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Numerical Methods for Fluid Dynamics: With Applications to Geophysics 2nd ed. 2010 [Kõva köide]

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  • Formaat: Hardback, 516 pages, kõrgus x laius: 235x155 mm, kaal: 955 g, XVI, 516 p., 1 Hardback
  • Sari: Texts in Applied Mathematics 32
  • Ilmumisaeg: 23-Sep-2010
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1441964118
  • ISBN-13: 9781441964113
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Numerical Methods for Fluid Dynamics: With Applications to Geophysics 2nd ed. 2010Suurem pilt
  • Formaat: Hardback, 516 pages, kõrgus x laius: 235x155 mm, kaal: 955 g, XVI, 516 p., 1 Hardback
  • Sari: Texts in Applied Mathematics 32
  • Ilmumisaeg: 23-Sep-2010
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1441964118
  • ISBN-13: 9781441964113
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781441964113.html
Märksõnad:
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

Arvustused

From the reviews of the second edition:

This is a largely self-contained and relatively far-reaching presentation of numerical fluid dynamics. It is aimed towards practitioners (meteorologists, physicists, engineers), providing a presentation of more mathematical depth than is frequently encountered in such books. (H. Muthsam, Monatshefte für Mathematik, Vol. 166 (1), April, 2012)

Durrans direct and yet information-rich style makes this an excellent reference book. This is a good book for postdocs and professors as well as students. For an atmospheric modeler, this is probably the first book to buy. book is a more direct path to algorithms for graduate students and researchers who already have some familiarity with atmospheric dynamics. is worth a look by computational fluid dynamicists in other fields, especially those looking for ideas and insights outside their own particular specialties. (SIAM Review, Vol. 54 (4), 2012)

This book is an introduction to numerical methods for fluid dynamics. The text could be useful to graduate students and scientists working in various branches of applied mathematics and engineering, not only in geophysical fluids. The material is intelligible to readers with a general mathematical background. The book includes exercises and is well illustrated with figures linking theoretical analyses to actual computations. (Titus Petrila, Zentralblatt MATH, Vol. 1214, 2011)

From the reviews:

"...an excellent reference...should be brought to the attention of readers in meteorology, oceanography, physics, mechanics and engineering... an excellent text book...the extensiveness, theoretical and practical extent this book reaches make it a classical work." Acta Meteorologica Sinica

"...The book's unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currentlyactively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean

