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Author : Vladislav Panferov
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (258 download)
Download or read book Convergence of Discrete-velocity Models to the Boltzmann Equation written by Vladislav Panferov and published by . This book was released on 1997 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nicola Bellomo
Publisher : World Scientific
ISBN 13 : 9789812796905
Total Pages : 320 pages
Book Rating : 4.7/5 (969 download)
Download or read book Lecture Notes on the Discretization of the Boltzmann Equation written by Nicola Bellomo and published by World Scientific. This book was released on 2003 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community. Contents: From the Boltzmann Equation to Discretized Kinetic Models (N Bellomo & R Gatignol); Discrete Velocity Models for Gas Mixtures (C Cercignani); Discrete Velocity Models with Multiple Collisions (R Gatignol); Discretization of the Boltzmann Equation and the Semicontinuous Model (L Preziosi & L Rondoni); Semi-continuous Extended Kinetic Theory (W Koller); Steady Kinetic Boundary Value Problems (H Babovsky et al.); Computational Methods and Fast Algorithms for the Boltzmann Equation (L Pareschi); Discrete Velocity Models and Dynamical Systems (A Bobylev & N Bernhoff); Numerical Method for the Compton Scattering Operator (C Buet & S Cordier); Discrete Models of the Boltzmann Equation in Quantum Optics and Arbitrary Partition of the Velocity Space (F Schrrer). Readership: Higher level postgraduates in applied mathematics.
Author : Nicola Bellomo
Publisher : World Scientific
ISBN 13 : 9814487066
Total Pages : 317 pages
Book Rating : 4.8/5 (144 download)
Download or read book Lecture Notes On The Discretization Of The Boltzmann Equation written by Nicola Bellomo and published by World Scientific. This book was released on 2003-01-24 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community.
Author : Alexander V. Bobylev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110550148
Total Pages : 289 pages
Book Rating : 4.1/5 (15 download)
Download or read book Landau Equation, Boltzmann-type Equations, Discrete Models, and Numerical Methods written by Alexander V. Bobylev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-23 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.
Author : Reinhard Illner
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (634 download)
Download or read book Global existence results for discrete velocity models of the Boltzmann equation in several dimensions written by Reinhard Illner and published by . This book was released on 1983 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Felix Sharipov
Publisher : John Wiley & Sons
ISBN 13 : 352741326X
Total Pages : 330 pages
Book Rating : 4.5/5 (274 download)
Download or read book Rarefied Gas Dynamics written by Felix Sharipov and published by John Wiley & Sons. This book was released on 2016-02-23 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at both researchers and professionals who deal with this topic in their routine work, this introduction provides a coherent and rigorous access to the field including relevant methods for practical applications. No preceding knowledge of gas dynamics is assumed.
Author :
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (227 download)
Download or read book APPLICATION OF A DISCRETE VELOCITY MODEL TO THE BOLTZMANN EQUATION IN SHEAR FLOWS. written by and published by . This book was released on 1963 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of a simple discrete velocity model to low Mach number Couette and Rayleigh flow is investigated. In the model, the molecular velocities are restricted to a finite set and in this study only eight equal speed velocities are allowed. The Boltzmann equation is reduced by this approximation to a set of coupled differential equations which are shown to be identical in form to those produced when the same approximation is applied to the Krook equation. The fluid velocity and shear stress in Couette flow are in approximate accord with those of Wang Chang and Uhlenbeck and of Lees over the complete range of Knudsen number.
Author : N. Bellomo
Publisher : World Scientific
ISBN 13 : 9789810240783
Total Pages : 360 pages
Book Rating : 4.2/5 (47 download)
Download or read book Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models written by N. Bellomo and published by World Scientific. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions. Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.
Author : Alexander V. Bobylev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110551004
Total Pages : 212 pages
Book Rating : 4.1/5 (15 download)
Download or read book Landau Equation, Boltzmann-type Equations, Discrete Models, and Numerical Methods written by Alexander V. Bobylev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-23 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.
Author : Timm Krüger
Publisher : Springer
ISBN 13 : 3319446495
Total Pages : 705 pages
Book Rating : 4.3/5 (194 download)
Download or read book The Lattice Boltzmann Method written by Timm Krüger and published by Springer. This book was released on 2016-11-07 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Anna DeMasi
Publisher : Springer
ISBN 13 : 3540466363
Total Pages : 204 pages
Book Rating : 4.5/5 (44 download)
Download or read book Mathematical Methods for Hydrodynamic Limits written by Anna DeMasi and published by Springer. This book was released on 2006-11-14 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.
