Fluid dynamics : theory, computation, and numerical simulation : accompanied by the software library FDLIB

Fluid Dynamics: Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner. The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming. This book serves as an introductory course in fluid mechanics, covering traditional topics in a way that unifies theory, computation, computer programming, and numerical simulation. The approach is truly introductory, in the sense that few prerequisites are required. The audience includes not only advanced undergraduate and entry-level graduate students, but also a broad class of scientists and engineers with a general interest in scientific computing. Two distinguishing features of the discourse are: solution procedures and algorithms are developed immediately after problem formulations are presented; and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty. A supplement to this book is the FORTRAN software library FDLIB, freely available through the Internet, whose programs explicitly illustrate how computational algorithms translate into computer code instructions. The codes of FDLIB range from introductory to advanced, and the problems considered span a broad range of applications; from laminar channel flows, to vortex flows, to flows in aerodynamics. Selected computer problems at the end of each section ask the student to run the programs for various flow conditions, and thereby study the effect of the various parameters determining or characterizing a flow. This text is a must for practitioners and students in all fields of engineering, computational physics, scientific computing, and applied mathematics. It can be used as a text in both undergraduate and graduate courses in fluid mechanics, aerodynamics, and computational fluid dynamics. Front Matter......Page 1 Preface......Page 3 Subject Index......Page 0 Table of Contents......Page 5 1.1 Fluids and Solids......Page 10 1.2 Fluid Parcels and Flow Kinematics......Page 11 1.3 Coordinates, Velocity, and Acceleration......Page 13 1.4 Fluid Velocity and Streamlines......Page 24 1.5 Point Particles and Their Trajectories......Page 27 1.6 Material Surfaces and Elementary Motions......Page 36 1.7 Interpolation......Page 47 2.1 Fundamental Modes of Fluid Parcel Motion......Page 58 2.2 Fluid Parcel Expansion......Page 70 2.3 Fluid Parcel Rotation and Vorticity......Page 71 2.4 Fluid Parcel Deformation......Page 77 2.5 Numerical Differentiation......Page 81 2.6 Areal and Volumetric Flow Rate......Page 87 2.7 Mass Flow Rate, Mass Conservation, and the Continuity Equation......Page 97 2.8 Properties of Point Particles......Page 103 2.9 Incompressible Fluids and Stream Functions......Page 111 2.10 Kinematic Conditions at Boundaries......Page 116 3.1 Flow Classification Based on Kinematics......Page 121 3.2 Irrotational Flows and the Velocity Potential......Page 124 3.3 Finite-Difference Methods......Page 132 3.4 Linear Solvers......Page 141 3.5 Two-Dimensional Point Sources and Point-Source Dipoles......Page 145 3.6 Three-Dimensional Point Sources and Point-Source Dipoles......Page 159 3.7 Point Vortices and Line Vortices......Page 164 4.1 Body Forces and Surface Forces......Page 174 4.2 Traction and the Stress Tensor......Page 176 4.3 Traction Jump across a Fluid Interface......Page 183 4.4 Stresses in a Fluid at Rest......Page 191 4.5 Viscous and Newtonian Fluids......Page 195 4.6 Simple Non-Newtonian Fluids......Page 204 4.7 Stresses in Polar Coordinates......Page 207 4.8 Boundary Condition on the Tangential Velocity......Page 213 4.9 Wall Stresses in Newtonian Fluids......Page 215 5.1 Equilibrium of Pressure and Body Forces......Page 218 5.2 Force Exerted on Immersed Surfaces......Page 227 5.3 Archimedes' Principle......Page 234 5.4 Shapes of Two-Dimensional Interfaces......Page 237 5.5 A Semi-Infinite Interface Attached to an Inclined Plate......Page 241 5.6 Meniscus between Two Parallel Plates......Page 245 5.7 A Two-Dimensional Drop on a Horizontal Plane......Page 251 5.8 Axisymmetric Shapes......Page 256 6.1 Newton's Second Law for the Motion of a Parcel......Page 262 6.2 Integral Momentum Balance......Page 268 6.3 Cauchy's Equation of Motion......Page 273 6.4 Euler's and Bernoulli's Equations......Page 280 6.5 The Navier-Stokes Equation......Page 291 6.6 Vorticity Transport......Page 298 6.7 Dynamic Similitude, the Reynolds Number, and Dimensionless Numbers in Fluid Dynamics......Page 306 7.1 Steady Flow in a Two-Dimensional Channel......Page 316 7.2 Steady Film Flow Down an Inclined Plane......Page 