Preface vii
1 Introduction
1(34)
1.1 Partial Differential Equations: Some Basics
2(9)
1.1.1 First-Order Hyperbolic Equations
4(3)
1.1.2 Linear Second-Order Equations in Two Independent Variables
7(4)
1.2 Wave Equations in Geophysical Fluid Dynamics
11(15)
1.2.1 Hyperbolic Equations
12(8)
1.2.2 Filtered Equations
20(6)
1.3 Strategies for Numerical Approximation
26(7)
1.3.1 Approximating Calculus with Algebra
26(4)
1.3.2 Marching Schemes
30(3)
Problems
33(2)
2 Ordinary Differential Equations
35(54)
2.1 Stability, Consistency, and Convergence
36(4)
2.1.1 Truncation Error
36(2)
2.1.2 Convergence
38(2)
2.1.3 Stability
40(1)
2.2 Additional Measures of Stability and Accuracy
40(9)
2.2.1 A-Stability
41(1)
2.2.2 Phase-Speed Errors
42(2)
2.2.3 Single-Stage, Single-Step Schemes
44(3)
2.2.4 Looking Ahead to Partial Differential Equations
47(1)
2.2.5 L-Stability
48(1)
2.3 Runge-Kutta (Multistage) Methods
49(9)
2.3.1 Explicit Two-Stage Schemes
50(3)
2.3.2 Explicit Three-and Four-Stage Schemes
53(2)
2.3.3 Strong-Stability-Preserving Methods
55(2)
2.3.4 Diagonally Implicit Runge-Kutta Methods
57(1)
2.4 Multistep Methods
58(14)
2.4.1 Explicit Two-Step Schemes
58(4)
2.4.2 Controlling the Leapfrog Computational Mode
62(5)
2.4.3 Classical Multistep Methods
67(5)
2.5 Stiff Problems
72(9)
2.5.1 Backward Differentiation Formulae
73(2)
2.5.2 Ozone Photochemistry
75(2)
2.5.3 Computing Backward-Euler Solutions
77(1)
2.5.4 Rosenbrock Runge-Kutta Methods
78(3)
2.6 Summary
81(4)
Problems
85(4)
3 Finite-Difference Approximations for One-Dimensional Transport
89(58)
3.1 Accuracy and Consistency
89(3)
3.2 Stability and Convergence
92(8)
3.2.1 The Energy Method
94(2)
3.2.2 Von Neumann's Method
96(2)
3.2.3 The Courant-Friedrichs-Lewy Condition
98(2)
3.3 Space Differencing for Simulating Advection
100(17)
3.3.1 Differential-Difference Equations and Wave Dispersion
101(8)
3.3.2 Dissipation, Dispersion, and the Modified Equation
109(1)
3.3.3 Artificial Dissipation
110(4)
3.3.4 Compact Differencing
114(3)
3.4 Fully Discrete Approximations to the Advection Equation
117(11)
3.4.1 The Discrete-Dispersion Relation
119(3)
3.4.2 The Modified Equation
122(1)
3.4.3 Stable Schemes of Optimal Accuracy
123(1)
3.4.4 The Lax-Wendroff Method
124(4)
3.5 Diffusion, Sources, and Sinks
128(11)
3.5.1 Advection and Diffusion
130(7)
3.5.2 Advection with Sources and Sinks
137(2)
3.6 Summary
139(2)
Problems
141(6)
4 Beyond One-Dimensional Transport
147(56)
4.1 Systems of Equations
147(10)
4.1.1 Stability
148(5)
4.1.2 Staggered Meshes
153(4)
4.2 Three or More Independent Variables
157(12)
4.2.1 Scalar Advection in Two Dimensions
157(10)
4.2.2 Systems of Equations in Several Dimensions
167(2)
4.3 Splitting into Fractional Steps
169(7)
4.3.1 Split Explicit Schemes
170(3)
4.3.2 Split Implicit Schemes
173(1)
4.3.3 Stability of Split Schemes
174(2)
4.4 Linear Equations with Variable Coefficients
176(12)
4.4.1 Aliasing Error
178(6)
4.4.2 Conservation and Stability
184(4)
4.5 Nonlinear Instability
188(9)
4.5.1 Burgers's Equation
189(4)
4.5.2 The Barotropic Vorticity Equation
193(4)
Problems
197(6)
5 Conservation Laws and Finite-Volume Methods
203(78)
5.1 Conservation Laws and Weak Solutions
205(6)
5.1.1 The Riemann Problem
206(1)
5.1.2 Entropy-Consistent Solutions
207(4)
5.2 Finite-Volume Methods and Convergence
211(6)
5.2.1 Monotone Schemes
213(1)
5.2.2 Total Variation Diminishing Methods
214(3)
5.3 Discontinuities in Geophysical Fluid Dynamics
217(4)
5.4 Flux-Corrected Transport
221(5)
5.4.1 Flux Correction: The Original Proposal
222(1)
5.4.2 The Zalesak Corrector
223(3)
5.4.3 Iterative Flux Correction
226(1)
5.5 Flux-Limiter Methods
226(9)
5.5.1 Ensuring That the Scheme Is TVD
227(3)
5.5.2 Possible Flux Limiters
230(4)
5.5.3 Flow Velocities of Arbitrary Sign
234(1)
5.6 Subcell Polynomial Reconstruction
235(8)
5.6.1 Godunov's Method
235(3)
5.6.2 Piecewise-Linear Functions
238(2)
5.6.3 The Piecewise-Parabolic Method
240(3)
5.7 Essentially Nonoscillatory and Weighted Essentially Nonoscillatory Methods
243(10)
5.7.1 Accurate Approximation of the Flux Divergence
244(2)
5.7.2 ENO Methods
246(3)
5.7.3 WENO Methods
249(4)
5.8 Preserving Smooth Extrema
253(2)
5.9 Two Spatial Dimensions
255(16)
5.9.1 FCT in Two Dimensions
