Computational Turbulent Incompressible Flow

Applied Mathematics: Body and Soul 4

By: Johan Hoffman, Claes Johnson

Write A Review

Hardcover | 5 January 2007

At a Glance

Hardcover
420 Pages

Dimensions(cm)
23.5 x 15.88 x 1.91

Hardcover

$84.99

or 4 interest-free payments of $21.25 with

Ships in 5 to 7 business days

Applied Mathematics: Body&Soul is a mathematics education reform p- gram including a series of books, together with associated educational ma- rial and open source software freely available from the project web page at www.bodysoulmath.org. Body&Soul re?ects the revolutionary new possibilities of mathematical modeling opened by the modern computer in the form of Computational C- culus (CC), which is now changing the paradigm of mathematical modeling in science and technology with new methods, questions and answers, as a modern form of the classical calculus of Leibniz and Newton. The Body&Soul series of books presents CC in a synthesis of com- tational mathematics (Body) and analytical mathematics (Soul) including applications. Volumes 1-3 [36] give a modern version of calculus and linear algebra including computation starting at a basic undergraduate level, and subsequent volumes on a graduate level cover di?erent areas of applications with focus on computational methods: - Volume 4: Computational Turbulent Incompressible Flow. - Volume 5: Computational Thermodynamics. - Volume 6: Computational Dynamical Systems. The present book is Volume 4, with Volumes 5 and 6 to appear in 2007 and further volumes on solid mechanics and electro-magnetics being planned. A gentle introduction to the Body&Soul series is given in [63].

Industry Reviews

From the reviews:

"This book considers the numerical simulation of incompressible turbulent flows which are modeled by the Euler equations or the Navier-Stokes equations. ... Throughout the book, a lot of numerical examples are presented. ... they might be used in courses to illustrate the features of turbulent flows for students." (John Volker, Mathematical Reviews, Issue 2008 d)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Fluids Science Physics Classical Mathematics Fluid Mechanics Mathematics Applied Mathematics Chemistry

Calculus & Mathematical Analysis Numerical Analysis Mechanical Engineering Technology in General Maths for Engineers

