutrinos may be substantial. Another place where we can do ''radiation hydrodynamics'' without using any sophisticated theory is deep within stars or other bodies, where the material is so opaque to the radiation that the mean free path of photons is entirely negligible compared with the size of the system, the distance over which any fluid quantity varies, and so on. In this case we can suppose that the radiation is in equilibrium with the matter locally, and its energy, pressure and momentum can be lumped in with those of the rest of the fluid. That is, it is no more necessary to distinguish photons from atoms, nuclei and electrons, than it is
DEFF Research Database (Denmark)
Hansen, Jesper Schmidt; Dyre, Jeppe C.; Daivis, Peter J.
2011-01-01
We show by nonequilibrium molecular dynamics simulations that the Navier-Stokes equation does not correctly describe water flow in a nanoscale geometry. It is argued that this failure reflects the fact that the coupling between the intrinsic rotational and translational degrees of freedom becomes...... important for nanoflows. The coupling is correctly accounted for by the extended Navier-Stokes equations that include the intrinsic angular momentum as an independent hydrodynamic degree of freedom. © 2011 American Physical Society....
RAA vs. v2 of heavy and light hadrons within a linear Boltzmann transport model
Cao, Shanshan; Pang, Long-Gang; Luo, Tan; He, Yayun; Qin, Guang-You; Wang, Xin-Nian
2017-08-01
We establish a linear Boltzmann transport (LBT) model coupled to hydrodynamical background to study hard parton evolution in heavy-ion collisions. Both elastic and inelastic scatterings are included in our calculations; and heavy and light flavor partons are treated on the same footing. Within this LBT model, we provide good descriptions of heavy and light hadron suppression from RHIC to the LHC energies. Possible solutions to the RAA vs. v2 puzzle are discussed.
Spherical-harmonic type expansion for the Boltzmann equation in semiconductor devices
Directory of Open Access Journals (Sweden)
Armando Majorana
1998-10-01
Full Text Available The Boltzmann equation for an electron gas in a semiconductor is considered. The electron energy is assumed to have a very general form, so that, for instance, parabolic or non parabolic band approximations can be treated. A technique, which recalls the classical moment method due to Grad, to deduce an approximate quasi-hydrodynamical model is shown and compared with the spherical harmonic expansion. Some characteristics of the model, as entropy inequality, are explicitly presented.
Atis, S.; Saha, S.; Auradou, H.; Martin, J.; Rakotomalala, N.; Talon, L.; Salin, D.
2012-09-01
Autocatalytic reaction fronts between two reacting species in the absence of fluid flow, propagate as solitary waves. The coupling between autocatalytic reaction front and forced simple hydrodynamic flows leads to stationary fronts whose velocity and shape depend on the underlying flow field. We address the issue of the chemico-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. Towards that purpose, we perform experiments over a wide range of flow velocities with the well characterized iodate arsenious acid and chlorite-tetrathionate autocatalytic reactions in transparent packed beads porous media. The characteristics of these porous media such as their porosity, tortuosity, and hydrodynamics dispersion are determined. In a pack of beads, the characteristic pore size and the velocity field correlation length are of the order of the bead size. In order to address these two length scales separately, we perform lattice Boltzmann numerical simulations in a stochastic porous medium, which takes into account the log-normal permeability distribution and the spatial correlation of the permeability field. In both experiments and numerical simulations, we observe stationary fronts propagating at a constant velocity with an almost constant front width. Experiments without flow in packed bead porous media with different bead sizes show that the front propagation depends on the tortuous nature of diffusion in the pore space. We observe microscopic effects when the pores are of the size of the chemical front width. We address both supportive co-current and adverse flows with respect to the direction of propagation of the chemical reaction. For supportive flows, experiments and simulations allow observation of two flow regimes. For adverse flow, we observe upstream and downstream front motion as well as static front behaviors over a wide range of flow rates. In order to understand better these observed static state fronts, flow
Persistent superconductor currents in holographic lattices.
Iizuka, Norihiro; Ishibashi, Akihiro; Maeda, Kengo
2014-07-04
We consider a persistent superconductor current along the direction with no translational symmetry in a holographic gravity model. Incorporating a lattice structure into the model, we numerically construct novel solutions of hairy charged stationary black branes with momentum or rotation along the latticed direction. The lattice structure prevents the horizon from rotating, and the total momentum is only carried by matter fields outside the black brane horizon. This is consistent with the black hole rigidity theorem, and it suggests that in dual field theory with lattices, superconductor currents are made up of "composite" fields, rather than "fractionalized" degrees of freedom. We also show that our solutions are consistent with the superfluid hydrodynamics.
Birkhoff, Garrett
1940-01-01
Since its original publication in 1940, this book has been revised and modernized several times, most notably in 1948 (second edition) and in 1967 (third edition). The material is organized into four main parts: general notions and concepts of lattice theory (Chapters I-V), universal algebra (Chapters VI-VII), applications of lattice theory to various areas of mathematics (Chapters VIII-XII), and mathematical structures that can be developed using lattices (Chapters XIII-XVII). At the end of the book there is a list of 166 unsolved problems in lattice theory, many of which still remain open. I
Anisotropic hydrodynamics for conformal Gubser flow
Energy Technology Data Exchange (ETDEWEB)
Strickland, Michael; Nopoush, Mohammad [Kent State University, Kent OH 44242 (United States); Ryblewski, Radoslaw [The H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, PL-31342 Kraków (Poland)
2016-12-15
In this proceedings contribution, we review the exact solution of the anisotropic hydrodynamics equations for a system subject to Gubser flow. For this purpose, we use the leading-order anisotropic hydrodynamics equations which assume that the distribution function is ellipsoidally symmetric in local-rest-frame momentum. We then prove that the SO(3){sub q} symmetry in de Sitter space constrains the anisotropy tensor to be of spheroidal form with only one independent anisotropy parameter remaining. As a consequence, the exact solution reduces to the problem of solving two coupled non-linear differential equations. We show that, in the limit that the relaxation time goes to zero, one obtains Gubser's ideal hydrodynamic solution and, in the limit that the relaxation time goes to infinity, one obtains the exact free streaming solution obtained originally by Denicol et al. For finite relaxation time, we solve the equations numerically and compare to the exact solution of the relaxation-time-approximation Boltzmann equation subject to Gubser flow. Using this as our standard, we find that anisotropic hydrodynamics describes the spatio-temporal evolution of the system better than all currently known dissipative hydrodynamics approaches.
Three-dimensional coupled double-distribution-function lattice ...
