The Application of the Chebyshev Spectral Method in Transport Phenomena

Author: Weidong Guo
Publisher: Springer Science & Business Media
ISBN: 3642340881
Format: PDF, ePub
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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

Author: David Gottlieb
Publisher: SIAM
ISBN: 0898710235
Format: PDF
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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.

Identification of Damage Using Lamb Waves

Author: Zhongqing Su
Publisher: Springer Science & Business Media
ISBN: 1848827849
Format: PDF, Kindle
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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.

Nonlinear Conservation Laws Fluid Systems and Related Topics

Author: Gui-Qiang Chen
Publisher: World Scientific
ISBN: 9814273279
Format: PDF, ePub, Mobi
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This book is a collection of lecture notes on Nonlinear Conservation Laws, Fluid Systems and Related Topics delivered at 2007 Shanghai Mathematics Summer School held at Fudan University, China, by world's leading experts in the field. The volume comprises ªve chapters that cover a range of topics from mathematical theory and numerical approximation of both incompressible and compressible ªuid ªows, kinetic theory and conservation laws, to statistical theories for ªuid systems. Researchers and graduate students who want to work in this field will benefit from this essential reference as each chapter leads readers from the basics to the frontiers of the current research in these areas.

Spectral and High Order Methods for Partial Differential Equations

Author: Jan S. Hesthaven
Publisher: Springer Science & Business Media
ISBN: 9783642153372
Format: PDF
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The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.

Numerical Techniques for Global Atmospheric Models

Author: Peter H. Lauritzen
Publisher: Springer Science & Business Media
ISBN: 9783642116407
Format: PDF, Kindle
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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.

Computational Methods for Geodynamics

Author: Alik Ismail-Zadeh
Publisher: Cambridge University Press
ISBN: 1139489356
Format: PDF, ePub, Docs
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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.

Multiscale Methods in Computational Mechanics

Author: Rene de Borst
Publisher: Springer Science & Business Media
ISBN: 9789048198092
Format: PDF, Kindle
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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.

Theory and Applications of Fractional Differential Equations

Author: Anatoliĭ Aleksandrovich Kilbas
Publisher: Elsevier
ISBN: 9780444518323
Format: PDF, Kindle
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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.