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Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow [Kõva köide]

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  • Formaat: Hardback, 300 pages, kõrgus x laius: 229x152 mm
  • Ilmumisaeg: 30-Nov-2014
  • Kirjastus: American Society of Mechanical Engineers,U.S.
  • ISBN-10: 0791860337
  • ISBN-13: 9780791860335
Teised raamatud teemal:
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid FlowSuurem pilt
  • Formaat: Hardback, 300 pages, kõrgus x laius: 229x152 mm
  • Ilmumisaeg: 30-Nov-2014
  • Kirjastus: American Society of Mechanical Engineers,U.S.
  • ISBN-10: 0791860337
  • ISBN-13: 9780791860335
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780791860335.html
Märksõnad:
When students once master the concepts of the finite element method (and meshing), its not long before they begin to look at other numerical techniques and applications, especially the boundary element and meshless methods (since a mesh is not required). The expert authors of this book provide a simple explanation of these three powerful numerical schemes and show how they all fall under the umbrella of the more universal method of weighted residuals.

The book is structured in four sections. The first introductory section provides the method of weighted residuals development of finite differences, finite volume, finite element, boundary element, and meshless methods along with 1D examples of each method. The following three sections of the book present a more detailed development of the finite element method, then progress through the boundary element method, and end with meshless methods. Each section serves as a stand-alone description, but it is apparent how each conveniently leads to the other techniques. It is recommended that the reader begin with the finite element method, as this serves as the primary basis for defining the method of weighted residuals.
Preface ix
Overview xi
The Method of Weighted Residuals (MWR) xi
MWR Example Problem: FDM, FVM, FEM, BEM and MM xiv
Finite Difference Method (FDM) -- Collocation MWR with Local Polynomial Trial Functions xv
Finite Volume Method -- Subdomain MWR with Local Polynomial Trial Functions xviii
Finite Element Method -- Galerkin MWR with Local Polynomial Trial Functions xxi
Boundary Element Method -- Collocation MWR of Boundary Integral Equation xxv
Meshless Method -- Collocation MWR with Global Radial-Basis Function (RBF) Trial Functions xxviii
References xxxiii
Appendix A Derivation of the 1D Fundamental Solution for T" + T = --δ(x--xi) xxxii
Appendix B MATLAB xxxv
Appendix C MAPLE xlix
PART I THE FINITE ELEMENT METHOD
1(70)
Chapter 1 Introduction
3(2)
Chapter 2 Governing Equations
5(2)
2.1 Mass Conservation
5(1)
2.2 Navier-Stokes
5(1)
2.3 Energy Conservation
5(1)
2.4 Mass Transport
6(1)
2.5 Boundary Conditions
6(1)
Chapter 3 The Finite Element Method
7(20)
3.1 Error in Finite Element Approximation
8(1)
3.2 One-Dimensional Elements
8(2)
3.2.1 Linear Element
8(1)
3.2.2 Quadratic and Higher Order Elements
9(1)
3.3 Two-Dimensional Elements
10(7)
3.3.1 Triangular Elements
10(2)
3.3.2 Quadrilateral Elements
12(1)
3.3.3 Isoparametric Elements
13(4)
3.4 Three-Dimensional Elements
17(1)
3.5 Quadrature
18(2)
3.6 Reduced Integration
20(1)
3.7 Time Dependence
21(2)
3.7.1 The θ Method
21(1)
3.7.2 Mass Lumping
22(1)
3.8 Petrov-Galerkin Method
23(2)
3.9 Taylor-Galerkin Method
25(2)
Chapter 4 Mesh Generation
27(10)
4.1 Mesh Generation Guidelines
27(2)
4.2 Bandwidth
29(1)
4.3 Adaptation
30(7)
4.3.1 Mesh Regeneration
31(1)
4.3.2 Element Subdivision
32(1)
4.3.3 Adaptation Rules
33(1)
4.3.4 Mesh Adaptation Example
34(3)
Chapter 5 Fluid Flow Applications
37(24)
5.1 Constant-Density Flows
38(7)
5.1.1 Mixed Formulation
38(4)
5.1.2 Fractional Step Method
42(1)
5.1.3 Penalty Function Formulation
43(1)
5.1.4 Calculation of Pressure
44(1)
5.1.5 Open Boundaries
44(1)
5.2 Free Surface Flows
45(1)
5.3 Flows in Rotating Systems
46(1)
5.4 Isothermal Flow Past a Circular Cylinder
47(1)
5.5 Turbulent Flow
48(7)
5.5.1 Large Eddy Simulation (LES)
51(3)
5.5.2 Subgrid-Scale (SGS) Modeling
54(1)
5.6 Compressible Flow
55(6)
5.6.1 Supersonic Flow Impinging on a Cylinder
57(1)
5.6.2 Transonic Flow Through a Rectangular Nozzle
58(3)
Chapter 6 List of Commercial Codes
61(4)
Chapter 7 Conclusion
65(6)
References
66(5)
APPENDIX A
71(4)
Symbols
71(2)
Subscripts
73(1)