Indian Academy of Sciences (India)
Two three-dimensional (3D) lattice Boltzmann models in the framework of coupled double-distribution function approach for compressible flows, in which specific-heat ratio and Prandtl number can be adjustable, aredeveloped in this paper. The main differences between the two models are discrete equilibrium density and ...
Guyon, Etienne; Petit, Luc; Mitescu, Catalin D
2015-01-01
This new edition is an enriched version of the textbook of fluid dynamics published more than 10 years ago. It retains the same physically oriented pedagogical perspective. This book emphasizes, as in the first edition, experimental inductive approaches and relies on the study of the mechanisms at play and on dimensional analysis rather than more formal approaches found in many classical textbooks in the field. The need for a completely new version also originated from the increase, over the last few decades, of the cross-overs between the mechanical and physical approaches, as is visible in international meetings and joint projects. Hydrodynamics is more widely linked today to other fields of experimental sciences: materials, environment, life sciences and earth sciences, as well as engineering sciences.
Renilson, Martin
2015-01-01
This book adopts a practical approach and presents recent research together with applications in real submarine design and operation. Topics covered include hydrostatics, manoeuvring, resistance and propulsion of submarines. The author briefly reviews basic concepts in ship hydrodynamics and goes on to show how they are applied to submarines, including a look at the use of physical model experiments. The issues associated with manoeuvring in both the horizontal and vertical planes are explained, and readers will discover suggested criteria for stability, along with rudder and hydroplane effectiveness. The book includes a section on appendage design which includes information on sail design, different arrangements of bow planes and alternative stern configurations. Other themes explored in this book include hydro-acoustic performance, the components of resistance and the effect of hull shape. Readers will value the author’s applied experience as well as the empirical expressions that are presented for use a...
Energy Technology Data Exchange (ETDEWEB)
Pomraning, G.C.
1982-12-31
This course was intended to provide the participant with an introduction to the theory of radiative transfer, and an understanding of the coupling of radiative processes to the equations describing compressible flow. At moderate temperatures (thousands of degrees), the role of the radiation is primarily one of transporting energy by radiative processes. At higher temperatures (millions of degrees), the energy and momentum densities of the radiation field may become comparable to or even dominate the corresponding fluid quantities. In this case, the radiation field significantly affects the dynamics of the fluid, and it is the description of this regime which is generally the charter of radiation hydrodynamics. The course provided a discussion of the relevant physics and a derivation of the corresponding equations, as well as an examination of several simplified models. Practical applications include astrophysics and nuclear weapons effects phenomena.
Thermodynamic stabilities of the generalized Boltzmann entropies
Wada, Tatsuaki
2004-09-01
We consider the thermodynamic stability conditions (TSC) on the Boltzmann entropies generalized by Tsallis’ q- and Kaniadakis’ κ-deformed logarithmic functions. It is shown that the corresponding TSCs are not necessarily equivalent to the concavity of the generalized Boltzmann entropies with respect to internal energy. Nevertheless, both the TSCs are equivalent to the positivity of standard heat capacity.
Thermo-hydrodynamic lubrication in hydrodynamic bearings
Bonneau, Dominique; Souchet, Dominique
2014-01-01
This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the thermo-hydrodynamic and the thermo-elasto-hydrodynamic lubrication. The algorithms are methodically detailed and each section is thoroughly illustrated.
An introduction to the theory of the Boltzmann equation
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
Boltzmann Transport in Hybrid PIC HET Modeling
2015-07-01
Paper 3. DATES COVERED (From - To) July 2015-July 2015 4. TITLE AND SUBTITLE Boltzmann transport in hybrid PIC HET modeling 5a. CONTRACT NUMBER In...reproduce experimentally observed mobility trends derived from HPHall, a workhorse hybrid- PIC HET simulation code. 15. SUBJECT TERMS 16. SECURITY...Std. 239.18 Boltzmann transport in hybrid PIC HET modeling IEPC-2015- /ISTS-2015-b- Presented at Joint Conference of 30th International
Student understanding of the Boltzmann factor
Directory of Open Access Journals (Sweden)
Trevor I. Smith
2015-09-01
Full Text Available [This paper is part of the Focused Collection on Upper Division Physics Courses.] We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations of student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students’ abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students’ appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.
Relativistic entropy and related Boltzmann kinetics
Energy Technology Data Exchange (ETDEWEB)
Kaniadakis, G. [Politecnico di Torino (Italy). Dipartimento di Fisica
2009-06-15
It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmann equation, fixes univocally the entropy of the system, which turns out to be the Boltzmann-Gibbs-Shannon entropy. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect to its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitly remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the relativistic kinetics is governed by the Boltzmann-Gibbs-Shannon entropy. Indeed the ordinary relativistic Boltzmann equation admits as stationary stable distribution, the exponential Juttner distribution. Here, we show that the special relativity laws and the maximum entropy principle suggest a relativistic generalization also of the two-particle correlation function and then of the entropy. The so obtained, fully relativistic Boltzmann equation, obeys the H-theorem and predicts a stationary stable distribution, presenting power law tails in the high-energy region. The ensued relativistic kinetic theory preserves the main features of the classical kinetics, which recovers in the c{yields}{infinity} limit. (orig.)
Hydrodynamics challenge problem
Energy Technology Data Exchange (ETDEWEB)
Hornung, R. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Keasler, J. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Gokhale, M. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2011-06-09
The hydrodynamics challenge problem represents a classical HPC physics problem, namely high deformation event modeling via Lagrangian shock hydrodynamics. This challenge problem solves the Sedov blast wave problem for one material in three dimensions. The problem has an analytic solution, and can be scaled to arbitrarily large problem sizes. The reference code is drawn from a production LLNL hydrodynamics code.
Active particles in periodic lattices
Chamolly, Alexander; Ishikawa, Takuji; Lauga, Eric
2017-11-01
Both natural and artificial small-scale swimmers may often self-propel in environments subject to complex geometrical constraints. While most past theoretical work on low-Reynolds number locomotion addressed idealised geometrical situations, not much is known on the motion of swimmers in heterogeneous environments. As a first theoretical model, we investigate numerically the behaviour of a single spherical micro-swimmer located in an infinite, periodic body-centred cubic lattice consisting of rigid inert spheres of the same size as the swimmer. Running a large number of simulations we uncover the phase diagram of possible trajectories as a function of the strength of the swimming actuation and the packing density of the lattice. We then use hydrodynamic theory to rationalise our computational results and show in particular how the far-field nature of the swimmer (pusher versus puller) governs even the behaviour at high volume fractions.
