This book provides the first detailed survey of lbe theory and its major. An efficient and accurate approach for heat transfer evaluation on curved boundaries is proposed in the thermal lattice boltzmann equation. Lattice boltzmann method for 3d flows with curved boundary. The method of lattice boltzmann equation lbe is a kineticbased approach for.
Latticeboltzmann method with immersed boundary conditions. February 2000an accurate curved boundary treatment. A practical introduction to the lattice boltzmann method. On pressure and velocity boundary conditions for the lattice boltzmann bgk model.
A lattice boltzmann boundary condition for simulation of fluid flow using simple extrapolation is proposed. The pml formulation was derived by recasting the lattice boltzmann equation in terms of acoustic distribution functions to obtain a linear homogeneous hyperbolic system of equations. Hlbm refines the details gas and liquid behaviour, as they interact with each other and their surroundings. Modeling of static contact angles with curved boundaries using a multiphase lattice. Lattice boltzmann method introduces the lattice boltzmann method lbm for solving transport phenomena flow, heat and mass transfer in a systematic way. Lattice boltzmann model deals with physical interactions on the kinetic level, where it is much simpler accounted, than on the hydrodynamic level. Curved boundary conditions for the lattice boltzmann method. An investigation into curved and moving boundary treatments in the lattice boltzmann method journal of computational physics, vol. The lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems. The velocity and temperature profiles in the developing region predicted by lattice boltzmann. This algorithm is designed to model problems of multiple mixtures using lattice boltzmann method which in turn can interact with complex objects modeled with immersed boundaries. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The flow around a circular cylinder was investigated as a typical case and satisfactory results in terms of precision and performance were obtained. In this work, a secondorder accurate treatment of the boundary condition in the lbe method is developed for a curved.
Pdf study of curved boundary treatments in lattice boltzmann. The phenomena of twophase flow with large density ratio about. In this work, we investigate two issues that are important to computational efficiency and. In this article, the natural convection flow in eccentric annulus is simulated numerically by lattice boltzmann model lbm based on doublepopulation approach. The lbm for twophase fluid flows with the same density and the lbm combined with the immersed boundary method are described. The lattice boltzmann method is a powerful technique for the computational modeling of a wide variety of complex fluid flow problems including single and multiphase flow in complex geometries. Comparison between different approximation methods. The proposed flux boundary scheme has a firstorder accuracy for both straight boundaries and curved boundaries. Research highlights derivation of a curved boundary condition for the lattice boltzmann method. Since the lattice boltzmann method lbm originally carries out the simulations on the regular cartesian lattices.
On boundary conditions in lattice boltzmann methods. The most popular boundary condition for the lattice boltzmann equation lbe method is the bounceback scheme. The lattice boltzmann lb method has gained much success in a variety of fields involving fluid flow andor heat transfer. Assuming that boltzmann transport equation is valid, thermal conductivity can be written as. An efficient implementation of the lattice boltzmann method lbm using the compute unified device architecture cuda provided by nvidia was presented to simulate flows with curved boundaries. Explain step in lattice boltzmann method computational. We use a hybrid method of lattice boltzmann and finite differences to simulate flat and curved. This thesis aims to develop a numerical tool to simulate the twophase flow along curved solid boundaries with lattice boltzmann lb method.
Nonreflecting boundary conditions for the lattice boltzmann. One is for the treatment of boundaries situated at lattice nodes, and the other is for the approximation of boundaries that. This is the reason that recently a numerical method called lattice boltzmann has been developed for the simulation of. Generalized threedimensional lattice boltzmann colorgradient method for immiscible twophase porescale imbibition and drainage in porous media. A requirement is formulated for the distribution functions based on the tunable momentum balance at the walls, which is shown to be equivalent. Pdf boundary condition for lattice boltzmann modeling of. Because the method often uses uniform regular cartesian lattices in space, curved boundaries axe often approximated by a series of stairs that leads to reduction in computational accuracy. We propose a lbe boundary condition for moving boundaries by combination of the bounceback scheme and spatial interpolations of first or second order.
Fluctuations in the lattice boltzmann method a dissertation submitted to the graduate faculty of the north dakota state university of agriculture and applied science by goetz august ka. In this scheme, which is broadly based on the chapmanenskog expansion, the fictitious distributions are constructed exactly on the moving boundary. Because the method often uses uniform regular cartesian lattices in space, curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy. However, the existing methods either require at least two or three fluid nodes between nearby solid surfaces, a condition that cannot be. Implementation of curved wall boundary and absorbing open. Choice of boundary condition for latticeboltzmann simulation. Sep 15, 2012 in this study, the development of an absorbing boundary condition based on the perfectly matched layer concept for the lattice boltzmann method was investigated. Modified massconservative curved boundary scheme for lattice boltzmann simulations y. Slip on curved boundaries in the lattice boltzmann model. Second order accurate in space and stable for a relaxation frequency close to two. Physical properties assigned to the layer strongly in. In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice boltzmann equation lbe. In addition, the lbm on a moving multiblock grid is explained.
