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E-raamat: The Intermediate Finite Element Method: Fluid Flow And Heat Transfer Applications

(Univ. of Nevada, Las Vegas University Of Nevada Las Vegas, Las Vegas, NV, USA)
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The Intermediate Finite Element Method: Fluid Flow And Heat Transfer ApplicationsSuurem pilt
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Intended as a follow to the authors' previous The Finite Element Method: Basic Concepts and Applications (1992), this text is an intermediate-level approach to the application of finite element methods in computer programs for the simulation of such processes in heat transfer and fluid dynamics as compressible or incompressible flows and coupled transport. After a summary of the basic methodology, such topics as nonlinear solution algorithms, time integrators, and grid generation are discussed. Finally several real flow and transport application examples are explored. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Arvustused

""The authors have produced a very readable textbook covering a broad range of topics. There is a wealth of examples illustrating many subjects in fluid mechanics and heat transfer and associated literature references for in-depth study. The book is a worthwhile addition to the library of students and practitoners of the finite element method. The book contains much useful information on the derivation and applicaton of the finite element method in fluid mechanics and heat transfer." J. Michael Barton Analytical Methods, Inc.AIAA JournalVol.38, No.3, March 2000."

Foreword xv(2)
Preface xvii(4)
Disclaimer xxi
1 INTRODUCTION
1(10)
1.1 Overview
1(2)
1.2 Short History of the Finite Element Method
3(2)
1.3 Finite Element Concept
5(1)
1.4 Present Text
6(1)
1.5 Closure
7(1)
References
8(3)
2 BASIC EQUATIONS OF FLUID DYNAMICS
11(10)
2.1 Overview
11(1)
2.2 Substantial Derivative
11(1)
2.3 Mass Conservation Equation
12(1)
2.4 Navier-Stokes Equations
13(2)
2.5 Equation of Energy Conservation
15(1)
2.6 Mass Transport
16(1)
2.7 Wave Equation
17(1)
2.8 Boundary Conditions
18(1)
2.9 Closure
19(1)
References
19(2)
3 FUNDAMENTAL CONCEPTS
21(88)
3.1 Overview
21(1)
3.2 Linear Heat Conduction
21(4)
3.3 Linear Operators and Linear Function Spaces
25(3)
3.4 Weighted Residuals Formulation
28(9)
3.5 Galerkin Method
37(9)
3.5.1 Galerkin Method in One Dimension
39(1)
3.5.1.1 Approximation 1
40(3)
3.5.1.2 Approximation 2
43(2)
3.5.2 Galerkin Method in Two Dimensions
45(1)
3.6 Finite Element Method in One Dimension
46(27)
3.6.1 Basic Piecewise Linear Spaces
46(8)
3.6.2 Heat Conduction in One Dimension
54(5)
3.6.3 Error in the Finite Element Approximation
59(3)
3.6.4 Boundary Fluxes
62(4)
3.6.5 Interelement Conditions
66(7)
3.7 Finite Element Method in Two Dimensions
73(22)
3.7.1 Basic Piecewise Bilinear Space
73(4)
3.7.2 Heat Conduction in Two Dimensions
77(10)