Overview
Main Objective	p. 3
Computational Turbulent Incompressible Flow	p. 3
Mysteries and Secrets	p. 29
Mysteries	p. 29
Secrets	p. 30
Turbulent Flow and History of Aviation	p. 33
Leonardo da Vinci, Newton and d'Alembert	p. 33
Cayley and Lilienthal	p. 34
Kutta, Zhukovsky and the Wright Brothers	p. 34
The Euler Equations	p. 39
Foundation of Fluid Dynamics	p. 39
Derivation of the Euler Equations	p. 40
The Euler Equations as a Continuum Model	p. 41
Incompressible Flow	p. 42
The Incompressible Euler and Navier-Stokes Equations	p. 43
The Incompressible Euler Equations	p. 43
The Incompressible Navier-Stokes Equations	p. 44
What is Viscosity?	p. 44
What is Heat Conductivity?	p. 46
Friction Boundary Conditions	p. 46
Einstein's Ideal	p. 46
Euler and NS as Dynamical Systems	p. 47
Triumph and Failure of Mathematics	p. 49
Triumph: Celestial Mechanics	p. 49
Failure: Potential Flow	p. 50
Laminar and Turbulent Flow	p. 51
Reynolds	p. 51
Applications and Reynolds Numbers	p. 53
Computational Turbulence	p. 57
Are Turbulent Flows Computable?	p. 57
Typical Outputs: Drag and Lift	p. 58
What about Boundary Layers?	p. 59
Approximate Weak Solutions: G2	p. 59
G2 Error Control and Stability	p. 60
What about Mathematics of Euler and NS?	p. 60
When is a Flow Turbulent?	p. 61
G2 vs Physics	p. 61
Computability and Predictability	p. 62
A First Study of Stability	p. 65
The Linearized Euler Equations	p. 65
Flow in a Corner or at Separation	p. 66
Couette Flow	p. 69
Resolution of Sommerfeld's Mystery	p. 70
Reflections on Stability and Perspectives	p. 70
d'Alembert's Mystery and Bernoulli's Law	p. 73
Introduction	p. 73
Bernoulli, Euler, Ideal Fluids and Potential Solutions	p. 74
d'Alembert's Mystery	p. 74
A Vector Calculus Identity	p. 75
Bernoulli's Law	p. 75
Potential Flow around a Circular Cylinder	p. 76
Zero Drag/Lift of Potential Flow	p. 76
Ideal Fluids and Vorticity	p. 78
d'Alembert's Computation of Zero Drag/Lift	p. 78
A Reformulation of the Momentum Equation	p. 79
Prandtl's Resolution of d'Alembert's Mystery	p. 81
Quotation from a Standard Source	p. 81
Quotation from Prandtl's 1904 report	p. 82
Discussion of Prandtl's Resolution	p. 83
New Resolution of d'Alembert's Mystery	p. 87
Introduction	p. 87
Drag of a Circular Cylinder	p. 87
The Role of the Boundary Layer	p. 92
Analysis of Instability of the Potential Solution	p. 92
Sum up of the New Resolution	p. 94
Mathematics of Turbulence
Turbulence and Chaos	p. 97
Introduction	p. 97
Weather as Deterministic Chaos	p. 97
Predicting the Temperature in Malilla	p. 99
Chaotic Dynamical System	p. 99
The Harmonic Oscillator as a Chaotic System	p. 101
Randomness and Foundations of Probability	p. 102
NS Chaotic rather than Random	p. 106
Observability vs Computability	p. 107
Lorenz System	p. 107
Lorenz, Newton and Free Will	p. 109
Algorithmic Information Theory	p. 110
Statistical Mechanics and Roulette	p. 111
A $1 Million Prize Problem	p. 113
The Clay Institute Impossible $1 Million Prize	p. 113
Towards a Possible Formulation	p. 114
Well-Posedness According to Hadamard	p. 115
[Element]-Weak Solutions	p. 116
Existence of [Element]-Weak Solutions by Regularization	p. 118
Output Sensitivity and the Dual Problem	p. 119
Reformulation of the Prize Problem	p. 120
The Standard Approach to Uniqueness	p. 122
Weak Uniqueness by Computation	p. 123
Introduction	p. 123
Uniqueness of c[subscript D] and c[subscript L]	p. 124
Non-Uniqueness of D(t)	p. 126
Stability of the Dual Solution with Respect to Time Sampling	p. 128
Conclusion	p. 128
Existence of [Element]-Weak Solutions by G2	p. 131
Introduction	p. 131
The Basic Energy Estimate for the Navier-Stokes Equations	p. 132
Existence by G2	p. 133
A Posteriori Output Error Estimate for G2	p. 135
Stability Aspects of Turbulence in Model Problems	p. 137
The Linearized Dual Problem	p. 137
Rotating Flow	p. 138
A Model Dual Problem for Rotating Flow	p. 140
A Model Dual Problem for Oscillating Reaction	p. 141
Model Dual Problem Summary	p. 142
The Dual Solution for Bluff Body Drag	p. 143
Duality for a Model Problem	p. 143
Ensemble Averages and Input Variance	p. 144
A Convection-Diffusion Model Problem	p. 147
Introduction	p. 147
Pointwise vs Mean Value Residuals	p. 147
Artificial Viscosity From Least Squares Stabilization	p. 149
G2 for Euler	p. 151
Introduction	p. 151
EG2 as a Model of the World	p. 153
Solution of the Euler Equations by G2	p. 153
Drag of a Square Cylinder	p. 154
Instability of the Potential Solution	p. 156
Temperature	p. 162
G2 as Dissipative Weak Solutions	p. 164
Comparison with Viscous Regularization	p. 164
Finite Limit of Turbulent Dissipation	p. 165
The 2nd Law of Thermodynamics	p. 165
A Global Form of the 2nd Law	p. 166
Understanding a Basic Fact	p. 167
Proof that EG2 is a Dissipative Weak Solution	p. 167
Summary of Mathematical Aspects	p. 169
Outputs of [Element]-weak Solutions	p. 169
Chaos and Turbulence	p. 170
Computational Turbulence	p. 171
Irreversibility	p. 171
Secrets
Secrets of Ball Sports	p. 175
Introduction	p. 175
Dimples of a Golf Ball: Drag Crisis	p. 175
Topspin in Tennis: Magnus Effect	p. 176
Roberto Carlos: Magnus Effect	p. 178
Pitching: Drag Crisis and Magnus Effect	p. 180
Secrets of Flight	p. 181
Generation of Lift	p. 181
Simulation of Take-off	p. 182
More on Generation of Drag	p. 188
A Critical View on Kutta-Zhukovsky	p. 188
The Challenge	p. 189
Secrets of Sailing	p. 191
The Sail	p. 191
The Keel	p. 192
The Challenge	p. 193
Secrets of Racing	p. 195
Downforce	p. 195
The Wheels	p. 196