The goal is to observe how well different lbm methods for capturing a curved wall bounadry condition behave. A numerical strategy presents for dealing with curved boundaries of second order accuracy for both velocity and temperature fields. Force evaluation in the lattice boltzmann method involving. The lattice boltzmann method is derived from kinetic theory by discretizing multiples fluid boltzmann equations in which crosscollisions and selfcollisions are. Lattice boltzmann simulation of 2d flow in a random porous medium background for the project. The proposed method is tested in two flows past an impulsively started cylinder moving in a channel in two dimensions. The socalled lattice boltzmann models describe the fluid. Lattice boltzmann methods lbm is a class of computational fluid dynamics cfd methods for fluid simulation. An applicability study of advanced latticeboltzmann.
Kinetic boundary conditions in the lattice boltzmann method. Two techniques, based on the exchange of momentum and the integration of stress tensor, for the evaluation of the hydrodynamic forces in the lattice boltzmann simulations are investigated on the curved and moving boundaries in two dimensions. The proposed treatment of the curved boundaries is an improvement of a scheme due to o. In particular we want to mention chapter 3 and 4, where he develops the fundamentals, like theory of gas kinetics and the boltzmann equation. Providing explanatory computer codes throughout the book, the author guides readers through many practical examples, such as. Furthermore, curved boundary treatments can be extended to the modeling of moving boundary problems simply by adding a momentum term to the bounced distribution functions. In general, the lattice velocity is taken to be u lbm 0.
Specifically, we use our recently proposed singlenode scheme for the noslip boundary condition and a new scheme is. A heuristic curvedboundary treatment in lattice boltzmann method. A latticeboltzmann study of active boundary layer flow control. A heuristic curvedboundary treatment in lattice boltzmann. Wen school of energy science and engineering, central south university, changsha 410083, china. Lattice boltzmann methods for fluid dynamics steven orszag department of mathematics yale university in collaboration with hudong chen, isaac goldhirsch, and rick shock. A flux boundary scheme in the lattice boltzmann method and. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and natural to parallelize. Curved boundary treatments provide a way to improve the computational accuracy of the conventional stairshaped approximation used in lattice boltzmann lb simulations. Ab in membrane desalination processes, such as brackish water and seawater desalination, the concentration polarization cp and surface fouling are remarkable features affecting the performance of these filtration technologies. We present a new boundary condition in the lattice boltzmann method to model slip flow along curved boundaries. An efficient and accurate approach for heat transfer evaluation on curved boundaries is proposed in the thermal lattice boltzmann equation tlbe method. I want to learn about the lattice boltzmann equation in fluid. Since then the lbm emerged as an alternative powerful method for solving.
Books for theoretical understanding towards lbm, i would recommend the lattice boltzmann equation for fluid dynamics and beyon. While one cannot expect from the scope of this book to address those issues directly, it is a pity that the book. An applicability study of advanced latticeboltzmann techniques for moving, noslip boundaries and local grid re. The proposed boundary condition is a simple, robust, efficient, and accurate scheme. Numerical simulation of whistles using lattice boltzmann.
Note that this assumption breaks down when the dimensions of the system are comparable to or smaller than the wavelength of the phonons responsible for thermal. A heuristic interpretation of noslip boundary conditions for lattice boltzmann and lattice gas simulations is developed. Analysis of lattice boltzmann nodes initialization in moving boundary problems a. Section 3 deals with the implementation of the curved boundary conditions with an interpolated o lattice scheme. May 15, 2009 a lattice boltzmann method was employed to simulate active boundary layer flow control by means of a lowtemperature surface plasma. I would recommend you to start of with some basics of statistical mechanics and the concept of cellular automata. Boundary conditions for lattice boltzmann simulations. An accurate curved boundary treatment in the lattice boltzmann.
An introduction for geoscientists and engineers at. Curved boundaries in multilayer shallow water lattice boltzmann methods. The method is based on the simple bounceback boundary scheme and interpolations. Incompressible limits of lattice boltzmann equations using. Fundamentals and acoustics published in 2014, delivers a clear and complete introduction for beginners. Curved boundary treatments provide a means of improving the computational accuracy of the conventional stairshaped approximation used in lattice boltzmann lb simulations.