3.7.3 Error in Two-dimensional Approximation
87(1)
3.7.4 Interelement Conditions
88(7)
3.8 Finite Element Method in Three Dimensions
95(2)
3.8.1 Trilinear Element
95(1)
3.8.2 Heat Conduction in Three Dimensions
96(1)
3.9 Closure
97(1)
References
98(1)
Exercises
99(10)
4 HIGHER ORDER ELEMENTS
109(66)
4.1 Overview
109(1)
4.2 One-Dimensional Elements
110(6)
4.3 Two-Dimensional Elements
116(14)
4.3.1 Triangular Elements
117(7)
4.3.2 Rectangular Elements
124(3)
4.3.3 Error Bounds for Two-dimensional Elements
127(3)
4.4 Isoparametric Elements
130(17)
4.4.1 Difficulty 1
130(2)
4.4.2 Difficulty 2
132(15)
4.5 Blending Function Interpolation
147(16)
4.6 Three-Dimensional Elements
163(2)
4.7 Closure
165(1)
References
166(3)
Exercises
169(6)
5 NUMERICAL INTEGRATION
175(34)
5.1 Overview
175(1)
5.2 Quadrature Formulae
175(7)
5.2.1 Newton-Cotes Formulae
178(2)
5.2.2 Gaussian Quadrature
180(2)
5.3 Multiple Integrals
182(2)
5.4 Minimum and Optimal Order of Integration
184(10)
5.5 Reduced Integration, Evaluating Gradients
194(10)
5.5.1 Reduced and Selective Integration
194(2)
5.5.2 Evaluating Gradients
196(8)
5.6 Closure
204(1)
References
204(1)
Exercises
205(4)
6 NONLINEARITY
209(48)
6.1 Overview
209(1)
6.2 Basic Methods for Nonlinear Equations
210(15)
6.2.1 The Newton-Raphson Method
210(10)
6.2.2 Direct Iteration Methods
220(5)
6.3 Nonlinear Examples
225(24)
6.3.1 Heat Transfer with Temperature-Dependent Conductivity
225(3)
6.3.2 Stationary Navier-Stokes Equations
228(15)
6.3.3 Steady State Natural Convection
243(6)
6.4 Closure
249(1)
References
250(1)
Exercises
251(6)
7 TIME DEPENDENCE
257(56)
7.1 Overview
257(1)
7.2 Diffusion Equations
257(18)
7.2.1 Semidiscrete Galerkin Method
258(2)
7.2.2 The Theta Method
260(5)
7.2.3 Accuracy and Stability of the Theta Method
265(3)
7.2.4 Mass Lumping
268(7)
7.3 Runge-Kutta Methods
275(8)
7.4 Generalized Newmark Algorithms
283(22)
7.4.1 Newmark Method for Second-Order Hyperbolic Equations
284(13)
7.4.2 Generalized Newmark Method for Parabolic Equations
297(8)
7.5 Closure
305(1)
References
305(2)
Exercises
307(6)
8 STEADY STATE CONVECTIVE TRANSPORT
313(44)
8.1 Overview
313(1)
8.2 One-Dimensional Convection-Diffusion
314(7)
8.3 Petrov-Galerkin Method
321(10)
8.4 Petrov-Galerkin Method in Two Dimensions
331(9)
8.5 Petrov-Galerkin Method in Three Dimensions
340(2)
8.6 Nonlinear Equations
342(4)
8.7 Closure
346(1)
References
347(3)
Exercises
350(7)
9 TIME-DEPENDENT CONVECTION-DIFFUSION
357(46)
9.1 Overview
357(1)
9.2 Time-Dependent Convection
357(13)
9.2.1 Numerical Damping
361(7)
9.2.2 Phase Error
368(2)
9.3 Petrov-Galerkin Method for Time-Dependent Convection-Diffusion
370(14)
9.3.1 Quadratic in Time, Linear in Space Weights
371(6)
9.3.2 Stability Analysis
377(7)
9.4 Multidimensional Time-Dependent Convection-Diffusion
384(11)
9.5 Closure
395(1)
References
395(2)
Exercises
397(6)
10 VISCOUS INCOMPRESSIBLE FLUID FLOW
403(62)
10.1 Overview
403(1)
10.2 Basic Form of the Navier-Stokes Equations
