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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781721509799
Category :
Languages : en
Pages : 32
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Book Description
We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations. Bouzidi, MHamed and DHumieres, Dominique and Lallemand, Pierre and Luo, Li-Shi and Bushnell, Dennis M. (Technical Monitor) Langley Research Center NASA/CR-2002-211658, NAS 1.26:211658, ICASE-2002-18
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781721509799
Category :
Languages : en
Pages : 32
Get Book Here
Book Description
We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations. Bouzidi, MHamed and DHumieres, Dominique and Lallemand, Pierre and Luo, Li-Shi and Bushnell, Dennis M. (Technical Monitor) Langley Research Center NASA/CR-2002-211658, NAS 1.26:211658, ICASE-2002-18
Author: M'Hamed Bouzidi
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized disperson equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean in variance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions: (b) Poiseuille flow with an arbitrary inclined angle with respect to the lattice orientation; and (c) a cylinder asymmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.
Author: Haoda Min
Publisher:
ISBN: 9781369124330
Category :
Languages : en
Pages : 62
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Book Description
The lattice-Boltzmann method (LBM) is a mesoscopic computational scheme which solves the hydrodynamic (continuum) flow by using a set of discrete particle (or model molecular) velocities. The continuum flow evolution such as pressure and hydrodynamic velocity emerges as the average behaviors ( i.e., moments) of the mesoscopic model particles which undergo repeated collisions and propagations on a prescribed lattice. While LBM is now a viable alternative to convectional computational fluid dynamics (CFD) methods, it also has its limitations in terms of computational efficiency, which motivates this thesis work. In the LBM simulation for fluid flow, the domain is usually discretized with a square lattice in 2D or a cubic lattice in 3D. Some previous studies were made to investigate the possibility of establishing a LBM model with non-standard lattice grid, namely, a rectangular lattice grid in 2D and a non-cubic (cuboid) lattice grid in 3D. The non-standard lattices are computationally more efficient when simulating a non-isotropic and inhomogeneous flows, e.g., the turbulent channel flow. In some previous non-standard lattice LBM developed by others, the Navier-Stokes equation is not correctly recovered because the resulting viscosity is anisotropic. The anisotropy is caused by the use of different lattice sizes in different directions; and it cannot be fixed without additional degrees of freedom. Recently at the University of Delaware, several new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the multiple-relaxation-time (MRT) collision model, either by redesigning some moments to add a new free parameter, or by extending the equilibrium moments to include higher-order terms. These models can then satisfy all isotropy conditions as required by the Navier-Stokes equations. In this thesis, based on the similar idea used in the successful design of LBM on a rectangular lattice, we developed a lattice Boltzmann model on a 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. Using the multi-scale Chapman-Enskog analysis, we designed the moment equations resulting from our MRT-LBM model, to be fully consistent with the Navier-Stokes equations. A second-order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities. The form of the second-order term and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the shear viscosity can be adjusted, independent of the stress-moment relaxation parameter, thus improving the numerical stability of the model. The resulting cuboid MRT-LBM model is then validated through several benchmark simulations, including the transient laminar channel flow, the fully developed single phase turbulent channel flow, and the 3D time-dependent, energy-cascading Taylor-Green vortex flow. In addition, the second-order accuracy of the proposed model is demonstrated in the simulation of 3D Taylor-Green vortex flow and transient laminar channel flow.
Author: Dragos B. Chirila
Publisher: Springer
ISBN: 3642370098
Category : Science
Languages : en
Pages : 268
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Book Description
This work provides a short "getting started" guide to Fortran 90/95. The main target audience consists of newcomers to the field of numerical computation within Earth system sciences (students, researchers or scientific programmers). Furthermore, readers accustomed to other programming languages may also benefit from this work, by discovering how some programming techniques they are familiar with map to Fortran 95. The main goal is to enable readers to quickly start using Fortran 95 for writing useful programs. It also introduces a gradual discussion of Input/Output facilities relevant for Earth system sciences, from the simplest ones to the more advanced netCDF library (which has become a de facto standard for handling the massive datasets used within Earth system sciences). While related works already treat these disciplines separately (each often providing much more information than needed by the beginning practitioner), the reader finds in this book a shorter guide which links them. Compared to other books, this work provides a much more compact view of the language, while also placing the language-elements in a more applied setting, by providing examples related to numerical computing and more advanced Input/Output facilities for Earth system sciences. Naturally, the coverage of the programming language is relatively shallow, since many details are skipped. However, many of these details can be learned gradually by the practitioner, after getting an overview and some practice with the language through this book.