A dynamically adaptive lattice boltzmann method for thermal convection problems kai feldhusena,b,ralf deiterdingc. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and. In this work, we aim at investigating the implementation of contact angles in the pseudopotential lb simulations with curved. Instead of solving the navierstokes equations directly, a fluid density on a lattice is simulated with streaming and collision relaxation processes. Kinetic boundary conditions in the lattice boltzmann method santosh ansumali and iliya v. Boundary conditions for lattice boltzmann simulations with complex. In this work, a secondorder accurate treatment of boundary condition in the lbe method is developed for a curved boundary. Similarly, the characteristic lattice length l lbm represents the number of points used in the lattice domain to represent the characteristic length in the physical domain.
Boghosian1,2 1department of mathematics, tufts university 2american university of armenia, yerevan, armenia as of september 2010 dsfd 2010, cnr rome, 6 july 2010. The lattice boltzmann methods lbms for moving boundary flows are presented. Force evaluation in the lattice boltzmann method involving curved geometry renwei mei, dazhi yu, and wei shyy university of florida, gainesville, florida. Lattice boltzmann equations using multiple relaxation times are intended to be more stable than those using a single relaxation time. Nov 01, 2012 modeling blood flow in larger vessels using lattice boltzmann methods comes with a challenging set of constraints. Plasma was generated by an ac input voltage over a surface electrode and an embedded electrode, resulting in an uneven distribution of charges and an induced flow near the vicinity of the surface. This matlab code aims at solving lattice botlzmann method lbm in a 2d channel flow. Several types of boundary conditions are adjusted to. Lattice boltzmann method is implemented to study hydrodynamically and thermally developing steady laminar flows in a channel.
Pdf analysis of lattice boltzmann nodes initialisation in. Lattice boltzmann methods for moving boundary flows iopscience. An introduction for geoscientists and engineers sukop, michael c. Sheng chen, sheng bao, zhaohui liu, jing li, chao yi and chuguang. Casa seminar boundary conditions for the lattice boltzmann. An improvement is suggested which consists of including the wall nodes in the collision operation. Boundary conditions for the lattice boltzmann equation bruce m.
Hybrid lattice boltzmann method hlbm university of florida. In this paper, the pressure interaction between an inlet boundary and the interior of the. New boundary treatment methods for lattice boltzmann. The key point of this method is to implement the boundary conditions on curved solid boundaries. Improved treatment of the open boundary in the method of. Abstract we propose a novel scheme to handle moving boundaries, both straight and curved, within the lattice boltzmann method lbm. Implementation of curved wall boundary and absorbing open boundary conditions for the d3q19 lattice boltzmann method for simulation of in compressible fluid flows. The lattice boltzmann method principles and practice. Simulations were performed to examine the effect of various. We propose a novel scheme to handle moving boundaries, both straight and curved, within the lattice boltzmann method lbm.
Fluctuations in the lattice boltzmann method a dissertation. In 1988, the lattice boltzmann method lbm was introduced by mcnamara and zanetti to overcome the drawbacks of the lattice gas cellular automata. Everyday low prices and free delivery on eligible orders. A curved noslip boundary condition for the lattice boltzmann.
The lattice velocity must remain significantly below this value for it to properly simulate incompressibility. A new curved boundary treatment for the lattice boltzmann method. Secondorder curved boundary treatments of the lattice boltzmann. We will cover the lattice boltzmann approach in the next lecture. Building a lattice boltzmannbased wind tunnel with the. Two types of boundary treatment methods for lattice boltzmann method lbm are proposed. A requirement is formulated for the distribution functions based on the tunable. Modified massconservative curved boundary scheme for lattice. The following results are obtained by numerical simulations. The application of the procedure of the sponge layer technique near the open boundaries is also described in section 3. In this work, we propose a phasefieldbased lattice boltzmann method to simulate moving contact line mcl problems on curved boundaries. Numerical simulation of twodimensional convective heat transfer problem is conducted using twodimensional, nine directional d2q9 thermal lattice boltzmann arrangements.
A unified boundary treatment in lattice boltzmann method. We propose a lattice boltzmann method to treat moving boundary problems for solid objects moving in a fluid. An accurate curved boundary treatment in the lattice boltzmann method. The lattice boltzmann equation for fluid dynamics and beyond. Modified massconservative curved boundary scheme for.