404(5)
10.3 Constant-Density Flows in Two Dimensions
409(25)
10.3.1 Mixed Formulation
409(13)
10.3.2 Fractional Step Method
422(2)
10.3.3 Penalty Function Formulation
424(10)
10.4 Stratified Flows
434(18)
10.4.1 Finite Element Approximations
436(10)
10.4.2 Calculation of the Pressure
446(2)
10.4.3 Open Boundaries
448(4)
10.5 Free Surface Flows
452(4)
10.6 Closure
456(2)
References
458(3)
Exercises
461(4)
11 MESH GENERATION
465(70)
11.1 Overview
465(1)
11.2 Introduction
466(8)
11.2.1 Types of Meshes
466(4)
11.2.2 Popular Mesh Generation Schemes
470(1)
11.2.2.1 Manual Generation
470(1)
11.2.2.2 Semi-Automatic Generation
470(1)
11.2.2.3 Transport Mapping
471(1)
11.2.2.4 Explicit Solution of PDEs
471(1)
11.2.2.5 Overlapping and Deformation
472(1)
11.2.2.6 Advancing-front Method
473(1)
11.2.2.7 Combination
473(1)
11.3 Mesh Generation Techniques
474(21)
11.3.1 Structured Meshes
475(1)
11.3.1.1 One Dimension
475(1)
11.3.1.2 Two Dimensions
476(1)
11.3.1.3 Three Dimensions
476(1)
11.3.1.4 Boundary Fitted Coordinates
477(7)
11.3.2 Unstructured Meshes
484(1)
11.3.2.1 General Types of Elements
485(1)
11.3.2.2 One-dimensional Elements
485(1)
11.3.2.3 Two-dimensional Elements
486(2)
11.3.2.4 Three-dimensional Elements
488(2)
11.3.3 Mesh Generation Guidelines
490(5)
11.4 Bandwidth
495(13)
11.4.1 Nodal Renumbering Schemes
498(1)
11.4.1.1 Gibbs Method
499(1)
11.4.1.2 Groom's Method
500(1)
11.4.1.3 Lipton-Tajan Method
500(1)
11.4.1.4 Akhras and Dhatt Method
500(1)
11.4.1.5 Frontal Method
501(1)
11.4.1.6 Element Colorization Method
501(1)
11.4.1.7 Nested Dissection Method
501(1)
11.4.2 Simple Bandwidth Reduction Algorithm
501(4)
11.4.3 Delaunay Triangulation
505(3)
11.5 Adaptation
508(19)
11.5.1 Types of Adaptation
508(3)
11.5.2 Error Estimates and Adaptation Criteria
511(6)
11.5.3 Simple h-adaptive Technique
517(1)
11.5.3.1 Mesh Regeneration
517(3)
11.5.3.2 Element Subdivision
520(1)
11.5.3.3 Adaptation Parameters
521(3)
11.5.3.4 Adaptation Rules
524(1)
11.5.4 Mesh Adaptation Example
525(2)
11.6 Closure
527(2)
References
529(4)
Exercises
533(2)
12 FURTHER APPLICATIONS
535(36)
12.1 Overview
535(1)
12.2 Time-Dependent Flows and Flows in Rotating Systems
535(12)
12.2.1 Isothermal Flow Past a Circular Cylinder
540(2)
12.2.2 Natural Convection in a Horizontal Circular Cylinder
542(3)
12.2.3 Lubricant Flow in a Microgap
545(2)
12.3 Turbulent Flow
547(5)
12.4 Compressible Flow
552(12)
12.4.1 Supersonic Flow Impinging on a Cylinder
558(2)
12.4.2 Chemically Reacting Supersonic Flow
560(4)
12.5 Three-dimensional Flow
564(4)
12.5.1 Natural Convection Within a Sphere
564(2)
12.5.2 Transonic Flow Through a Rectangular Nozzle
566(2)
12.6 Closure
568(1)
References
568(3)
APPENDIX A: LINEAR OPERATIONS 571(6)
A.1 Linear Vector Spaces 571(4)
A.2 Linear Operators 575(2)
APPENDIX B: UNITS 577(2)
APPENDIX C: NOMENCLATURE 579(6)
INDEX 585
Juan C. Heinrich, Darrell W. Pepper
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