Energy Technology Data Exchange (ETDEWEB)
Schaefer, Stefan [DESY (Germany). Neumann Inst. for Computing
2016-11-01
These configurations are currently in use in many on-going projects carried out by researchers throughout Europe. In particular this data will serve as an essential input into the computation of the coupling constant of QCD, where some of the simulations are still on-going. But also projects computing the masses of hadrons and investigating their structure are underway as well as activities in the physics of heavy quarks. As this initial project of gauge field generation has been successful, it is worthwhile to extend the currently available ensembles with further points in parameter space. These will allow to further study and control systematic effects like the ones introduced by the finite volume, the non-physical quark masses and the finite lattice spacing. In particular certain compromises have still been made in the region where pion masses and lattice spacing are both small. This is because physical pion masses require larger lattices to keep the effects of the finite volume under control. At light pion masses, a precise control of the continuum extrapolation is therefore difficult, but certainly a main goal of future simulations. To reach this goal, algorithmic developments as well as faster hardware will be needed.
Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel
2017-11-01
Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.
Hydrodynamic charge and heat transport on inhomogeneous curved spaces
Scopelliti, Vincenzo; Schalm, Koenraad; Lucas, Andrew
2017-08-01
We develop the theory of hydrodynamic charge and heat transport in strongly interacting quasirelativistic systems on manifolds with inhomogeneous spatial curvature. In solid-state physics, this is analogous to strain disorder in the underlying lattice. In the hydrodynamic limit, we find that the thermal and electrical conductivities are dominated by viscous effects and that the thermal conductivity is most sensitive to this disorder. We compare the effects of inhomogeneity in the spatial metric to inhomogeneity in the chemical potential and discuss the extent to which our hydrodynamic theory is relevant for experimentally realizable condensed-matter systems, including suspended graphene at the Dirac point.
The Boltzmann equation from quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Drewes, Marco, E-mail: marco.drewes@tum.de [Institut fuer Theoretische Teilchenphysik und Kosmologie, RWTH Aachen, 52056 Aachen (Germany); Physik Department T70, Technische Universitaet Muenchen, James Franck Strasse 1, D-85748 Garching (Germany); Mendizabal, Sebastian [Institut fuer Theoretische Physik, Goethe-Universitaet, 60438 Frankfurt am Main (Germany); Weniger, Christoph [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany)
2013-01-08
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff-Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.
The Boltzmann Equation in Fluorescent Lamp Theory
Lister, Graeme
Ken Hines was a wonderful mentor in my formative years as a physicist, and a great friend and companion throughout the rest of his life. He introduced me to the Fokker-Planck equation, which formed the basis of my Masters thesis, and showed me how to use it to derive the Boltzmann equation. Many years later, when my research took me into the field of gas discharge lighting, I was to re-discover the Boltzmann equation and apply it to fluorescent lamp modelling. Herein I discuss the important role the electron energy distribution function plays in understanding the physics of fluorescent lamps, and I describe some of the important insights gained from interpreting the Boltzmann equation.
Boltzmann-Electron Model in Aleph.
Energy Technology Data Exchange (ETDEWEB)
Hughes, Thomas Patrick; Hooper, Russell
2014-11-01
We apply the Boltzmann-electron model in the electrostatic, particle-in-cell, finite- element code Aleph to a plasma sheath. By assuming a Boltzmann energy distribution for the electrons, the model eliminates the need to resolve the electron plasma fre- quency, and avoids the numerical "grid instability" that can cause unphysical heating of electrons. This allows much larger timesteps to be used than with kinetic electrons. Ions are treated with the standard PIC algorithm. The Boltzmann-electron model re- quires solution of a nonlinear Poisson equation, for which we use an iterative Newton solver (NOX) from the Trilinos Project. Results for the spatial variation of density and voltage in the plasma sheath agree well with an analytic model
Celebrating Cercignani's conjecture for the Boltzmann equation
Villani, Cédric
2011-01-01
Cercignani\\'s conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann\\'s nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s. © American Institute of Mathematical Sciences.
On classical integrability of the hydrodynamics of quantum integrable systems
Bulchandani, Vir B.
2017-10-01
Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable systems was discovered. In the diffusionless limit, this is equivalent to a certain ‘Bethe-Boltzmann’ kinetic equation, which has the form of an integro-differential conservation law in (1+1) D. The purpose of the present work is to investigate the sense in which the Bethe-Boltzmann equation defines an ‘integrable kinetic equation’. To this end, we study a class of N dimensional systems of evolution equations that arise naturally as finite-dimensional approximations to the Bethe-Boltzmann equation. We obtain non-local Poisson brackets and Hamiltonian densities for these equations and derive an infinite family of first integrals, parameterized by N functional degrees of freedom. We find that the conserved charges arising from quantum integrability map to Casimir invariants of the hydrodynamic bracket and their group velocities map to Hamiltonian flows. Some results from the finite-dimensional setting extend to the underlying integro-differential equation, providing evidence for its integrability in the hydrodynamic sense.
Quantum Heat Engine and Negative Boltzmann Temperature
Xi, Jing-Yi; Quan, Hai-Tao
2017-09-01
To clarify the ambiguity on negative Boltzmann temperature in literature, we study the Carnot and the Otto cycle with one of the heat reservoirs at the negative Boltzmann temperature based on a canonical ensemble description. The work extraction, entropy production and the efficiency of these cycles are explored. Conditions for constructing and properties of these thermodynamic cycles are elucidated. We find that the apparent “violation” of the second law of thermodynamics in these cycles are due to the fact that the traditional definition of thermodynamic efficiency is inappropriate in this situation. When properly understanding the efficiency and the adiabatic processes, in which the system crosses over “absolute ZERO” in a limit sense, the Carnot cycle with one of the heat reservoirs at a negative Boltzmann temperature can be understood straightforwardly, and it contradicts neither the second nor the third law of thermodynamics. Hence, negative Boltzmann temperature is a consistent concept in thermodynamics. We use a two-level system and an Ising spin system to illustrate our central results. Support from the National Science Foundation of China under Grants Nos. 11375012, 11534002, and The Recruitment Program of Global Youth Experts of China
The Quantum Boltzmann Equation in Semiconductor Physics
Snoke, D. W.
2010-01-01
The quantum Boltzmann equation, or Fokker-Planck equation, has been used to successfully explain a number of experiments in semiconductor optics in the past two decades. This paper reviews some of the developments of this work, including models of excitons in bulk materials, electron-hole plasmas, and polariton gases.