Drag and Fuel Consumption	p. 197
Computational Method
Reynolds Stresses In and Out	p. 201
Introducing Reynolds Stresses	p. 201
Removing Reynolds Stresses	p. 202
Smagorinsky Viscosity In and Out	p. 203
Introducing Smagorinsky Viscosity	p. 203
Removing Smagorinsky Viscosity	p. 204
Friction Boundary Condition as Wall Model	p. 207
A Skin Friction Wall Model	p. 207
G2 for Navier-Stokes Equations	p. 209
Introduction	p. 209
Development of G2	p. 210
The Incompressible Navier-Stokes Equations	p. 211
G2 as Eulerian cG(p)dG(q)	p. 211
Neumann Boundary Conditions	p. 213
No Slip and Slip Boundary Conditions	p. 213
Outflow Boundary Conditions	p. 213
Shock Capturing	p. 213
Basic Energy Estimate for cG(p)dG(q)	p. 214
G2 as Eulerian cG(1)dG(0)	p. 214
Eulerian cG(1)cG(1)	p. 215
Basic Energy Estimate for cG(1)cG(1)	p. 216
Slip with Friction Boundary Conditions	p. 216
A Discrete Solver	p. 219
Fixed Point Iteration Using Multigrid/GMRES	p. 219
G2 as Adaptive DNS/LES	p. 221
An A Posteriori Error Estimate	p. 221
Proof of the A Posteriori Error Estimate	p. 223
Interpolation Error Estimates	p. 223
G2 as Adaptive DNS/LES	p. 225
Computation of Multiple Outputs	p. 226
Mesh Refinement	p. 227
Implementation of G2 with FEniCS	p. 229
The FEniCS Project	p. 229
Moving Meshes and ALE Methods	p. 231
Introduction	p. 231
G2 Formulation	p. 231
Free Boundary	p. 233
Laplacian Mesh Smoothing	p. 233
Mesh Smoothing by Local Optimization	p. 234
Object in a Box	p. 235
Sliding Mesh	p. 238
Flow Fundamentals
Bluff Body Flow	p. 245
Introduction	p. 245
Drag and Lift	p. 246
An Alternative Formula for Drag and Lift	p. 246
A Posteriori Error Estimation	p. 247
Surface Mounted Cube	p. 250
The drag coefficient c[subscript D]	p. 250
Dual solution and a posteriori error estimates	p. 253
Comparison with reference data	p. 253
Flow Past a Car	p. 254
Square Cylinder	p. 257
Computing mean drag: time vs. phase averages	p. 257
Dual solution and a posteriori error estimates	p. 261
Comparison with reference data	p. 263
Circular Cylinder	p. 264
Comparison with reference data	p. 265
Dual solution and a posteriori error estimates	p. 275
Sphere	p. 275
Comparison with reference data	p. 275
Dual solution and a posteriori error estimates	p. 276
Boundary Layers	p. 279
Introduction	p. 279
Flat Plate Laminar Boundary Layer	p. 280
Skin Friction for Laminar Boundary Layers	p. 280
Skin Friction for Turbulent Boundary Layers	p. 281
Computing Skin Friction by G2	p. 282
Summary	p. 283
Separation	p. 285
Introduction	p. 285
Simulation of Blood Flow	p. 285
Drag Reduction for a Square Cylinder	p. 286
Drag Crisis	p. 286
Drag Crisis for a Circular Cylinder	p. 290
EG2 and Turbulent Euler Solutions	p. 292
The Dual Problem for EG2	p. 293
EG2 for a Circular Cylinder	p. 295
The Magnus Effect	p. 296
Flow Past an Airfoil	p. 298
Flow Due to a Cylinder Rolling Along Ground	p. 298
Transition to Turbulence	p. 305
Modal and Non-Modal Schools	p. 305
Difficulties of Experimental Transition Studies	p. 306
Possibilities of Computational Transition	p. 307
The Challenge	p. 307
Modal and Non-Modal Perturbation Growth	p. 308
Different Perturbations and Threshold Levels	p. 308
Analytical Stability of the Linearized NS	p. 309
Worst Case Exponential Perturbation Growth	p. 310
Linear perturbation growth in shear flow	p. 311
Computational Transition in Shear Flows	p. 313
Couette Flow	p. 314
Linear Perturbation Growth	p. 314
Periodic Span-wise Boundary Conditions	p. 322
Random Force Perturbation	p. 323
Poiseuille Flow - Reynolds Experiment	p. 327
Taylor-Gortler Perturbations	p. 329
Unstable Jet Flow	p. 329
Test for Optimal Perturbations	p. 330
A Critical Review of Classical Theory	p. 334
Comparison with Bifurcation towards Stability	p. 337
An ODE-Model for Transition	p. 337
A Bifurcating ODE-Model	p. 340
Summary	p. 342
Loschmidt's Mystery
Thermodynamics	p. 347
Objective	p. 347
What is Thermodynamics?	p. 348
EG2 as a Model of Thermodynamics	p. 348
The Classical Laws of Thermodynamics	p. 349
What is the Role of the 2nd Law?	p. 350
Joule's 1845 Experiment	p. 351
The Experiment	p. 351
Compressible Euler in 1d	p. 357
The Compressible Euler Equations in 1d	p. 357
Euler is Formally Reversible	p. 358
All Wrong	p. 358
The 2nd Law in Local Form	p. 359
The 2nd Law in Global Form	p. 360
Irreversibility by the 2nd Law	p. 361
Compression and Expansion	p. 361
Burgers' Equation	p. 363
A Model of the Euler Equations	p. 363
The Rankine-Hugoniot Condition	p. 364
Rarefaction wave	p. 364
Shock	p. 365
Weak solutions may be non-unique	p. 366
The 2nd Law for Burgers' Equation	p. 367
Destruction of Information	p. 367
Compressible Euler in 3d	p. 369
The 2nd Law in Local Form	p. 369
Incompressible Flow	p. 370
The 2nd Law in Global Form	p. 370
Irreversibility by the 2nd Law	p. 371
Trend Towards Equilibrium by the 2nd Law	p. 371
Comparison with Classical Entropy	p. 372
Heat Capacities and the Gas Constant	p. 372
EG2 for Compressible Flow	p. 375
G2 for the Compressible Euler Equations	p. 375
EG2 Satisfies the 2nd Law	p. 376
EG2 and the Classical Entropy	p. 376
Philosophy of EG2	p. 377
Dijkstra's Vision	p. 377
The Role of Least Squares Stabilization in G2	p. 378
Aspects of Irreversibility	p. 379
Imperfect Nature and Mathematics?	p. 381
A New Paradigm of Computation	p. 382
The Clay Prize Problem Again	p. 382
Does God Really Play Dice?	p. 383
Einstein and Modern Physics	p. 383
Boltzmann and Statistical Mechanics	p. 384
Summary	p. 386
References	p. 389
Index	p. 395
Table of Contents provided by Ingram. All Rights Reserved.

