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Numerical Methods For Fluid Dynamics

Author: Dale R. Durran
Publisher: Springer Science & Business Media
ISBN: 9781441964120
Size: 62.31 MB
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This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean

Numerical Methods For Wave Equations In Geophysical Fluid Dynamics

Author: Dale R. Durran
Publisher: Springer Science & Business Media
ISBN: 1475730810
Size: 31.90 MB
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Covering a wide range of techniques, this book describes methods for the solution of partial differential equations which govern wave propagation and are used in modeling atmospheric and oceanic flows. The presentation establishes a concrete link between theory and practice.

Geophysical Fluid Dynamics

Author: J. Pedlosky
Publisher: Springer Science & Business Media
ISBN: 1468400711
Size: 40.10 MB
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The content of this book is based, largely, on the core curriculum in geophys ical fluid dynamics which I and my colleagues in the Department of Geophysical Sciences at The University of Chicago have taught for the past decade. Our purpose in developing a core curriculum was to provide to advanced undergraduates and entering graduate students a coherent and systematic introduction to the theory of geophysical fluid dynamics. The curriculum and the outline of this book were devised to form a sequence of courses of roughly one and a half academic years (five academic quarters) in length. The goal of the sequence is to help the student rapidly advance to the point where independent study and research are practical expectations. It quickly became apparent that several topics (e. g. , some aspects of potential theory) usually thought of as forming the foundations of a fluid-dynamics curriculum were merely classical rather than essential and could be, however sadly, dispensed with for our purposes. At the same time, the diversity of interests of our students is so great that no curriculum can truly be exhaust ive in such a curriculum period. It seems to me that the best that can be achieved as a compromise is a systematic introduction to some important segment of the total scope of geophysical fluid dynamics which is illustrative of its most fruitful methods.

Numerical Partial Differential Equations Finite Difference Methods

Author: J.W. Thomas
Publisher: Springer Science & Business Media
ISBN: 9780387979991
Size: 42.35 MB
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Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. This text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation. Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient.

Special Functions Of Mathematical Geo Physics

Author: Willi Freeden
Publisher: Springer Science & Business Media
ISBN: 3034805632
Size: 38.16 MB
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Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.

Hydrobiological Modelling

Author: Brian J. Williams
Publisher: Lulu.com
ISBN: 1847289606
Size: 38.32 MB
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The book describes models of aquatic ecosystems, ranging from lakes to estuaries to the deep ocean. It provides a background in the physical and biological processes, numerical methods and elementary ecosystem models. It describes two of the most widely used hydrodynamic models and presents a number of case studies. The practice of modelling in management is discussed.

High Order Methods For Incompressible Fluid Flow

Author: M. O. Deville
Publisher: Cambridge University Press
ISBN: 9780521453097
Size: 44.29 MB
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This book covers the development of high-order numerical methods for the simulation of incompressible fluid flows in complex domains.

Geometric Theory Of Incompressible Flows With Applications To Fluid Dynamics

Author: Tian Ma
Publisher: American Mathematical Soc.
ISBN: 0821836935
Size: 66.41 MB
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This book presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows, and applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications has gone well beyond the original motivation, which was the study of oceanic dynamics. One such development is a rigorous theory for boundary layer separation of incompressible fluid flows. This study of incompressible flows has two major parts, which are interconnected. The first is the development of a global geometric theory of divergence-free fields on general two-dimensional compact manifolds. The second is the study of the structure of velocity fields for two-dimensional incompressible fluid flows governed by the Navier-Stokes equations or the Euler equations. Motivated by the study of problems in geophysical fluid dynamics, the program of research in this book seeks to develop a new mathematical theory, maintaining close links to physics along the way. In return, the theory is applied to physical problems, with more problems yet to be explored.

Fundamentals Of Computational Fluid Dynamics

Author: H. Lomax
Publisher: Springer Science & Business Media
ISBN: 3662046547
Size: 70.40 MB
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The chosen semi-discrete approach of a reduction procedure of partial differential equations to ordinary differential equations and finally to difference equations gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.

Partial Differential Equations With Numerical Methods

Author: Stig Larsson
Publisher: Springer Science & Business Media
ISBN: 3540887059
Size: 74.31 MB
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The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.