256(1)
5.9.2 Flux-Limiter Methods for Uniform Two-Dimensional Flow
257(3)
5.9.3 Nonuniform Nondivergent Flow
260(2)
5.9.4 Operator Splitting
262(2)
5.9.5 A Numerical Example
264(5)
5.9.6 When is a Limiter Necessary?
269(2)
5.10 Schemes for Positive-Definite Advection
271(4)
5.10.1 An FCT Approach
271(2)
5.10.2 Antidiffusion via Upstream Differencing
273(2)
5.11 Curvilinear Coordinates
275(2)
Problems
277(4)
6 Series-Expansion Methods
281(76)
6.1 Strategies for Minimizing the Residual
281(3)
6.2 The Spectral Method
284(15)
6.2.1 Comparison with Finite-Difference Methods
285(8)
6.2.2 Improving Efficiency Using the Transform Method
293(5)
6.2.3 Conservation and the Galerkin Approximation
298(1)
6.3 The Pseudospectral Method
299(4)
6.4 Spherical Harmonics
303(17)
6.4.1 Truncating the Expansion
305(3)
6.4.2 Elimination of the Pole Problem
308(2)
6.4.3 Gaussian Quadrature and the Transform Method
310(5)
6.4.4 Nonlinear Shallow-Water Equations
315(5)
6.5 The Finite-Element Method
320(19)
6.5.1 Galerkin Approximation with Chapeau Functions
322(2)
6.5.2 Petrov-Galerkin and Taylor-Galerkin Methods
324(3)
6.5.3 Quadratic Expansion Functions
327(9)
6.5.4 Two-Dimensional Expansion Functions
336(3)
6.6 The Discontinuous Galerkin Method
339(11)
6.6.1 Modal Implementation
341(2)
6.6.2 Nodal Implementation
343(3)
6.6.3 An Example: Advection
346(4)
Problems
350(7)
7 Semi-Lagrangian Methods
357(36)
7.1 The Scalar Advection Equation
358(11)
7.1.1 Constant Velocity
359(6)
7.1.2 Variable Velocity
365(4)
7.2 Finite-Volume Integrations with Large Time Steps
369(3)
7.3 Forcing in the Lagrangian Frame
372(5)
7.4 Systems of Equations
377(6)
7.4.1 Comparison with the Method of Characteristics
377(2)
7.4.2 Semi-implicit Semi-Lagrangian Schemes
379(4)
7.5 Alternative Trajectories
383(5)
7.5.1 A Noninterpolating Leapfrog Scheme
384(2)
7.5.2 Interpolation via Parameterized Advection
386(2)
7.6 Eulerian or Semi-Lagrangian?
388(2)
Problems
390(3)
8 Physically Insignificant Fast Waves
393(60)
8.1 The Projection Method
394(6)
8.1.1 Forward-in-Time Implementation
395(2)
8.1.2 Leapfrog Implementation
397(1)
8.1.3 Solving the Poisson Equation for Pressure
398(2)
8.2 The Semi-implicit Method
400(16)
8.2.1 Large Time Steps and Poor Accuracy
401(2)
8.2.2 A Prototype Problem
403(2)
8.2.3 Semi-implicit Solution of the Shallow-Water Equations
405(3)
8.2.4 Semi-implicit Solution of the Euler Equations
408(6)
8.2.5 Numerical Implementation
414(2)
8.3 Fractional-Step Methods
416(13)
8.3.1 Completely Split Operators
417(5)
8.3.2 Partially Split Operators
422(7)
8.4 Summary of Schemes for Nonhydrostatic Models
429(2)
8.5 The Quasi-Hydrostatic Approximation
431(2)
8.6 Primitive Equation Models
433(15)
8.6.1 Pressure and σ Coordinates
434(4)
8.6.2 Spectral Representation of the Horizontal Structure
438(2)
8.6.3 Vertical Differencing
440(2)
8.6.4 Energy Conservation
442(4)
8.6.5 Semi-implicit Time Differencing
446(2)
Problems
448(5)
9 Nonreflecting Boundary Conditions
453(44)
9.1 One-Dimensional Flow
455(15)
9.1.1 Well-Posed Initial-Boundary-Value Problems
455(2)
9.1.2 The Radiation Condition
457(2)
9.1.3 Time-Dependent Boundary Data
459(1)
9.1.4 Reflections at an Artificial Boundary: The Continuous Case
460(1)
9.1.5 Reflections at an Artificial Boundary: The Discretized Case
461(5)
9.1.6 Stability in the Presence of Boundaries
466(4)
9.2 Two-Dimensional Shallow-Water Flow
470(7)
9.2.1 One-Way Wave Equations
471(4)
9.2.2 Numerical Implementation
475(2)
9.3 Two-Dimensional Stratified Flow
477(11)
9.3.1 Lateral Boundary Conditions
477(1)
9.3.2 Upper Boundary Conditions
477(9)
9.3.3 Numerical Implementation of the Radiation Upper Boundary Condition
486(2)
9.4 Wave-Absorbing Layers
488(4)
9.5 Summary
492(1)
Problems
493(4)
A Numerical Miscellany
497(4)
A.1 Finite-Difference Operator Notation
497(1)
A.2 Tridiagonal Solvers
498(3)
A.2.1 Code for a Tridiagonal Solver
498(1)
A.2.2 Code for a Periodic Tridiagonal Solver
499(2)
References 501(10)
Index 511
Dale Durran is a professor in the Atmospheric Sciences Department at the University of Washington in Seattle, WA. His research interests include Mesoscale Dynamic, Meteorology, Numerical Methods, Mountain Meteorology, Atmospheric Waves.