Computational Turbulent Incompressible Flow

Applied Mathematics: Body and Soul 4

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Maths for Engineers

Modern Engineering Mathematics

6th Edition

Bird's Higher Engineering Mathematics

9th Edition

Mathematics for Technicians

7th Edition

Engineering Mathematics

8th edition

Engineering Mathematics

5th edition

Sustainability and Reliability of Networks

Technology and Applications

Risk Analysis in Engineering and Economics

Fuzzy Sets and Triangular Norms

Aggregation in Decision-Aided Intelligent Systems

Dynamic Characteristics of Layered Structures

Mathematical Modelling and Numerical Simulations

Mathematical Methods for Physics and Engineering

A Comprehensive Guide

Advanced Engineering Mathematics, International Adaptation

ISE Numerical Methods for Engineers

8th edition

Control of Nonlinear Systems

Stability and Performance

Foundation Engineering Mathematics

Engineering Mathematics and Operations Research

Application of Group Theory to Symmetric Structures

Model-Based Enterprise

Achieving Lasting Value with MBD and MBE

Advancements in Machining Processes Through Hybrid and Sequential Approaches

Epileptic Seizure Prediction Using Electroencephalogram Signals

Mathematical Analysis for Engineering and Applied Sciences

Foundational and Fundamental Aspects

Mathematical Modelling for Engineering and Physical Applications

Practical Examples and Case Studies

System Reliability Analysis

Transition from Binary to Multi-state Models

Why Don't Rabbits Rule The World?

Mathematical answers to life's key questions

Bolted Joint Design

Easily Understandable Explanation and Failure Analysis Without Omission

Performance-Based Seismic Design of Reinforced Concrete Buildings

Advanced Modeling and Applications

This product is categorised by