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Introduction to the Numerical Analysis of Incompressible Viscous Flows [Pehme köide]

3.00/5 (6 hinnangut Goodreads-ist)
(University of Pittsburgh)
  • Formaat: Paperback / softback, 232 pages, kõrgus x laius x paksus: 229x152x11 mm, kaal: 437 g, ill
  • Sari: Computational Science & Engineering
  • Ilmumisaeg: 30-Aug-2008
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716578
  • ISBN-13: 9780898716573
Teised raamatud teemal:
Introduction to the Numerical Analysis of Incompressible Viscous FlowsSuurem pilt
  • Formaat: Paperback / softback, 232 pages, kõrgus x laius x paksus: 229x152x11 mm, kaal: 437 g, ill
  • Sari: Computational Science & Engineering
  • Ilmumisaeg: 30-Aug-2008
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716578
  • ISBN-13: 9780898716573
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780898716573.html
Märksõnad:
Layton (mathematics, U. of Pittsburgh) assumes readers have minimal background in the numerical analysis of finite element computational fluid dynamics as he covers finite element methods and the derivation, behavior, analysis, and numerical analysis of Navier-Stokes equations. He also describes surveillance and turbulence models used in simulations. With chapters alternating between theory and numerical analysis, including numerous exercises, he gives the mathematical foundations of energy in stress (including Hilbert space), approximating scalars, including the Galerkin-Finite element method, and vector and tensor analysis. He then details study fluid flow phenomena, including approximating vector functions, the equations of fluid motion, the steady Navier-Stokes equations, and approximating city flows. Under the general subject of time dependent fluid flow phenomenon, he describes the time-dependent Navier-Stokes equations, approximating time-dependent flows, and models of turbulent flow. A very assessing appendix describes nomenclature, and Layton provides a comprehensive bibliography. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

A unified treatment of fluid mechanics, analysis and numerical analysis appropriate for first year graduate students.

Muu info

A unified treatment of fluid mechanics, analysis and numerical analysis appropriate for first year graduate students.
List of Figures
ix
Foreword xi
Preface xiii
I Mathematical Foundations
1(50)
Mathematical Preliminaries: Energy and Stress
3(14)
Finite Kinetic Energy: The Hilbert Space L2 (Ω)
3(5)
Other norms
7(1)
Finite Stress: The Hilbert Space X := H10 (Ω)
8(4)
Weak derivatives and some useful inequalities
10(2)
Some Snapshots in the History of the Equations of Fluid Motion
12(3)
Remarks on
Chapter 1
15(1)
Exercises
15(2)
Approximating Scalars
17(20)
Introduction to Finite Element Spaces
17(9)
An Elliptic Boundary Value Problem
26(4)
The Galerkin-Finite Element Method
30(3)
Remarks on
Chapter 2
33(1)
Exercises
34(3)
Vector and Tensor Analysis
37(14)
Scalars, Vectors, and Tensors
37(2)
Vector and Tensor Calculus
39(4)
Conservation Laws
43(5)
Remarks on
Chapter 3
48(1)
Exercises
49(2)
II Steady Fluid Flow Phenomena
51(86)
Approximating Vector Functions
53(18)
Introduction to Mixed Methods for Creeping Flow
53(3)
Variational Formulation of the Stokes Problem
56(3)
The Galerkin Approximation
59(4)
More About the Discrete Inf-Sup Condition
63(3)
Other div-stable elements
66(1)
Remarks on
Chapter 4
66(2)
Exercises
68(3)
The Equations of Fluid Motion
71(28)
Conservation of Mass and Momentum
71(3)
Stress and Strain in a Newtonian Fluid
74(4)
More about internal forces
75(1)
More about V
76(2)
Boundary Conditions
78(5)
The Reynolds Number
83(4)
Boundary Layers
87(4)
An Example of Fluid Motion: The Taylor Experiment
91(1)
Remarks on
Chapter 5
92(3)
Exercises
95(4)
The Steady Navier-Stokes Equations
99(22)
The Steady Navier-Stokes Equations
99(7)
Uniqueness for Small Data
106(4)
The Oseen problem
108(2)
Existence of Steady Solutions
110(4)
The Structure of Steady Solutions
114(3)
Remarks on
Chapter 6
117(1)
Exercises
117(4)
Approximating Steady Flows
121(16)
Formulation and Stability of the Approximation
121(3)
A Simple Example
124(1)
Errors in Approximations of Steady Flows
125(6)
More on the Global Uniqueness Conditions
131(1)
Remarks on
Chapter 7
132(1)
Exercises
133(4)
III Time-Dependent Fluid Flow Phenomena
137(60)
The Time-Dependent Navier-Stokes Equations
139(12)
Introduction
139(2)
Weak Solution of the NSE
141(4)
Kinetic Energy and Energy Dissipation
145(2)
Remarks on
Chapter 8
147(1)
Exercises
148(3)
Approximating Time-Dependent Flows
151(28)
Introduction
151(3)
Stability and Convergence of the Semidiscrete Approximations
154(4)
Rates of Convergence
158(3)
Time-Stepping Schemes
161(4)
Convergence Analysis of the Trapezoid Rule
165(10)
Notation for the discrete time method
165(3)
Error analysis of the trapezoid rule
168(7)
Remarks on
Chapter 9
175(1)
Exercises
176(3)
Models of Turbulent Flow
179(18)
Introduction to Turbulence
179(2)
The K41 Theory of Homogeneous, Isotropic Turbulence
181(5)
Fourier series
182(1)
The inertial range
183(3)
Models in Large Eddy Simulation
186(4)
A first choice of vT
189(1)
The Smagorinsky Model for vT
190(2)
Near Wall Models: Boundary Conditions for the Large Eddies
192(2)
Remarks on
Chapter 10
194(1)
Exercises
195(2)
Appendix Nomenclature
197(6)
Vectors and Tensors
197(1)
Fluid Variables
197(1)
Basic Function Spaces and Norms
198(1)
Other norms
198(1)
Velocity and Pressure Spaces and Norms
199(1)
Finite Element Notation
200(1)
Turbulence
200(3)
Bibliography 203(8)
Index 211
William Layton is a Professor of Mathematics at the University of Pittsburgh. He is author of numerous papers in computational fluid dynamics and is currently interested in turbulence modelling and simulation.