Author: Timm Krüger
Publisher: Springer
ISBN: 3319446495
Category : Science
Languages : en
Pages : 705
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Book Description
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 variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.
Author: Dieter A. Wolf-Gladrow
Publisher: Springer
ISBN: 3540465863
Category : Mathematics
Languages : en
Pages : 320
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Book Description
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.
Author: Chuan-Yu Wu
Publisher: Royal Society of Chemistry
ISBN: 1849735034
Category : Science
Languages : en
Pages : 294
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Book Description
Discrete Element Methods (DEM) is a numerical technique for analysing the mechanics and physics of particulate systems. Originated in the late seventies for analysing geotechnical problems, it has seen significant development and is now employed extensively across disciplines. Produced in celebration of the 70th Birthday of Colin Thornton, this book contains a selection of papers concerning advances in discrete element modelling which were presented at the International Symposium on Discrete Element Modelling of Particulate Media held at Birmingham, UK on 28-30th March, 2012. The book showcases the wide application of discrete element modelling in gas-solid fluidisation, particulate flows, liquid-solid systems and quasi-static behaviour. It also reports the recent advancement in coupled DEM with computational fluid dynamics, Lattice Boltzmann Methods for multiphase systems and the novel application of DEM in contact electrification and fracture of granular systems. Aimed at research communities dealing with this technique in the powder handling and formulation industries, this will be a welcomed addition to the literature in this area.
Author: Valero-Lara, Pedro
Publisher: IGI Global
ISBN: 1522547614
Category : Computers
Languages : en
Pages : 461
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Book Description
Programming has become a significant part of connecting theoretical development and scientific application computation. Fluid dynamics provide an important asset in experimentation and theoretical analysis. Analysis and Applications of Lattice Boltzmann Simulations provides emerging research on the efficient and standard implementations of simulation methods on current and upcoming parallel architectures. While highlighting topics such as hardware accelerators, numerical analysis, and sparse geometries, this publication explores the techniques of specific simulators as well as the multiple extensions and various uses. This book is a vital resource for engineers, professionals, researchers, academics, and students seeking current research on computational fluid dynamics, high-performance computing, and numerical and flow simulations.
Author: Michael C. Sukop
Publisher: Springer Science & Business Media
ISBN: 3540279822
Category : Science
Languages : en
Pages : 178
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Book Description
Here is a basic introduction to Lattice Boltzmann models that emphasizes intuition and simplistic conceptualization of processes, while avoiding the complex 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 whose interest is in model application over detailed mathematics will find this a powerful 'quick start' guide. Example simulations, exercises, and computer codes are included.
Author: Yoshio Sone
Publisher: Springer Science & Business Media
ISBN: 146120061X
Category : Science
Languages : en
Pages : 358
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Book Description
This monograph is intended to provide a comprehensive description of the rela tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented. In addition, various interesting physical phenomena derived from the asymptotic theory are explained. The background of the asymptotic studies is explained in Chapter 1, accord ing to which the fluid-dynamic-type equations that describe the behavior of a gas in the continuum limit are to be studied carefully. Their detailed studies depending on physical situations are treated in the following chapters. What is striking is that the classical gas dynamic system is incomplete to describe the behavior of a gas in the continuum limit (or in the limit that the mean free path of the gas molecules vanishes). Thanks to the asymptotic theory, problems for a slightly rarefied gas can be treated with the same ease as the corresponding classical fluid-dynamic problems. In a rarefied gas, a temperature field is di rectly related to a gas flow, and there are various interesting phenomena which cannot be found in a gas in the continuum limit.
