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Finite Element and Finite Volume Methods for Heat Transfer and Fluid Dynamics [Kõva köide]

4.50/5 (4 hinnangut Goodreads-ist)
(Texas A & M University), (Lawrence Livermore National Laboratory, California), (Texas A & M University)
  • Formaat: Hardback, 402 pages, kõrgus x laius x paksus: 250x175x22 mm, kaal: 870 g, Worked examples or Exercises
  • Ilmumisaeg: 27-Oct-2022
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1009275488
  • ISBN-13: 9781009275484
Teised raamatud teemal:
Finite Element and Finite Volume Methods for Heat Transfer and Fluid DynamicsSuurem pilt
  • Formaat: Hardback, 402 pages, kõrgus x laius x paksus: 250x175x22 mm, kaal: 870 g, Worked examples or Exercises
  • Ilmumisaeg: 27-Oct-2022
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1009275488
  • ISBN-13: 9781009275484
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781009275484.html
Märksõnad:
Introduces the two most common numerical methods for heat transfer and fluid dynamics equations, using clear and accessible language. This unique approach covers all necessary mathematical preliminaries at the beginning of the book for the reader to sail smoothly through the chapters. Students will work step-by-step through the most common benchmark heat transfer and fluid dynamics problems, firmly grounding themselves in how the governing equations are discretized, how boundary conditions are imposed, and how the resulting algebraic equations are solved. Providing a detailed discussion of the discretization steps and time approximations, and clearly presenting concepts of explicit and implicit formulations, this graduate textbook has everything an instructor needs to prepare students for their exams and future careers. Each illustrative example shows students how to draw comparisons between the results obtained using the two numerical methods, and at the end of each chapter they can test and extend their understanding by working through the problems provided. A solutions manual is also available for instructors.

A unified and accessible introduction for graduate courses in computational fluid dynamics and heat transfer. This unique approach covers all necessary mathematical preliminaries before walking the student through the most common heat transfer and fluid dynamics problems, then testing their understanding further with ample end-of-chapter problems.

Arvustused

'I am delighted to recommend this textbook to beginners and early career researchers wanting to work in computational heat and fluid flow problems. This book is a useful tool for teaching postgraduate and senior undergraduate courses and will be an excellent addition to the bookshelves of senior researchers.' Perumal Nithiarasu, Swansea University