Author : Vinicio C Boffi
Publisher : World Scientific
ISBN 13 : 9814554456
Total Pages : 284 pages
Book Rating : 4.8/5 (145 download)
Download or read book Nonlinear Kinetic Theory And Mathematical Aspects Of Hyperbolic Systems written by Vinicio C Boffi and published by World Scientific. This book was released on 1992-10-28 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Mathematical Biology and Kinetic Theory Evolution of the Dominance in a Population of Interacting Organisms (N Bellomo & M Lachowicz)Formation of Maxwellian Tails (A V Bobylev)On Long Time Asymptotics of the Vlasov-Poisson-Boltzmann System (J Dolbeault)The Classical Limit of a Self-Consistent Quantum-Vlasov Equation in 3-D (P A Markowich & N J Mauser)Simple Balance Methods for Transport in Stochastic Mixtures (G C Pomraning)Knudsen Layer Analysis by the Semicontinuous Boltzmann Equation (L Preziosi)Remarks on a Self Similar Fluid Dynamic Limit for the Broadwell System (M Slemrod & A E Tzavaras)On Extended Kinetic Theory with Chemical Reaction (C Spiga)Stability and Exponential Convergence in Lp for the Spatially Homogeneous Boltzmann Equation (B Wennberg)and other papers Readership: Applied mathematicians. keywords:Proceedings;Workshop;Rapallo (Italy);Kinetic Theory;Hyperbolic Systems;Nonlinear Kinetic Theory
Author : Martin Rheinländer
Publisher : GRIN Verlag
ISBN 13 : 3638784754
Total Pages : 380 pages
Book Rating : 4.6/5 (387 download)
Download or read book Analysis of Lattice-Boltzmann Methods written by Martin Rheinländer and published by GRIN Verlag. This book was released on 2007-08-20 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2007 in the subject Mathematics - Analysis, University of Constance (Fachbereich Mathematik & Statistik), language: English, abstract: Lattice-Boltzmann algorithms represent a quite novel class of numerical schemes, which are used to solve evolutionary partial differential equations (PDEs). In contrast to other methods (FEM,FVM), lattice-Boltzmann methods rely on a mesoscopic approach. The idea consists in setting up an artificial, grid-based particle dynamics, which is chosen such that appropriate averages provide approximate solutions of a certain PDE, typically in the area of fluid dynamics. As lattice-Boltzmann schemes are closely related to finite velocity Boltzmann equations being singularly perturbed by special scalings, their consistency is not obvious. This work is concerned with the analysis of lattice-Boltzmann methods also focusing certain numeric phenomena like initial layers, multiple time scales and boundary layers. As major analytic tool, regular (Hilbert) expansions are employed to establish consistency. Exemplarily, two and three population algorithms are studied in one space dimension, mostly discretizing the advection-diffusion equation. It is shown how these model schemes can be derived from two-dimensional schemes in the case of special symmetries. The analysis of the schemes is preceded by an examination of the singular limit being characteristic of the corresponding scaled finite velocity Boltzmann equations. Convergence proofs are obtained using a Fourier series approach and alternatively a general regular expansion combined with an energy estimate. The appearance of initial layers is investigated by multiscale and irregular expansions. Among others, a hierarchy of equations is found which gives insight into the internal coupling of the initial layer and the regular part of the solution. Next, the consistency of the model algorithms is considered followed by a discussion of stability. Apart from proving stability for several cases entailing convergence as byproduct, the spectrum of the evolution operator is examined. Based on this, it is shown that the CFL-condition is necessary and sufficient for stability in the case of a two population algorithm discretizing the advection equation. Furthermore, the presentation touches upon the question whether reliable stability statements can be obtained by rather formal arguments. To gather experience and prepare future work, numeric boundary layers are analyzed in the context of a finite difference discretization for the one-dimensional Poisson equation.
Author : Monaco Roberto
Publisher : World Scientific
ISBN 13 : 9813104392
Total Pages : 288 pages
Book Rating : 4.8/5 (131 download)
Download or read book Fluid Dynamic Applications Of The Discrete Boltzmann Equation written by Monaco Roberto and published by World Scientific. This book was released on 1991-11-15 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents applications to several fluid dynamics problems in both the bounded and unbounded domains in the framework of the discrete velocity models of kinetic theory. The proposition of new models for dense gases, gases with multi-components, and gases with chemical reactions are also included. This is an up-to-date book on the applications of the discrete Boltzmann equation.
Author : Alexander Sinitsyn
Publisher : Elsevier
ISBN 13 : 0123877806
Total Pages : 321 pages
Book Rating : 4.1/5 (238 download)
Download or read book Kinetic Boltzmann, Vlasov and Related Equations written by Alexander Sinitsyn and published by Elsevier. This book was released on 2011-06-17 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance. Reviews the whole field from the beginning to today Includes practical applications Provides classical and modern (semi-analytical) solutions
Author : Pierre Degond
Publisher : Springer Science & Business Media
ISBN 13 : 0817682007
Total Pages : 360 pages
Book Rating : 4.8/5 (176 download)
Download or read book Modeling and Computational Methods for Kinetic Equations written by Pierre Degond and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.
Author : V.V. Aristov
Publisher : Springer Science & Business Media
ISBN 13 : 9401008663
Total Pages : 305 pages
Book Rating : 4.4/5 (1 download)
Download or read book Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows written by V.V. Aristov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.