Full Boltzmann equations for leptogenesis including scattering
Hahn-Woernle, F; Wong, Y Y Y
2009-01-01
We study the evolution of a cosmological baryon asymmetry produced via leptogenesis by means of the full classical Boltzmann equations, without the assumption of kinetic equilibrium and including all quantum statistical factors. Beginning with the full mode equations we derive the usual equations of motion for the right-handed neutrino number density and integrated lepton asymmetry, and show explicitly the impact of each assumption on these quantities. For the first time, we investigate also the effects of scattering of the right-handed neutrino with the top quark to leading order in the Yukawa couplings by means of the full Boltzmann equations. We find that in our full Boltzmann treatment the final lepton asymmetry can be suppressed by as much as a factor of 1.5 in the weak wash-out regime (K1), the full Boltzmann treatment and the integrated approach give nearly identical final lepton asymmetries (within 10 % of each other at K>3). Finally, we show that the opposing effects of quantum statistics on decays/i...
Two generalizations of the Boltzmann equation
Biro, T. S.; Kaniadakis, G.
2005-01-01
We connect two different generalizations of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities or equivalently by using nontrivial energy composition rules in the energy conservation constraint. Direct transformation formulas between key functions of the two approaches are given.
Elementary classical hydrodynamics
Chirgwin, B H; Langford, W J; Maxwell, E A; Plumpton, C
1967-01-01
Elementary Classical Hydrodynamics deals with the fundamental principles of elementary classical hydrodynamics, with emphasis on the mechanics of inviscid fluids. Topics covered by this book include direct use of the equations of hydrodynamics, potential flows, two-dimensional fluid motion, waves in liquids, and compressible flows. Some general theorems such as Bernoulli's equation are also considered. This book is comprised of six chapters and begins by introducing the reader to the fundamental principles of fluid hydrodynamics, with emphasis on ways of studying the motion of a fluid. Basic c
Elasto-hydrodynamic lubrication
Dowson, D; Hopkins, D W
1977-01-01
Elasto-Hydrodynamic Lubrication deals with the mechanism of elasto-hydrodynamic lubrication, that is, the lubrication regime in operation over the small areas where machine components are in nominal point or line contact. The lubrication of rigid contacts is discussed, along with the effects of high pressure on the lubricant and bounding solids. The governing equations for the solution of elasto-hydrodynamic problems are presented.Comprised of 13 chapters, this volume begins with an overview of elasto-hydrodynamic lubrication and representation of contacts by cylinders, followed by a discussio
Transformations of integrable hydrodynamic chains and their hydrodynamic reductions
Pavlov, Maxim V.
2006-01-01
Hydrodynamic reductions of the hydrodynamic chain associated with dispersionless limit of 2+1 Harry Dym equation are found by the Miura type and reciprocal transformations applied to the Benney hydrodynamic chain.
Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems
Thüroff, Florian; Weber, Christoph A.; Frey, Erwin
2014-10-01
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 Treatment of the Boltzmann Equation for Self-Propelled Particle Systems
Directory of Open Access Journals (Sweden)
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.
Congruence amalgamation of lattices
Grätzer, G; Wehrung, F; Gr\\"{a}tzer, George; Lakser, Harry; Wehrung, Friedrich
2000-01-01
J. Tuma proved an interesting "congruence amalgamation" result. We are generalizing and providing an alternate proof for it. We then provide applications of this result: --A.P. Huhn proved that every distributive algebraic lattice $D$ with at most $\\aleph\\_1$ compact elements can be represented as the congruence lattice of a lattice $L$. We show that $L$ can be constructed as a locally finite relatively complemented lattice with zero. --We find a large class of lattices, the $\\omega$-congruence-finite lattices, that contains all locally finite countable lattices, in which every lattice has a relatively complemented congruence-preserving extension.
Montessori, A; Falcucci, G; Prestininzi, P; La Rocca, M; Succi, S
2014-05-01
We investigate the accuracy and performance of the regularized version of the single-relaxation-time lattice Boltzmann equation for the case of two- and three-dimensional lid-driven cavities. The regularized version is shown to provide a significant gain in stability over the standard single-relaxation time, at a moderate computational overhead.
Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics
Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; Tartakovsky, Alexandre M.; Parks, Michael L.
2017-04-01
We present a consistent implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent I2SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.
Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; Tartakovsky, Alexandre M.; Parks, Michael L.
2017-04-01
We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.
Nonequilibrium thermodynamics of restricted Boltzmann machines
Salazar, Domingos S. P.
2017-08-01
In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as restricted Boltzmann machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov process and how the detailed balance condition and the Maxwell-Boltzmann equilibrium distribution are sufficient conditions for a complete thermodynamics description, including nonequilibrium fluctuation theorems. Numerical simulations in a fully trained RBM are performed and the heat exchange fluctuation theorem is verified with excellent agreement to the theory. We observe how the contrastive divergence functional, mostly used in unsupervised learning of RBMs, is closely related to nonequilibrium thermodynamic quantities. We also use the framework to interpret the estimation of the partition function of RBMs with the annealed importance sampling method from a thermodynamics standpoint. Finally, we argue that unsupervised learning of RBMs is equivalent to a work protocol in a system driven by the laws of thermodynamics in the absence of labeled data.
Generalized Boltzmann equation for neutron stars
Energy Technology Data Exchange (ETDEWEB)
Kaniadakis, G. [Politecnico di Torino (Italy). Dipt. di Fisica]|[Istituto Nazionale di Fisica Nucleare, Sezione di Torino (Italy)]|[INFM, Torino (Italy); Lavagno, A. [Politecnico di Torino (Italy). Dipt. di Fisica]|[Istituto Nazionale di Fisica Nucleare, Sezione di Torino (Italy)]|[INFM, Torino (Italy); Quarati, P. [Politecnico di Torino (Italy). Dipt. di Fisica]|[Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari (Italy)]|[INFM, Torino (Italy)
1997-08-04
Baryon pairing and neutron superfluidity are believed to play an important role in the evolution of neutron stars. The pairing interaction provides a partial antisymmetrization of the nucleons in the stars with the evidence that fractional statistics must hold. By using a kinetic approach recently proposed [G. Kaniadakis, A. Lavagno and P. Quarati, Nucl. Phys. B 466 (1996) 527], we derive a non-linear Boltzmann equation which takes into account collective effects introduced by an exclusion-inclusion principle. This equation describes the dynamics of particles ruled by a fractional statistics. In addition, we extend this Boltzmann equation to the relativistic case and discuss the relevance of the quark matter in the star core. (orig.).