Simple bounceback is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many. Lattice boltzmann methods lbm, originated from the lattice gas automata lga method hardypomeaupazzis and frischhasslacherpomeau models, is a class of computational fluid dynamics cfd methods for fluid simulation. Heat transfer evaluation on curved boundaries in thermal lattice. In this work, a secondorder accurate treatment of the boundary condition in the lbe method is developed for a curved boundary. In practical fluid dynamic simulations, the boundary condition should be treated carefully because it always has crucial influence on the numerical accuracy, stability and efficiency. A novel scheme for curved moving boundaries in the lattice. Fundamentals and engineering applications with computer codes 2011 by mohamad, a.
Momentum transfer of a boltzmannlattice fluid with boundaries. Analysis of lattice boltzmann nodes initialization in moving. The lattice boltzmann method is a numerical scheme based on a xedgrid. Lattice boltzmann method implementation in matlab for curved boundaries. The following questions should be considered in the project work. Major advantages of the method are owing to the fact that the solution. The lattice boltzmann equation for fluid dynamics and beyond numerical mathematics and scientific computation succi, sauro on. The history of the lattice boltzmann method and its application to fluid. Boundary conditions for the lattice boltzmann equation.
The calculation of fluid flow inside a porous medium is one of the important problems in the field of environmental fluid dynamics, mostly in the context of aquifer contamination and movement of solutes in the subsoil layers. In lbe, the distribution functions on various boundaries are often derived approximately. Heat transfer evaluation on curved boundaries in thermal. Lallemand and luo 7 combined the bounceback scheme and interpolation scheme to treat a moving curved boundary by the lattice boltzmann method. We study the velocity boundary condition for curved boundaries in the lattice boltzmann equation lbe. While one cannot expect from the scope of this book to address those issues directly, it is a pity that the book doesnt prepare in any way for those issues. Lattice boltzmann simulations of slip flow of newtonian and nonnewtonian fluids in microgeometries. Lattice boltzmann method for moving boundaries semantic. If you want to do something real with lattice boltzmann, you will need to address more advanced issues like how to deal with curved boundaries, or with higherorder lattices. Gpu implementation of lattice boltzmann method for flows. The master thesis will focus on curved boundary conditions of the lattice boltzmann method. Force evaluations in lattice boltzmann simulations with.
Introductionmoving boundary conditionscylinder in transient couette flowcollisionadvection process lattice boltzmann method for moving boundaries. Read gpu implementation of lattice boltzmann method for flows with curved boundaries, computer methods in applied mechanics and engineering on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. The benchmark is chosen to be the drag coefficient obtained from flow over a cylinder, while different methods are applied to capture the curved boundary. Can you please share with some books on lattice boltzmann methods, the most books are very. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. Numerical simulation of whistles using lattice boltzmann methods y. Caiazzo fraunhofer itwm, fraunhoferplatz, 1, d67663 kaiserslautern, germany email.
In this paper, we present a kind of secondorder curved boundary treatments for the lattice boltzmann method solving twodimensional convectiondiffusion. The boundary heat fluxes in the discrete velocity directions of the tlbe model are obtained using the given thermal boundary condition and the temperature distribution functions at the lattice. In this paper, for the first time, the ghostfluid lattice boltzmann method gflbm is combined with a refilling scheme to simulate the heat transfer from moving bodies with curved boundaries. Scavone a acomputational acoustic modeling laboratory caml, centre for interdisciplinary research in music media and technology cirmmt, mcgill university, 555 rue.
The hybrid lattice boltzmann method, or hlbm, is a hybrid method the of particle level set method plsm and the lattice boltzmann method lbm. An absorbing boundary condition for the lattice boltzmann. An accurate curved boundary treatment in the lattice. Eulerian description of highorder bounceback scheme for. A phasefieldbased lattice boltzmann method for moving. Modified curved boundary scheme for twophase lattice boltzmann. Lattice boltzmann simulation of natural convection heat. Flow simulations using two dimensional thermal lattice. The pseudopotential multiphase lattice boltzmann lb model is a popular model in the lb community for simulating multiphase flows. The additional relaxation times may be adjusted to suppress nonhydrodynamic modes that do not appear directly in the continuum equations, but may contribute to instabilities on the grid scale. Curved boundaries in multilayer shallow water lattice. Dealing with moving boundary problems, proper routines are needed to.
59 1519 747 1051 466 1073 1047 1497 972 311 279 1257 232 1482 812 1265 1357 1145 1438 1285 460 1019 1055 313 1125 1012 210 888 389 1010 1481 627 616 1101 1168 499 20 202 1015 1115 1069 1094 668 989 823