Numerical Methods for Geophysical Fluid Dynamics

Dale R. Durran

466 pages, parution le 01/08/1998

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Résumé

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 book the author has provided 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 the theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. Numerical Methods for Geophysical Fluid Dynamics will be useful as a senior undergraduate and graduate text and reference for those teaching numerical methods particularly those concentrating on fluid dynamics. Dynamics will be useful as a senior undergraduate and graduate text, and as a reference for those teaching or using numerical methods, particularly for those concentrating on fluid dynamics.

1: Introduction: 1.1: Partial Differential Equations---Some Basics; 1.2: Wave Equations in Geophysical Fluid Dynamics; 1.3: Strategies for Numerical Approximation; Problems
2: Basic Finite-Difference Methods: 2.1: Accuracy and Consistency; 2.2: Stability and Convergence; 2.3: Time-Differencing; 2.4: Space Differencing; 2.5: Combined Time and Space Differencing; 2.6: Summary Discussion of Elementary Methods; Problems
3: Beyond the One-Wave Equation: 3.1: Systems of Equations; 3.2: Three or more independent variables; 3.3: Splitting into Fractional Steps; 3.4: Diffusion, Sources and Sinks; 3.5: Linear Equations with Variable Coefficients; 3.6: Nonlinear Instability; Problems
4: Series-Expansion Methods: 4.1: Strategies for Minimizing the Residual; 4.2: The Spectral Method; 4.3: The Pseudospectral Method; 4.4: Spherical Harmonics; 4.5: The Finite Element Method; Problems
5: Finite Volume Methods: 5.1: Conservation Laws and Weak Solutions; 5.2: Finite-Volume Methods and Convergence; 5.3: Discontinuities in Geophysical Fluid Dynamics; 5.4: Flux-Corrected Transport; 5.5: Flux Limiter Methods; 5.6: Approximation with Local Polynomials; 5.7: Two Spatial Dimensions; 5.8: Schemes for Positive-Definite Advection; 5.9: Curvilinear Coordinates; Problems
6: Semi-Lagrangian Methods: 6.1: The Scalar Advection Equation; 6.2: Forcing in the Lagrangian Frame; 6.3: Systems of Equations; 6.4: Alternative Trajectories; 6.5: Eulerian or Semi-Lagrangian?; Problems
7: Physically Insignificant Fast Waves: 7.1: The projection method; 7.2: The Semi-Implicit Method; 7.3: Fractional step methods; 7.4: Summary of Schemes for Nonhydrostatic Models; 7.5: The Hydrostatic Approximation; 7.6: Primitive Equation Models; Problems
8: Non-reflecting Boundary Conditions: 8.1: One-dimensional flow; 8.2: Two-dimensional shallow-water flow; 8.3: Two-dimensional stratified flow; 8.4: Wave-absorbing layers; 8.5: Summary; Problems
A: Numerical Miscellany: A.1: Finite-Difference Operator Notation; A.2: Tridiagonal Solvers
Bibliography

L'auteur - Dale R. Durran

Dale R. Durran is a Professor at the University of Washington, Seattle

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Dale R. Durran
Parution	01/08/1998
Nb. de pages	466
Format	16 x 24
Couverture	Relié
Poids	550g
Intérieur	Noir et Blanc
EAN13	9780387983769
ISBN13	978-0-387-98376-9