Generalized Boltzmann Equation for Neutron Stars
Kaniadakis, G.; Lavagno, A.; Quarati, P.
1997-02-01
Baryon pairing and neutron superfluidity are believed to play an important role in the evolution of neutron stars. The pairing interaction provides a partial antisymmetrization of the nucleons in the stars with the evidence that fractional statistics must hold. By using a kinetic approach recently proposed [G. Kaniadakis, A. Lavagno and P. Quarati, Nucl. Phys. B 466 (1996) 527], we derive a non-linear boltzmann equation which takes into account collective effects introduced by an exclusion-inclusion principle. This equation describes the dynamics of particles ruled by a fractional statistics. In addition, we extend this Boltzmann equation to the relativistic case and discuss the relevance of the quark matter in the star core.
The quantum Boltzmann equation in semiconductor physics
Energy Technology Data Exchange (ETDEWEB)
Snoke, D.W. [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, 15260 (United States)
2011-01-15
The quantum Boltzmann equation, or Fokker-Planck equation, has been used to successfully explain a number of experiments in semiconductor optics in the past two decades. This paper reviews some of the developments of this work, including models of excitons in bulk materials, electron-hole plasmas, and polariton gases. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Two generalizations of the Boltzmann equation
Energy Technology Data Exchange (ETDEWEB)
Biro, T.S. [KFKI Research Institute for Particle and Nuclear Physics, Budapest (Hungary); Kaniadakis, G. [Instituto Nazionale di Fisica della Materia, Politecnico di Torino, Dipt. di Fisica, Torino (Italy)
2006-03-15
We connect two different extensions of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities or equivalently by using nontrivial energy composition rules in the energy conservation constraint part. Direct transformation formulas between key functions of the two approaches are given. (authors)
On the full Boltzmann equations for leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Garayoa, J.; Pastor, S.; Pinto, T.; Rius, N.; Vives, O., E-mail: garayoa@ific.uv.es, E-mail: pastor@ific.uv.es, E-mail: teguayco@gmail.com, E-mail: nuria@ific.uv.es, E-mail: vives@ific.uv.es [Depto. de Física Teórica and IFIC, Universidad de Valencia-CSIC, Edificio de Institutos de Paterna, Apt. 22085, 46071 Valencia (Spain)
2009-09-01
We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T = 0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ∼< 1) the final lepton asymmetry can change up to a factor four with respect to previous estimates.
Phonon hydrodynamics and its applications in nanoscale heat transport
Guo, Yangyu; Wang, Moran
2015-09-01
Phonon hydrodynamics is an effective macroscopic method to study heat transport in dielectric solid and semiconductor. It has a clear and intuitive physical picture, transforming the abstract and ambiguous heat transport process into a concrete and evident process of phonon gas flow. Furthermore, with the aid of the abundant models and methods developed in classical hydrodynamics, phonon hydrodynamics becomes much easier to implement in comparison to the current popular approaches based on the first-principle method and kinetic theories involving complicated computations. Therefore, it is a promising tool for studying micro- and nanoscale heat transport in rapidly developing micro and nano science and technology. However, there still lacks a comprehensive account of the theoretical foundations, development and implementation of this approach. This work represents such an attempt in providing a full landscape, from physical fundamental and kinetic theory of phonons to phonon hydrodynamics in view of descriptions of phonon systems at microscopic, mesoscopic and macroscopic levels. Thus a systematical kinetic framework, summing up so far scattered theoretical models and methods in phonon hydrodynamics as individual cases, is established through a frame of a Chapman-Enskog solution to phonon Boltzmann equation. Then the basic tenets and procedures in implementing phonon hydrodynamics in nanoscale heat transport are presented through a review of its recent wide applications in modeling thermal transport properties of nanostructures. Finally, we discuss some pending questions and perspectives highlighted by a novel concept of generalized phonon hydrodynamics and possible applications in micro/nano phononics, which will shed more light on more profound understanding and credible applications of this new approach in micro- and nanoscale heat transport science.
Hirano, Tetsufumi; van der Kolk, Naomi; Bilandzic, Ante
The main purpose of the lecture was to lead students and young postdocs to the frontier of the hydrodynamic description of relativistic heavy-ion collisions (H.I.C.) in order for them to understand talks and posters presented in the Quark Matter 2008 (QM08) conference in Jaipur, India [1]. So the most recent studies were not addressed in this lecture as they would be presented during the QM08 conference itself. Also, we try to give a very pedagogical lecture here. For the readers who may want to study relativistic hydrodynamics and its application to H.I.C. as an advanced course, we strongly recommend them to consult the references. This lecture note is divided into three parts. In the first part we give a brief introduction to relativistic hydrodynamics in the context of H.I.C. In the second part we present the formalism and some fundamental aspects of relativistic ideal and viscous hydrodynamics.
Privacy-preserving restricted boltzmann machine.
Li, Yu; Zhang, Yuan; Ji, Yue
2014-01-01
With the arrival of the big data era, it is predicted that distributed data mining will lead to an information technology revolution. To motivate different institutes to collaborate with each other, the crucial issue is to eliminate their concerns regarding data privacy. In this paper, we propose a privacy-preserving method for training a restricted boltzmann machine (RBM). The RBM can be got without revealing their private data to each other when using our privacy-preserving method. We provide a correctness and efficiency analysis of our algorithms. The comparative experiment shows that the accuracy is very close to the original RBM model.
Privacy-Preserving Restricted Boltzmann Machine
Directory of Open Access Journals (Sweden)
Yu Li
2014-01-01
Full Text Available With the arrival of the big data era, it is predicted that distributed data mining will lead to an information technology revolution. To motivate different institutes to collaborate with each other, the crucial issue is to eliminate their concerns regarding data privacy. In this paper, we propose a privacy-preserving method for training a restricted boltzmann machine (RBM. The RBM can be got without revealing their private data to each other when using our privacy-preserving method. We provide a correctness and efficiency analysis of our algorithms. The comparative experiment shows that the accuracy is very close to the original RBM model.
Bachoc, Christine
2005-01-01
We study the Grassmannian 4-designs contained in lattices, in connection with the local property of the Rankin constant. We prove that the sequence of Barnes-Wall lattices contain Grassmannian 6-designs.
New integrable lattice hierarchies
Energy Technology Data Exchange (ETDEWEB)
Pickering, Andrew [Area de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos, c/ Tulipan s/n, 28933 Mostoles, Madrid (Spain); Zhu Zuonong [Departamento de Matematicas, Universidad de Salamanca, Plaza de la Merced 1, 37008 Salamanca (Spain) and Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: znzhu2@yahoo.com.cn
2006-01-23
In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula.