Muu info

A unified and accessible introduction for graduate courses in computational fluid dynamics and heat transfer.
Preface xi
Symbols xv
Part I Preliminaries
1(90)
1 Mathematical Preliminaries
3(40)
1.1 Introduction
3(1)
1.2 Mathematical Models
4(15)
1.2.1 Preliminary Comments
4(1)
1.2.2 Types of Differential Equations
5(3)
1.2.3 Examples of Mathematical Models
8(3)
1.2.4 Numerical Solution of First-Order Ordinary Differential Equations
11(6)
1.2.5 Partial Differential Equations and their Classification
17(2)
1.3 Numerical Methods
19(11)
1.3.1 Introduction
19(1)
1.3.2 The Finite Difference Method
20(3)
1.3.3 The Finite Volume Method
23(3)
1.3.4 The Finite Element Method
26(4)
1.4 Errors and Convergence
30(6)
1.4.1 Types of Errors
30(1)
1.4.2 Numerical Convergence
31(2)
1.4.3 Order of Accuracy and Grid Convergence Index
33(3)
1.5 Veracity of Numerical Solutions
36(4)
1.5.1 Verification and Validation
36(1)
1.5.2 Manufactured Solutions for Verification
37(3)
1.6 Present Study
40(3)
Problems
41(2)
2 Equations of Heat Transfer and Fluid Mechanics
43(20)
2.1 Introduction
43(1)
2.2 Elements of Vectors and Tensors
44(6)
2.2.1 Introduction
44(1)
2.2.2 Coordinate Systems and Summation Convention
45(2)
2.2.3 Calculus of Vectors and Tensors
47(3)
2.3 Governing Equations of a Continuous Medium
50(8)
2.3.1 Descriptions of Motion
50(1)
2.3.2 Material Time Derivative
50(2)
2.3.3 Velocity Gradient Tensor
52(1)
2.3.4 Conservation of Mass
53(1)
2.3.5 Reynolds Transport Theorem
54(1)
2.3.6 Conservation of Momenta
54(2)
2.3.7 Conservation of Energy
56(1)
2.3.8 Equation of State
56(1)
2.3.9 Constitutive Equations
57(1)
2.4 Summary
58(5)
Problems
60(3)
3 Solution Methods for Algebraic Equations
63(28)
3.1 Introduction
63(1)
3.2 Linearization of Nonlinear Equations
63(10)
3.2.1 Introduction
63(2)
3.2.2 The Picard Iteration Method
65(3)
3.2.3 The Newton Iteration Method
68(5)
3.3 Solution of Linear Equations
73(18)
3.3.1 Introduction
73(3)
3.3.2 Direct Methods
76(4)
3.3.3 Iterative Methods
80(5)
3.3.4 Iterative Methods for the Finite Volume Method
85(4)
Problems
89(2)
Part II The Finite Element Method
91(124)
4 The Finite Element Method: Steady-State Heat Transfer
93(60)
4.1 The Basic Idea
93(2)
4.2 One-Dimensional Problems
95(24)
4.2.1 Model Differential Equation
95(1)
4.2.2 Division of the Whole into Parts
95(1)
4.2.3 Approximation over the Element
95(2)
4.2.4 Derivation of the Weak Form
97(1)
4.2.5 Approximation Functions
98(3)
4.2.6 Finite Element Model
101(3)
4.2.7 Axisymmetric Problems
104(1)
4.2.8 Numerical Examples
105(14)
4.3 Two-Dimensional Problems
119(26)
4.3.1 Model Differential Equation
119(2)
4.3.2 Finite Element Approximation
121(1)
4.3.3 Weak Form
121(2)
4.3.4 Finite Element Model
123(1)
4.3.5 Axisymmetric Problems
124(2)
4.3.6 Approximation Functions and Evaluation of Coefficients for Linear Elements
126(5)
4.3.7 Higher-Order Finite Elements
131(3)
4.3.8 Assembly of Elements
134(3)
4.3.9 Numerical Examples
137(8)
4.4 Summary
145(8)
Problems
145(8)
5 The Finite Element Method: Unsteady Heat Transfer
153(26)
5.1 Introduction
153(1)
5.2 One-Dimensional Problems
153(8)
5.2.1 Model Equation
153(1)
5.2.2 Steps in Finite Element Model Development
154(1)
5.2.3 Weak Form
155(1)
5.2.4 Semidiscrete Finite Element Model
155(1)
5.2.5 Time Approximations
156(3)
5.2.6 Fully Discretized Finite Element Equations
159(2)
5.3 Two-Dimensional Problems
161(2)
5.3.1 Model Equation
161(1)
5.3.2 Weak Form
162(1)
5.3.3 Semidiscrete Finite Element Model
162(1)
5.3.4 Fully Discretized Model
163(1)
5.4 Explicit and Implicit Formulations and Mass Lumping
163(2)
5.5 Numerical Examples
165(11)
5.5.1 One-Dimensional Problems
165(7)
5.5.2 Two-Dimensional Example
172(4)
5.6 Summary
176(3)
Problems
177(2)
6 Finite Element Analysis of Viscous Incompressible Flows
179(36)
6.1 Governing Equations
179(1)
6.2 Velocity-Pressure Finite Element Model
180(5)
6.2.1 Weak-Form Development
180(1)
6.2.2 Semidiscretized Finite Element Model
181(3)
6.2.3 Fully Discretized Equations
184(1)
6.3 Penalty Finite Element Model
185(15)
6.3.1 Weak Forms
185(2)
6.3.2 Finite Element Model
187(2)
6.3.3 Postcomputation
189(1)
6.3.4 Numerical Examples
190(10)
6.4 Nonlinear Penalty Finite Element Model
200(11)
6.4.1 Weak Forms and the Finite Element Model
200(1)
6.4.2 Tangent Matrix for the Penalty Finite Element Model
201(2)
6.4.3 Numerical Examples
203(8)
6.5 Summary
211(4)
Problems
211(4)
Part III The Finite Volume Method
215(158)
7 The Finite Volume Method: Diffusion Problems
217(52)
7.1 Introduction
217(1)
7.2 One-Dimensional Problems
217(24)
7.2.1 Governing Equations
217(1)
7.2.2 Grid Generation
218(1)
7.2.3 Development of Discretization Equations
219(5)
7.2.4 Neumann Boundary Condition: Prescribed Flux
224(1)
7.2.5 Mixed Boundary Condition: Convective Heat Flux
225(2)
7.2.6 Interface Properties
227(1)
7.2.7 Numerical Examples
228(8)
7.2.8 Axisymmetric Problems
236(5)
7.3 Two-Dimensional Diffusion
241(14)
7.3.1 Model Equation
241(1)
7.3.2 Grid Generation
242(1)
7.3.3 Discretization of the Model Equation
243(2)
7.3.4 Discrete Equations for Control Volumes and Nodes on the Boundary
245(10)
7.4 Unsteady Problems
255(10)
7.4.1 One-Dimensional Problems
255(3)
7.4.2 Two-Dimensional Problems
258(4)
7.4.3 Numerical Examples
262(3)
7.5 Summary