Superscripts
73(2)
APPENDIX B
75(6)
B.1 Matrix Equations and Solution Method
76(1)
B.2 Temporal Evolution of the Semi-Implicit Scheme
76(5)
B.2.1 Momentum
76(1)
B.2.2 Continuity
77(1)
B.2.3 Energy
78(1)
B.2.4 Turbulent Kinetic Energy and Specific Dissipation Rate (κ--ω)
78(1)
B.2.5 Matrix Formulation
79(1)
References
80(1)
PART II THE BOUNDARY ELEMENT METHOD
81(98)
Chapter 1 Introduction
83(2)
Chapter 2 BEM Fundamentals
85(24)
2.1 A Familiar Example: Green's Third Identity for Potential Problems
85(2)
2.2 The 2D Heat Conduction Problem
87(1)
2.3 Generating the Integral Equation: Weighting Function and Green's Second Identity
88(2)
2.4 Analytical Solution: Green's Function Method and the Auxiliary Problem
90(3)
2.5 Numerical Solution: The BEM and the Boundary Integral Equation
93(16)
Appendix A Derivation of the Green's Function for the 2D Problem in a Square
106(1)
Appendix B Derivation of the Green's Free Space (Fundamental) Solution to the Laplace Equation
107(2)
Chapter 3 Numerical Implementation of the BEM
109(20)
3.1 Two-Dimensional Boundary Elements
109(6)
3.2 Three-Dimensional Boundary Elements
115(4)
3.3 Adaptive Quadrature in 3D
119(2)
3.4 Numerical Solution of the BEM Equations
121(8)
Appendix A Conjugate Gradient and GMRES MATHCAD Pseudo-Codes
123(6)
Chapter 4 Steady Heat Conduction with Variable Heat Conductivity
129(10)
4.1 Nonlinear Thermal Conductivity
129(2)
4.2 Anisotropic Heat Conductivity
131(2)
4.3 Non-Homogenous Thermal Conductivity
133(6)
Chapter 5 Heat Conduction in Media with Energy Generation
139(10)
5.1 Special Form of Generation Leading to Contour Integrals
139(2)
5.2 Use of Particular Solutions
141(1)
5.3 The Dual Reciprocity Boundary Element Method
142(7)
Chapter 6 Applications of the BEM to Heat Transfer and Inverse Problems
149(24)
6.1 Axi-Symmetric Problems
149(2)
6.2 Heat Conduction in Thin Plates and Extended Surfaces
151(3)
6.3 Conjugate Heat Transfer
154(3)
6.4 Large-Scale Heat Transfer
157(5)
6.5 Non-Homogeneous Heat Conduction: Generalized BIE
162(4)
6.6 Inverse Problems Applications of the BEM
166(7)
Chapter 7 Conclusion
173(6)
References
173(6)
PART III THE MESHLESS METHOD
179
Chapter 1 Introduction and Background
181(2)
Chapter 2 Radial-Basis Function (RBF) Interpolation
183(4)
Chapter 3 The Localized Collocation Meshless Method (LCMM) Framework
187(6)
Chapter 4 The Moving Least-Squares (MLS) Smoothing Scheme
193(2)
Chapter 5 The Finite-Differencing Enhanced LCMM
195(4)
Chapter 6 Upwinding Schemes
199(8)
6.1 One-Dimensional LCMM Upwinding Test
200(3)
6.2 Two-Dimensional LCMM Upwinding Test for an Inclined Wave
203(2)
6.3 Two-Dimensional LCMM Upwinding Test for a Turning Wave
205(2)
Chapter 7 Automatic Point Distribution
207(2)
Chapter 8 Parallelization
209(2)
Chapter 9 Applications
211(54)
9.1 Incompressible Fluid Flow and Conjugate Heat Transfer
211(24)
9.1.1 Decaying Vortex Flow
215(3)
9.1.2 Lid-Driven Flow in a Square Cavity
218(2)
9.1.3 Air Jet into a Square Cavity
220(1)
9.1.4 Conjugate Heat Transfer between Parallel Plates
221(2)
9.1.5 Conjugate Heat Transfer Flow over a Rectangular Obstruction
223(2)
9.1.6 Conjugate Film-Cooling Heat Transfer
225(2)
9.1.7 Flow over a Cylinder
227(2)
9.1.8 Steady Blood Flow through a Femoral Bypass
229(4)
9.1.9 Pulsatile Blood Flow through a Femoral Bypass
233(2)
9.2 Natural Convection
235(4)
9.2.1 Buoyancy-Driven Flow in a Square Cavity
236(2)
9.2.2 Buoyancy-Driven Flow of Liquid Aluminum in a Rectangular Cavity
238(1)
9.3 Turbulent Fluid Flows
239(4)
9.3.1 Turbulent Flow over a Flat Plate
241(1)
9.3.2 Turbulent Flow over a Backward-Facing Step
242(1)
9.4 Compressible Fluid Flows
243(9)
9.4.1 Subsonic and Supersonic Smooth Expanding Diffuser
245(2)
9.4.2 Characteristic Nozzle Flow
247(1)
9.4.3 Subsonic and Supersonic Flow Past an Airfoil
248(3)
9.4.4 Turbulent Wake Flow
251(1)
9.5 Two-Phase Flow
252(2)
9.5.1 Dam-Breaking Test of Two-Phase Flow Formulation
253(1)
9.6 Solid Mechanics and Thermo-Elasticity
254(4)
9.6.1 Cantilever Beam under Constant Distributed Load
256(1)
9.6.2 Cortical Bone with Fixation Element under Bending Moment
256(2)
9.7 Porous Media Flow and Poro-Elasticity
258(7)
9.7.1 Rectangular Poro-Elastic Medium
260(1)
9.7.2 Air Flow Coupled with Poro-Elastic Balloon
260(2)
9.7.3 Coupled Tracheo-Bronchial Poro-Elastic Lung
262(1)
9.7.4 Groundwater Flow through a Poro-Elastic Levee
263(2)
Chapter 10 Conclusions
265
References
266