Dechant, Andreas; Shafier, Shalom Tzvi; Kessler, David A; Barkai, Eli
2016-08-01
The Boltzmann-Gibbs density, a central result of equilibrium statistical mechanics, relates the energy of a system in contact with a thermal bath to its equilibrium statistics. This relation is lost for nonthermal systems such as cold atoms in optical lattices, where the heat bath is replaced with the laser beams of the lattice. We investigate in detail the stationary phase-space probability for Sisyphus cooling under harmonic confinement. In particular, we elucidate whether the total energy of the system still describes its stationary state statistics. We find that this is true for the center part of the phase-space density for deep lattices, where the Boltzmann-Gibbs density provides an approximate description. The relation between energy and statistics also persists for strong confinement and in the limit of high energies, where the system becomes underdamped. However, the phase-space density now exhibits heavy power-law tails. In all three cases we find expressions for the leading-order phase-space density and corrections which break the equivalence of probability and energy and violate energy equipartition. The nonequilibrium nature of the steady state is corroborated by explicit violations of detailed balance. We complement these analytical results with numerical simulations to map out the intricate structure of the phase-space density.
Boltzmann and Einstein: Statistics and dynamics–An unsolved ...
Indian Academy of Sciences (India)
The struggle of Boltzmann with the proper description of the behavior of classical macroscopic bodies in equilibrium in terms of the properties of the particles out of which they consist will be sketched. He used both a dynamical and a statistical method. However, Einstein strongly disagreed with Boltzmann's statistical method ...
Boltzmann and Einstein: Statistics and dynamics – An unsolved ...
Indian Academy of Sciences (India)
Boltzmann and Einstein: Statistics and dynamics –. An unsolved problem. E G D COHEN. The Rockefeller University, 1230 York Avenue, New York, NY 10021, USA. E-mail: egdc@rockefeller.edu. Abstract. The struggle of Boltzmann with the proper description of the behavior of classical macroscopic bodies in equilibrium in ...
Soluble Boltzmann equations for internal state and Maxwell models
Futcher, E.; Hoare, M.R.; Hendriks, E.M.; Ernst, M.H.
We consider a class of scalar nonlinear Boltzmann equations describing the evolution of a microcanonical ensemble in which sub-systems exchange internal energy ‘randomly’ in binary interactions. In the continuous variable version these models can equally be interpreted as Boltzmann equations for
Atkinson, D; van Steenwijk, F.J.
The resistance between two arbitrary nodes in an infinite square lattice of:identical resistors is calculated, The method is generalized to infinite triangular and hexagonal lattices in two dimensions, and also to infinite cubic and hypercubic lattices in three and more dimensions. (C) 1999 American
The Einstein-Boltzmann equations revisited
Nadkarni-Ghosh, Sharvari; Refregier, Alexandre
2017-10-01
The linear Einstein-Boltzmann (E-B) equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed investigation of its mathematical properties. For this purpose, we focus on a simplified set of equations aimed at describing the broad features of the matter power spectrum. We first perform an eigenvalue analysis and study the onset of oscillations in the system signalled by the transition from real to complex eigenvalues. We then provide a stability criterion of different numerical schemes for this linear system and estimate the associated step size. We elucidate the stiffness property of the E-B system and show how it can be characterized in terms of the eigenvalues. While the parameters of the system are time dependent making it non-autonomous, we define an adiabatic regime where the parameters vary slowly enough for the system to be quasi-autonomous. We summarize the different regimes of the system for these different criteria as function of wavenumber k and scalefactor a. We also provide a compendium of analytic solutions for all perturbation variables in six limits on the k-a plane and express them explicitly in terms of initial conditions. These results are aimed to help the further development and testing of numerical cosmological Boltzmann solvers.
Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows
Lin, Chuandong; Xu, Aiguo; Zhang, Guangcai; Luo, Kai Hong; Li, Yingjun
2017-11-01
A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific-heat ratio and is described by one discrete Boltzmann equation (DBE). Independent discrete velocities are adopted for the two DBEs. The collision and force terms in the DBE account for the molecular collision and external force, respectively. Two types of force terms are exploited. In addition to recovering the modified Navier-Stokes equations in the hydrodynamic limit, the DBM has the capability of capturing detailed nonequilibrium effects. Furthermore, we use the DBM to investigate the dynamic process of the RTI. The invariants of tensors for nonequilibrium effects are presented and studied. For low Reynolds numbers, both global nonequilibrium manifestations and the growth rate of the entropy of mixing show three stages (i.e., the reducing, increasing, and then decreasing trends) in the evolution of the RTI. On the other hand, the early reducing tendency is suppressed and even eliminated for high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.
Exploring cluster Monte Carlo updates with Boltzmann machines
Wang, Lei
2017-11-01
Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.
Hydrodynamic Vortex on Surfaces
Ragazzo, Clodoaldo Grotta; de Barros Viglioni, Humberto Henrique
2017-10-01
The equations of motion for a system of point vortices on an oriented Riemannian surface of finite topological type are presented. The equations are obtained from a Green's function on the surface. The uniqueness of the Green's function is established under hydrodynamic conditions at the surface's boundaries and ends. The hydrodynamic force on a point vortex is computed using a new weak formulation of Euler's equation adapted to the point vortex context. An analogy between the hydrodynamic force on a massive point vortex and the electromagnetic force on a massive electric charge is presented as well as the equations of motion for massive vortices. Any noncompact Riemann surface admits a unique Riemannian metric such that a single vortex in the surface does not move ("Steady Vortex Metric"). Some examples of surfaces with steady vortex metric isometrically embedded in R^3 are presented.
Supermodular Programming on Lattices
Directory of Open Access Journals (Sweden)
Vladimir R. Khachaturov
2003-04-01
Full Text Available Questions, concerning the optimization of supermodular functions on finite lattices are considered in the paper. The systematic summary of main authors' and other researchers' results known before, new authors' results are given. There should be marked out the following three results among new results. The first - elaboration of the basic propositions of the theory of maximization of supermodular functions on Boolean lattices (they were worked out only for the problems of minimization before and establishing of relation between global minimum and maximum of supermodular function for main types of lattices. The second - elaboration of original combinatorial algorithms of automatized representation of hyper-cubes (booleans of large dimension on a plane in the form of various diagrams, on which the properties of boolean as a partially ordered set of its vertexes are kept (This provides us with ample opportunities for construction of various schemes of looking through the elements of atomic lattices and for visualization of the optimization process. The third - carrying out the basic propositions of the theory of optimization of supermodular functions to the main types of lattices: Boolean lattices, lattices with relative supplements (division lattices, lattices of vector subspaces of finite-dimensional vector space, geometrical spaces, lattices equal to Cartesian product of chains, distributive lattices, atomic lattices. These theoretical results and availability of the great amount of optimization problems for lattices with concrete forms of supermodular functions allow to consider methods and algorithms for solving the problems of optimization of supermodular functions on lattices as a new field of mathematical programming - supermodular programming [19].