265(4)
Problems
267(2)
8 The Finite Volume Method: Advection-Diffusion Problems
269(26)
8.1 Introduction
269(1)
8.2 Discretization of the Advection-Diffusion Flux
270(13)
8.2.1 General Discussion
270(1)
8.2.2 A General Two-Node Formulation
271(1)
8.2.3 Central Difference Approximation
272(1)
8.2.4 Upwind Scheme
273(2)
8.2.5 Exponential Scheme
275(2)
8.2.6 Hybrid Scheme
277(1)
8.2.7 Power-Law Scheme
278(1)
8.2.8 A Three-Node Formulation: QUICK Scheme
279(3)
8.2.9 A Numerical Example
282(1)
8.3 Numerical Diffusion
283(4)
8.4 Steady Two-Dimensional Problems
287(5)
8.5 Summary
292(3)
9 Finite Volume Methods for Viscous Incompressible Flows
295(52)
9.1 Governing Equations
295(2)
9.2 The Velocity--Pressure Formulation
297(18)
9.2.1 Introduction
297(3)
9.2.2 Discretized Equations
300(6)
9.2.3 Residuals and Declaring Convergence
306(1)
9.2.4 Boundary Conditions
307(8)
9.2.5 Treatment of Source Terms
315(1)
9.3 Collocated-Grid Method
315(5)
9.3.1 General Introduction
315(2)
9.3.2 Calculation of Control Volume Face Velocities
317(1)
9.3.3 Correction of Velocity and Pressure Fields by Enforcing the Incompressibility Condition
318(2)
9.4 Numerical Examples
320(17)
9.5 Treatment of Solid Obstacles in Flow Paths
337(4)
9.5.1 Preliminary Comments
337(1)
9.5.2 Domain Decomposition Method
337(1)
9.5.3 High-Viscosity Method
338(1)
9.5.4 Dominant-Source-Term Method
338(3)
9.6 Vorticity-Stream Function Equations
341(4)
9.6.1 Governing Equations in Terms of Vorticity and Stream Function
341(2)
9.6.2 Poisson's Equation for Pressure
343(2)
9.7 Summary
345(2)
Problems
345(2)
10 Advanced Topics
347(26)
10.1 Introduction
347(2)
10.1.1 General Remarks
347(1)
10.1.2 Periodic and Buoyancy-Driven Flows
347(1)
10.1.3 Non-Newtonian Fluids
348(1)
10.1.4 Solution Methods
348(1)
10.2 Periodically Fully Developed Flows
349(7)
10.2.1 Introduction
349(1)
10.2.2 Governing Equations
350(2)
10.2.3 Thermally Fully Developed Flows
352(1)
10.2.4 Uniform Heat Flux Condition
352(1)
10.2.5 Uniform Wall Temperature Condition
353(1)
10.2.6 Cyclic Tri-Diagonal Matrix Algorithm
354(2)
10.3 Natural Convection
356(7)
10.3.1 Governing Equations
356(2)
10.3.2 Discretized Equations
358(5)
10.4 Multigrid Algorithms
363(8)
10.4.1 Preliminary Comments
363(2)
10.4.2 Coarse-Grid Equations
365(2)
10.4.3 Grid-Transfer Operators
367(2)
10.4.4 Multigrid Cycles
369(2)
10.5 Summary
371(2)
References 373(8)
Index 381
Professor J. N. Reddy is a Distinguished Professor, Regents Professor, and holder of the O'Donnell Foundation Chair IV in the Department of Mechanical Engineering at Texas A & M University. As the author of twenty-four textbooks and several hundred journal papers, and a highly-cited researcher, Professor Reddy is internationally-recognized for his research and education in applied and computational mechanics. The finite element formulations and models he developed have been implemented into commercial software like ABAQUS, NISA, and HyperXtrude (Altair). He has won many major awards from professional societies (e.g., The S.P. Timoshenko Medal from ASME, the von Karman Medal from ASCE, the von Neumann Medal from USACM, and the Gauss-Newton Medal from IACM), and he is a fellow of AAM, AIAA, ASC, ASCE, ASI, ASME, IACM, and USACM. He is a member of the US National Academy of Engineering and Foreign Fellow of the Brazilian National Academy of Engineering, the Canadian Academy of Engineering, the Chinese Academy of Engineering, the Indian National Academy of Engineering, the Royal Academy of Engineering of Spain, the European Academy of Sciences, and the European Academy of Sciences and Arts. Professor N. K. Anand is a Regents Professor and James J. Cain '51 Professor III of Mechanical Engineering at Texas A&M University. He teaches and researches in the broad area of thermal sciences. Professor Anand is a recipient of the Association Former Students Distinguished Achievement Award in Teaching at the college level. He is an ASME Fellow and was awarded the 2020 ASME Harry Potter Gold Medal for 'outstanding contributions as a teacher of thermodynamics and related topics, and as a researcher who has advanced the state-of-the-art design of alternate refrigerant condensers, cooling strategies for electronic packages and aerosol transport lines'. He developed and continues to teach a course in the application of finite volume techniques to heat transfer and fluid flow for three decades. Dr. Pratanu Roy is a Staff Scientist at Lawrence Livermore National Laboratory (LLNL), California. He obtained his Ph.D. in Mechanical Engineering from Texas A & M University in 2014. Dr. Roy conducts research in computational fluid dynamics (finite volume method, multigrid methods), high-performance computing for CFD, transport in Carbon Capture and Storage (CCS), and turbulence modelling. Dr. Roy is the recipient of the 2015 American Rock Mechanics Association (ARMA) best paper award. He has also received the 2020 LLNL Physical and Life Sciences Directorate award for spearheading a brand new mentoring program within the lab. In 2022, he was awarded National Nuclear Security Administration (NNSA) Defense Programs Awards of Excellence in recognition of his 'contributions developing and rapidly deploying the reaction sorption transport (ReSorT) moisture model.'