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Fluid Dynamic Applications of the Discrete Boltzmann Equation

Author: Roberto Monaco

Publisher: World Scientific

Published: 1991

Total Pages: 296

ISBN-13: 9789810204662

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.

Lecture Notes on the Discretization of the Boltzmann Equation

Author: N. Bellomo

Publisher: World Scientific

Published: 2003

Total Pages: 317

ISBN-13: 9812382259

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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.

Lattice Boltzmann Method And Its Application In Engineering

Author: Zhaoli Guo

Publisher: World Scientific

Published: 2013-03-25

Total Pages: 420

ISBN-13: 9814508314

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Lattice Boltzmann method (LBM) is a relatively new simulation technique for the modeling of complex fluid systems and has attracted interest from researchers in computational physics. Unlike the traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh.This book will cover the fundamental and practical application of LBM. The first part of the book consists of three chapters starting form the theory of LBM, basic models, initial and boundary conditions, theoretical analysis, to improved models. The second part of the book consists of six chapters, address applications of LBM in various aspects of computational fluid dynamic engineering, covering areas, such as thermo-hydrodynamics, compressible flows, multicomponent/multiphase flows, microscale flows, flows in porous media, turbulent flows, and suspensions.With these coverage LBM, the book intended to promote its applications, instead of the traditional computational fluid dynamic method.

Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows

Author: V.V. Aristov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 305

ISBN-13: 9401008663

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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.

Computational Fluid Dynamics

Author: Dieter Leutloff

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 296

ISBN-13: 3642794408

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Computational methods and modelling is of growing importance in fundamental science as well as in applications in industry and in environmental research. In this topical volume the readers find important contributions in the field of turbulent boundary layers, the Tsunami problem, group invariant solution of hydrodynamic equations, non-linear waves, modelling of the problem of evaporation-condensation, the exact solution of discrete models of the Boltzmann equation etc. The book addresses researchers and engineers both in the mechanical sciences and in scientific computing.

High Accuracy Non-centered Compact Difference Schemes for Fluid Dynamics Applications

Author: A. I. Tolstykh

Publisher: World Scientific

Published: 1994

Total Pages: 340

ISBN-13: 9789810216689

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This is the first book which describes completely the nontraditional difference schemes which combine the ideas of Pad-type approximation and upwind differencing. These possess some favorable properties and can be used to solve various problems in fluid dynamics and related disciplines. They were proposed by the author in the seventies and are extensively used in Russia. However, they seem to be relatively unknown outside the country. In this book, the author presents the theory of the schemes, to provide some sophisticated algorithms for different computational fluid dynamics problems, to supply readers with useful information which would permit them to construct a rich variety of algorithms of this type and to illustrate the applications of these methods to the numerical simulation of various fluid dynamics phenomena, ranging from supersonic viscous flows to some atmosphere and ocean processes. This book is an essential guide for anyone keenly interested in this field.

Applications of Padé Approximation Theory in Fluid Dynamics

Author: A Pozzi

Publisher: World Scientific

Published: 1994-03-07

Total Pages: 252

ISBN-13: 9814504092

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Although Padé presented his fundamental paper at the end of the last century, the studies on Padé's approximants only became significant in the second part of this century. Padé procedure is related to the theory of continued fractions, and some convergence theorems can be expressed only in terms of continued fractions. Further, Padé approximants have some advantages of practical applicability with respect to the continued-fraction theory. Moreover, as Chisholm notes, a given power series determines a set of approximants which are usually unique, whereas there are many ways of writing an associated continued fraction. The principal advantage of Padé approximants with respect to the generating Taylor series is that they provide an extension beyond the interval of convergence of the series. Padé approximants can be applied in many parts of fluid-dynamics, both in steady and in nonsteady flows, both in incompressible and in compressible regimes. This book is divided into four parts. The first one deals with the properties of the Padé approximants that are useful for the applications and illustrates, with the aid of diagrams and tables, the effectiveness of this technique in the field of applied mathematics. The second part recalls the basic equations of fluid-dynamics (those associated with the names of Navier-Stokes, Euler and Prandtl) and gives a quick derivation of them from the general balance equation. The third shows eight examples of the application of Padé approximants to steady flows, also taking into account the influence of the coupling of heat conduction in the body along which a fluid flows with conduction and convection in the fluid itself. The fourth part considers two examples of the application of Padé approximants to unsteady flows. Contents:Part 1: Padé Approximants:Elements of Padé Approximants TheorySome Theoretical Aspects of Padé ApproximantsPart 2: The Fluid-Dynamic Equations:Balance EquationsInner-Outer ExpansionsPart 3: Some Examples of Application of Padé Approximants in Steady Flows:The Thermo-Fluid-Dynamic EquationsFlows Over Bodies in Forced Convection: The Flat Plate CaseForced Convection in Stagnation FlowAppendix: Motion Equations in the Odograph PlaneFlows Over Bodies in Forced Convection: The Wedge CaseThe Coupling of Conduction with Laminar Natural Convection Along a Vertical Flat PlateVariable-Properties Effects: Supersonic Wedge FlowVariable-Properties Effects: Free ConvectionPlane Jet into a Moving MediumPart 4: Some Examples of Application of Padé Approximants in Unsteady Flows:The Impulsively Started Flow Away From a Plane Stagnation PointThe Impulsively Started Flow Past a Circular Cylinder Readership: Applied mathematicians (fluid mechanics) and aerospace engineers. keywords:Pade' Approximants;Expansions in Series;Approximate Methods in Fluid-Mechanics;Boundary Layers Approximations

The Lattice Boltzmann Equation

Author: S. Succi

Publisher: Oxford University Press

Published: 2001-06-28

Total Pages: 308

ISBN-13: 9780198503989

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Certain forms of the Boltzmann equation, have emerged, which relinquish most mathematical complexities of the true Boltzmann equation. This text provides a detailed survey of Lattice Boltzmann equation theory and its major applications.

Lecture Notes on the Mathematical Theory of the Boltzmann Equation

Author: N. Bellomo

Publisher: World Scientific

Published: 1995

Total Pages: 276

ISBN-13: 9789810221669

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This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.

Microscopic Theory of Condensation in Gases and Plasma

Author: A L Itkin

Publisher: World Scientific

Published: 1997-06-16

Total Pages: 296

ISBN-13: 9814498009

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This book summarizes results on the creation of a new theory of condensation which has an impact on consideration of some microscopic effects left aside in the usual nucleation theories. In particular, the main idea of the authors' microscopic condensation theory is that it considers the violation of the equilibrium cluster distribution over the internal degrees of freedom due to co-occurring condensation and decay reactions of the clusters. Contents:Brief Review of the Existing Nucleation TheoriesMain Principles of the Microscopic Theory of CondensationJuxtaposition with the Other Theories and ExperimentsKinetic Theory of Photostimulated NucleationKinetic Theory of Iron-Induced NucleationConclusionsAppendices: Dimensionless Form of SystemLow-Pressure LimitQuasisteady Equations for ConcentrationsFORTRAN Subroutines for Computing Parameters of the Theory Readership: Applied mathematicians, physicists, chemists and aeronomers. keywords:Nucleation;Nonequilibrium;Kinetics;Internal Degrees of Freedom;Cluster;Ion-Induced;Photo-Stimulated;Diffusion Chamber;Analytical Solutions;New Rate Constants;Fortran Subroutines