Hydrodynamic separator sediment retention testing.
2010-03-01
Hydrodynamic separators are widely used in urban areas for removal of suspended sediments and floatables from : stormwater due to limited land availability for the installation of above ground stormwater best management : practices (BMPs). Hydrodynam...
Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers.
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.
Bosonization and quantum hydrodynamics
Indian Academy of Sciences (India)
Bosonization and quantum hydrodynamics. GIRISH S SETLUR. Department of Physics, Indian Institute of Technology, Guwahati, North Guwahati .... and Haldane [3] breaks up the Fermi surface into patches where the separation between the patches ∆kF ≫ Λ ∼ ∆q. Not only is this contrived, it involves the introduction of one ...
Skew resisting hydrodynamic seal
Conroy, William T.; Dietle, Lannie L.; Gobeli, Jeffrey D.; Kalsi, Manmohan S.
2001-01-01
A novel hydrodynamically lubricated compression type rotary seal that is suitable for lubricant retention and environmental exclusion. Particularly, the seal geometry ensures constraint of a hydrodynamic seal in a manner preventing skew-induced wear and provides adequate room within the seal gland to accommodate thermal expansion. The seal accommodates large as-manufactured variations in the coefficient of thermal expansion of the sealing material, provides a relatively stiff integral spring effect to minimize pressure-induced shuttling of the seal within the gland, and also maintains interfacial contact pressure within the dynamic sealing interface in an optimum range for efficient hydrodynamic lubrication and environment exclusion. The seal geometry also provides for complete support about the circumference of the seal to receive environmental pressure, as compared the interrupted character of seal support set forth in U.S. Pat. Nos. 5,873,576 and 6,036,192 and provides a hydrodynamic seal which is suitable for use with non-Newtonian lubricants.
Smoothed Particle Hydrodynamic Simulator
Energy Technology Data Exchange (ETDEWEB)
2016-10-05
This code is a highly modular framework for developing smoothed particle hydrodynamic (SPH) simulations running on parallel platforms. The compartmentalization of the code allows for rapid development of new SPH applications and modifications of existing algorithms. The compartmentalization also allows changes in one part of the code used by many applications to instantly be made available to all applications.
On the conditions of validity of the Boltzmann equation and Boltzmann H-theorem
Tessarotto, Massimo; Cremaschini, Claudio; Tessarotto, Marco
2013-03-01
In this paper the problem is posed of the formulation of the so-called ab initio approach to the statistical description of the Boltzmann-Sinai N -body classical dynamical system (CDS) formed by identical smooth hard spheres. This amounts to introducing a suitably generalized version of the axioms of Classical Statistical Mechanics. The latter involve a proper definition of the functional setting for the N -body probability density function (PDF), so that it includes also the case of the deterministic N -body PDF. In connection with this issue, a further development concerns the introduction of modified collision boundary conditions which differ from the usual ones adopted in previous literature. Both features are proved to be consistent with the validity of exact H-theorems for the N -body and 1 -body PDFs, respectively. Consequences of the axiomatic approach which concern the conditions of validity of the Boltzmann kinetic equation and the Boltzmann H-theorem are investigated. In particular, the role of the modified boundary conditions is discussed. It is shown that both theorems fail in the case in which the N -body PDF is identified with the deterministic PDF. Finally, the issue of applicability of the Zermelo and Loschmidt paradoxes to the ab initio approach presented here is discussed.
Boltzmann equation with double-well potentials
Chiacchiera, Silvia; Macrı, Tommaso; Trombettoni, Andrea
2016-10-01
We study the dynamics of an interacting classical gas trapped in a double-well potential at finite temperature. Two model potentials are considered: a cubic box with a square barrier in the middle, and a harmonic trap with a Gaussian barrier along one direction. The study is performed using the Boltzmann equation, solved numerically via the test-particle method. We introduce and discuss a simple analytical model that allows one to provide estimates of the relaxation time, which are compared with numerical results. Finally, we use our findings to make numerical and analytical predictions for the case of a fermionic mixture in the normal-fluid phase in a realistic double-well potential relevant for experiments with cold atoms.
Boltzmann babies in the proper time measure
Energy Technology Data Exchange (ETDEWEB)
Bousso, Raphael; Bousso, Raphael; Freivogel, Ben; Yang, I-Sheng
2007-12-20
After commenting briefly on the role of the typicality assumption in science, we advocate a phenomenological approach to the cosmological measure problem. Like any other theory, a measure should be simple, general, well defined, and consistent with observation. This allows us to proceed by elimination. As an example, we consider the proper time cutoff on a geodesic congruence. It predicts that typical observers are quantum fluctuations in the early universe, or Boltzmann babies. We sharpen this well-known youngness problem by taking into account the expansion and open spatial geometry of pocket universes. Moreover, we relate the youngness problem directly to the probability distribution for observables, such as the temperature of the cosmic background radiation. We consider a number of modifications of the proper time measure, but find none that would make it compatible with observation.
A Boltzmann Equation for the QCD Plasma
Blaizot, Jean-Paul; Blaizot, Jean-Paul; Iancu, Edmond
1999-01-01
We present a derivation of a Boltzmann equation for the QCD plasma, starting from the quantum field equations. The derivation is based on a gauge covariant gradient expansion which takes consistently into account all possible dependences on the gauge coupling assumed to be small. We point out a limitation of the gradient expansion arising when the range of the interactions becomes comparable with that of the space-time inhomogeneities of the system. The method is first applied to the case of scalar electrodynamics, and then to the description of long wavelength colour fluctuations in the QCD plasma, where our equation coincides with that recently proposed by Arnold, Son and Yaffe. We discuss interesting cancellations among various collision terms, which occur in the calculation of most transport coefficients, but not in that of the quasiparticle lifetime, or in that of the relaxation time of colour excitations.
Energy Technology Data Exchange (ETDEWEB)
Shindler, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2007-07-15
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
Hydrodynamics of Turning Flocks.
