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The Application of the Chebyshev Spectral Method in Transport Phenomena

The Application of the Chebyshev Spectral Method in Transport Phenomena Author Weidong Guo
ISBN-10 9783642340888
Release 2013-01-26
Pages 229
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Transport phenomena problems that occur in engineering and physics are often multi-dimensional and multi-phase in character. When taking recourse to numerical methods the spectral method is particularly useful and efficient. The book is meant principally to train students and non-specialists to use the spectral method for solving problems that model fluid flow in closed geometries with heat or mass transfer. To this aim the reader should bring a working knowledge of fluid mechanics and heat transfer and should be readily conversant with simple concepts of linear algebra including spectral decomposition of matrices as well as solvability conditions for inhomogeneous problems. The book is neither meant to supply a ready-to-use program that is all-purpose nor to go through all manners of mathematical proofs. The focus in this tutorial is on the use of the spectral methods for space discretization, because this is where most of the difficulty lies. While time dependent problems are also of great interest, time marching procedures are dealt with by briefly introducing and providing a simple, direct, and efficient method. Many examples are provided in the text as well as numerous exercises for each chapter. Several of the examples are attended by subtle points which the reader will face while working them out. Some of these points are deliberated upon in endnotes to the various chapters, others are touched upon in the book itself.



Numerical Analysis of Spectral Methods

Numerical Analysis of Spectral Methods Author David Gottlieb
ISBN-10 9780898710236
Release 1977-01-01
Pages 172
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A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.



Spectral Methods in MATLAB

Spectral Methods in MATLAB Author Lloyd N. Trefethen
ISBN-10 9780898714654
Release 2000-07-01
Pages 165
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Mathematics of Computing -- Numerical Analysis.



Identification of Damage Using Lamb Waves

Identification of Damage Using Lamb Waves Author Zhongqing Su
ISBN-10 9781848827844
Release 2009-09-01
Pages 346
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Lamb waves are guided waves that propagate in thin plate or shell structures. There has been a clear increase of interest in using Lamb waves for identifying structural damage, entailing intensive research and development in this field over the past two decades. Now on the verge of maturity for diverse engineering applications, this emerging technique serves as an encouraging candidate for facilitating continuous and automated surveillance of the integrity of engineering structures in a cost-effective manner. In comparison with conventional nondestructive evaluation techniques such as ultrasonic scanning and radiography which have been well developed over half a century, damage identification using Lamb waves is in a stage of burgeoning development, presenting a number of technical challenges in application that need to be addressed and circumvented. It is these two aspects that have encouraged us to write this book, with the intention of consolidating the knowledge and know-how in the field of Lamb-wave-based damage identification, and of promoting widespread attention to mature application of this technique in the practical engineering sphere. This book provides a comprehensive description of key facets of damage identification technique using Lamb waves, based on the authors’ knowledge, comprehension and experience, ranging from fundamental theory through case studies to engineering applications.



Computational Methods for Geodynamics

Computational Methods for Geodynamics Author Alik Ismail-Zadeh
ISBN-10 9781139489355
Release 2010-07-22
Pages
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Written as both a textbook and a handy reference, this text deliberately avoids complex mathematics assuming only basic familiarity with geodynamic theory and calculus. Here, the authors have brought together the key numerical techniques for geodynamic modeling, demonstrations of how to solve problems including lithospheric deformation, mantle convection and the geodynamo. Building from a discussion of the fundamental principles of mathematical and numerical modeling, the text moves into critical examinations of each of the different techniques before concluding with a detailed analysis of specific geodynamic applications. Key differences between methods and their respective limitations are also discussed - showing readers when and how to apply a particular method in order to produce the most accurate results. This is an essential text for advanced courses on numerical and computational modeling in geodynamics and geophysics, and an invaluable resource for researchers looking to master cutting-edge techniques. Links to supplementary computer codes are available online.



Numerical Techniques for Global Atmospheric Models

Numerical Techniques for Global Atmospheric Models Author Peter H. Lauritzen
ISBN-10 364211640X
Release 2011-03-29
Pages 564
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This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation properties, tracer transport, and considerations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find this book of particular relevance.



Theory and Applications of Fractional Differential Equations

Theory and Applications of Fractional Differential Equations Author Anatoliĭ Aleksandrovich Kilbas
ISBN-10 0444518320
Release 2006
Pages 523
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This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.



Multiscale Methods in Computational Mechanics

Multiscale Methods in Computational Mechanics Author Rene de Borst
ISBN-10 9048198097
Release 2010-10-09
Pages 446
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This work gives a modern, up-to-date account of recent developments in computational multiscale mechanics. Both upscaling and concurrent computing methodologies will be addressed for a range of application areas in computational solid and fluid mechanics: Scale transitions in materials, turbulence in fluid-structure interaction problems, multiscale/multilevel optimization, multiscale poromechanics. A Dutch-German research group that consists of qualified and well-known researchers in the field has worked for six years on the topic of computational multiscale mechanics. This text provides a unique opportunity to consolidate and disseminate the knowledge gained in this project. The addition of chapters written by experts outside this working group provides a broad and multifaceted view of this rapidly evolving field.



