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Numerical Methods For Fluid Dynamics

Author: Dale R. Durran
Publisher: Springer Science & Business Media
ISBN: 9781441964120
Size: 49.96 MB
Format: PDF, ePub
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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: 33.62 MB
Format: PDF
View: 6850
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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.

Numerical Partial Differential Equations Finite Difference Methods

Author: J.W. Thomas
Publisher: Springer Science & Business Media
ISBN: 9780387979991
Size: 56.90 MB
Format: PDF, ePub, Mobi
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What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.

Partial Differential Equations With Numerical Methods

Author: Stig Larsson
Publisher: Springer Science & Business Media
ISBN: 3540887059
Size: 55.87 MB
Format: PDF
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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.