Yang, Xingbo; Marchetti, M Cristina
2015-12-18
We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational inertia and alignment strength, are derived by coarse-graining the inertial spin model recently proposed by Cavagna et al. The interplay between orientational inertia and bend elasticity of the flock yields anisotropic spin waves that mediate the propagation of turning information throughout the flock. The coupling between spin-current density to the local vorticity field through a nonlinear friction gives rise to a hydrodynamic mode with angular-dependent propagation speed at long wavelengths. This mode becomes unstable as a result of the growth of bend and splay deformations augmented by the spin wave, signaling the transition to complex spatiotemporal patterns of continuously turning and swirling flocks.
Superluminous Supernovae hydrodynamic models
Orellana, M.
2017-07-01
We use our radiation hydrodynamic code in order to simulate magnetar powered Superluminous Supernovae (SLSNe). It is assumed that a central rapidly rotating magnetar deposits all its rotational energy into the ejecta where is added to the usual power. The magnetar luminosity and spin-down timescale are adopted as the free parameters of the model. For the case of ASASSN-15lh, which has been claimed as the most luminous supernova ever discovered, we have found physically plausible magnetar parameters can reproduce the overall shape of the bolometric light curve (LC) provided the progenitor mass is ≍ 8M⊙. The ejecta dynamics of this event shows signs of the magnetar energy input which deviates the expansion from the usually assumed homologous behaviour. Our numerical experiments lead us to conclude that the hydrodynamical modeling is necessary in order to derive the properties of powerful magnetars driving SLSNe.
Analysis of spectral methods for the homogeneous Boltzmann equation
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.
Testing the Maxwell-Boltzmann distribution using Brownian particles
National Research Council Canada - National Science Library
Mo, Jianyong; Simha, Akarsh; Kheifets, Simon; Raizen, Mark G
2015-01-01
.... We provide a direct verification of a modified Maxwell-Boltzmann velocity distribution and modified energy equipartition theorem that account for the kinetic energy of the liquid displaced by the particle...
Blaedel, Kenneth L.; Davis, Pete J.; Landram, Charles S.
2000-01-01
A saw having a self-pumped hydrodynamic blade guide or bearing for retaining the saw blade in a centered position in the saw kerf (width of cut made by the saw). The hydrodynamic blade guide or bearing utilizes pockets or grooves incorporated into the sides of the blade. The saw kerf in the workpiece provides the guide or bearing stator surface. Both sides of the blade entrain cutting fluid as the blade enters the kerf in the workpiece, and the trapped fluid provides pressure between the blade and the workpiece as an inverse function of the gap between the blade surface and the workpiece surface. If the blade wanders from the center of the kerf, then one gap will increase and one gap will decrease and the consequent pressure difference between the two sides of the blade will cause the blade to re-center itself in the kerf. Saws using the hydrodynamic blade guide or bearing have particular application in slicing slabs from boules of single crystal materials, for example, as well as for cutting other difficult to saw materials such as ceramics, glass, and brittle composite materials.
Hydrodynamics of fossil fishes
Fletcher, Thomas; Altringham, John; Peakall, Jeffrey; Wignall, Paul; Dorrell, Robert
2014-01-01
From their earliest origins, fishes have developed a suite of adaptations for locomotion in water, which determine performance and ultimately fitness. Even without data from behaviour, soft tissue and extant relatives, it is possible to infer a wealth of palaeobiological and palaeoecological information. As in extant species, aspects of gross morphology such as streamlining, fin position and tail type are optimized even in the earliest fishes, indicating similar life strategies have been present throughout their evolutionary history. As hydrodynamical studies become more sophisticated, increasingly complex fluid movement can be modelled, including vortex formation and boundary layer control. Drag-reducing riblets ornamenting the scales of fast-moving sharks have been subjected to particularly intense research, but this has not been extended to extinct forms. Riblets are a convergent adaptation seen in many Palaeozoic fishes, and probably served a similar hydrodynamic purpose. Conversely, structures which appear to increase skin friction may act as turbulisors, reducing overall drag while serving a protective function. Here, we examine the diverse adaptions that contribute to drag reduction in modern fishes and review the few attempts to elucidate the hydrodynamics of extinct forms. PMID:24943377
Hydrodynamics of insect spermatozoa
Pak, On Shun; Lauga, Eric
2010-11-01
Microorganism motility plays important roles in many biological processes including reproduction. Many microorganisms propel themselves by propagating traveling waves along their flagella. Depending on the species, propagation of planar waves (e.g. Ceratium) and helical waves (e.g. Trichomonas) were observed in eukaryotic flagellar motion, and hydrodynamic models for both were proposed in the past. However, the motility of insect spermatozoa remains largely unexplored. An interesting morphological feature of such cells, first observed in Tenebrio molitor and Bacillus rossius, is the double helical deformation pattern along the flagella, which is characterized by the presence of two superimposed helical flagellar waves (one with a large amplitude and low frequency, and the other with a small amplitude and high frequency). Here we present the first hydrodynamic investigation of the locomotion of insect spermatozoa. The swimming kinematics, trajectories and hydrodynamic efficiency of the swimmer are computed based on the prescribed double helical deformation pattern. We then compare our theoretical predictions with experimental measurements, and explore the dependence of the swimming performance on the geometric and dynamical parameters.
Hydrodynamics of fossil fishes.
Fletcher, Thomas; Altringham, John; Peakall, Jeffrey; Wignall, Paul; Dorrell, Robert
2014-08-07
From their earliest origins, fishes have developed a suite of adaptations for locomotion in water, which determine performance and ultimately fitness. Even without data from behaviour, soft tissue and extant relatives, it is possible to infer a wealth of palaeobiological and palaeoecological information. As in extant species, aspects of gross morphology such as streamlining, fin position and tail type are optimized even in the earliest fishes, indicating similar life strategies have been present throughout their evolutionary history. As hydrodynamical studies become more sophisticated, increasingly complex fluid movement can be modelled, including vortex formation and boundary layer control. Drag-reducing riblets ornamenting the scales of fast-moving sharks have been subjected to particularly intense research, but this has not been extended to extinct forms. Riblets are a convergent adaptation seen in many Palaeozoic fishes, and probably served a similar hydrodynamic purpose. Conversely, structures which appear to increase skin friction may act as turbulisors, reducing overall drag while serving a protective function. Here, we examine the diverse adaptions that contribute to drag reduction in modern fishes and review the few attempts to elucidate the hydrodynamics of extinct forms.