An Introduction to Computational Fluid Dynamics

An Introduction to Computational Fluid Dynamics Author Henk Kaarle Versteeg
ISBN-10 0131274988
Release 2007
Pages 503
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This book presents the fundamentals of computational fluid dynamics for the novice. It provides a thorough yet user-friendly introduction to the governing equations and boundary conditions of viscous fluid flows and its modelling.



Computational Methods for Electromagnetic Phenomena

Computational Methods for Electromagnetic Phenomena Author Wei Cai
ISBN-10 9781107021051
Release 2013-01-03
Pages 444
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The first book of its kind to cover a wide range of computational methods for electromagnetic phenomena, from atomistic to continuum scales, this integrated and balanced treatment of mathematical formulations, algorithms and the underlying physics enables us to engage in innovative and advanced interdisciplinary computational research.



Fluvial Hydrodynamics

Fluvial Hydrodynamics Author Subhasish Dey
ISBN-10 9783642190629
Release 2014-08-22
Pages 687
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The state-of-the-art in fluvial hydrodynamics can be examined only through a careful exploration of the theoretical development and applied engineering technology. The book is primarily focused, since most up-to-date research findings in the field are presented, on the research aspects that involve a comprehensive knowledge of sediment dynamics in turbulent flows. It begins with the fundamentals of hydrodynamics and particle motion followed by turbulence characteristics related to sediment motion. Then, the sediment dynamics is analysed from a classical perspective by applying the mean bed shear approach and additionally incorporating a statistical description for the role of turbulence. The work finally examines the local scour problems at hydraulic structures and scale models. It is intended to design as a course textbook in graduate / research level and a guide for the field engineers as well, keeping up with modern technological developments. Therefore, as a simple prerequisite, the background of the readers should have a basic knowledge in hydraulics in undergraduate level and an understanding of fundamentals of calculus.



Spectral Methods in Fluid Dynamics

Spectral Methods in Fluid Dynamics Author Claudio Canuto
ISBN-10 9783642841088
Release 2012-12-06
Pages 568
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This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.



Mixed and Hybrid Finite Element Methods

Mixed and Hybrid Finite Element Methods Author Franco Brezzi
ISBN-10 9781461231721
Release 2012-12-06
Pages 350
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Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.



Proceedings of the International Conference on Advances in Computational Mechanics 2017

Proceedings of the International Conference on Advances in Computational Mechanics 2017 Author Hung Nguyen-Xuan
ISBN-10 9789811071492
Release 2018-02-20
Pages 1170
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This book provides an overview of state-of-the-art methods in computational engineering for modeling and simulation. This proceedings volume includes a selection of refereed papers presented at the International Conference on Advances in Computational Mechanics (ACOME) 2017, which took place on Phu Quoc Island, Vietnam on August 2-4, 2017. The contributions highlight recent advances in and innovative applications of computational mechanics. Subjects covered include: biological systems; damage, fracture and failure; flow problems; multiscale multiphysics problems; composites and hybrid structures; optimization and inverse problems; lightweight structures; computational mechatronics; computational dynamics; numerical methods; and high-performance computing. The book is intended for academics, including graduate students and experienced researchers interested in state-of-the-art computational methods for solving challenging problems in engineering.



Radiation Hydrodynamics

Radiation Hydrodynamics Author John I. Castor
ISBN-10 0521540623
Release 2004
Pages 355
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This broad treatment provides an accessible introduction to the theory and the large-scale simulation methods currently used in radiation hydrodynamics. Chapters cover all the central topics, including: a review of the fundamentals of gas dynamics; methods for computational fluid dynamics; theory of radiative transfer and of the dynamical coupling of matter and radiation; and quantum mechanics of matter-radiation interaction. Also covered are the details of spectral line formation out of thermodynamic equilibrium; the theory of refraction and transfer of polarized light and current computational methods for radiation transport, and a description of some notable applications of the theory in astrophysics and laboratory plasmas. This is a valuable text for research scientists and graduate students in physics and astrophysics.



The Analysis of Fractional Differential Equations

The Analysis of Fractional Differential Equations Author Kai Diethelm
ISBN-10 9783642145742
Release 2010-08-18
Pages 247
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Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.



Chebyshev and Fourier Spectral Methods

Chebyshev and Fourier Spectral Methods Author John P. Boyd
ISBN-10 9780486141923
Release 2013-06-05
Pages 688
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Completely revised text applies spectral methods to boundary value, eigenvalue, and time-dependent problems, but also covers cardinal functions, matrix-solving methods, coordinate transformations, much more. Includes 7 appendices and over 160 text figures.