325 7.3 Steady Flow through a Circular or Annular Tube......Page 329 7.4 Steady Flow through Channels and Tubes with Various Cross-Sections......Page 337 7.5 Steady Swirling Flow......Page 346 7.6 Transient Flow in a Channel......Page 349 7.7 Oscillatory Flow in a Channel......Page 357 7.8 Transient and Oscillatory Flow in a Circular Tube......Page 364 8.1 Choice of Governing Equations......Page 374 8.2 Unidirectional Flow; Velocity/Pressure Formulation......Page 376 8.3 Unidirectional Flow; Velocity/Vorticity Formulation......Page 387 8.4 Unidirectional Flow; Stream Function/Vorticity Formulation......Page 392 8.5 Two-Dimensional Flow; Stream Function/Vorticity Formulation......Page 396 8.6 Velocity/Pressure Formulation......Page 405 8.7 Operator Splitting and Solenoidal Projection......Page 409 9. Flows at Low Reynolds Numbers......Page 420 9.1 Flows in Narrow Channels......Page 421 9.2 Film Flow on a Horizontal or Down Plane Wall......Page 434 9.3 Two-Layer Channel Flow......Page 446 9.4 Flow Due to the Motion of a Sphere......Page 454 9.5 Point Forces and Point Sources in Stokes Flow......Page 461 9.6 Two-Dimensional Stokes Flow......Page 470 9.7 Flow near Corners......Page 476 10. Flows at High Reynolds Numbers......Page 486 10.1 Changes in the Structure of a Flow with Increasing Reynolds Number......Page 487 10.2 Prandtl Boundary-Layer Analysis......Page 490 10.3 Prandtl Boundary Layer on a Flat Surface......Page 496 10.4 Von Karman's Integral Method......Page 512 10.5 Instability of Shear Flows......Page 524 10.6 Turbulent Motion......Page 537 10.7 Analysis of Turbulent Motion......Page 551 11. Vortex Motion......Page 560 11.1 Vorticity and Circulation in Two-Dimensional Flow......Page 561 11.2 Motion of Point Vortices......Page 563 11.3 Two-Dimensional Flow with Distributed Vorticity......Page 578 11.4 Vorticity, Circulation, and Three-Dimensional Flow Induced by Vorticity......Page 593 11.5 Axisymmetric Flow Induced by Vorticity......Page 598 11.6 Three-Dimensional Vortex Motion......Page 612 12. Aerodynamics......Page 618 12.1 General Features of Flow Past an Aircraft......Page 619 12.2 Airfoils and the Kutta-Joukowski Condition......Page 621 12.3 Vortex Panels......Page 624 12.4 Vortex Panel Method......Page 632 12.5 Vortex Sheet Representation......Page 641 12.6 Point-Source-Dipole Panels......Page 650 12.7 Point-Source Panels and Green's Third Identity......Page 657 FDLIB Software Library......Page 663 FDLIB Directories......Page 665 References......Page 678 B......Page 680 C......Page 682 D......Page 683 E......Page 684 F......Page 685 H......Page 686 K......Page 687 L......Page 688 N......Page 689 P......Page 690 S......Page 692 T......Page 694 V......Page 695 Y......Page 696 W......Page 697 Ready access to computers at an institutional and personal level has defined a new era in teaching and learning. The opportunity to extend the subject matter of traditional science and engineering disciplines into the realm of scientific computing has become not only desirable, but also necessary. Thanks to port ability and low overhead and operating costs, experimentation by numerical simulation has become a viable substitute, and occasionally the only alternative, to physical experiment at ion. The new environment has motivated the writing of texts and mono­ graphs with a modern perspective that incorporates numerical and com­ puter programming aspects as an integral part of the curriculum: meth­ ods, concepts, and ideas should be presented in a unified fashion that motivates and underlines the urgency of the new elements, but does not compromise the rigor of the classical approach and does not oversimplify. Interfacing fundamental concepts and practical methods of scientific computing can be done on different levels. In one approach, theory and implement at ion are kept complementary and presented in a sequential fashion. In a second approach, the coupling involves deriving compu­ tational methods and simulation algorithms, and translating equations into computer code instructions immediately following problem formu­ lations. The author of this book is a proponent of the second approach and advocates its adoption as a means of enhancing learning: interject­ ing methods of scientific computing into the traditional discourse offers a powerful venue for developing analytical skills and obtaining physical insight. We begin the study of fluid mechanics by pointing out the differences between fluids and solids, and by describing a flow in terms of the motion of elementary fluid parcels.