## Fluid Dynamics:
Theory, Computation, and Numerical Simulation;

Accompanied by the software library FDLIB

## C Pozrikidis

Kluwer (Springer), 2001; Reprinted unrevised in 2007; pp. 675; ISBN: 0792373510

## Why this book?

This book offers an introductory course in theoretical and computation fluid dynamics, presented in a way that unifies theory, scientific computer programming, and numerical computation. Computational algorithms are developed immediately after problem formulations, and numerical methods are introduced alongside. The approach is truly introductory with a minimum of prerequisites. Intended audience includes undergraduate and entry-level graduate students, and a broad class of scientists and engineers with a general interest in scientific computing.

## Software

This book is accompanied by the software library FDLIB whose directories explicitly illustrate how algorithms translate into code insructions. The codes of FDLIB range from introductory to advanced, and the problems considered span a wide range of applications. The programs are written in a modular fashion that allows modification and post-processing, including graphics and animation.## Excerpts from the preface

Ready access to computers on an institutional and personal level has defined a new era in learning and teaching. The opportunity to extend the subject matter of traditional scientific and engineering disciplines into the realm of scientific computing has become not only desirable, but also necessary as an effective tool of teaching and learning. Thanks to portability and low overhead and operating cost, experimentation by numerical simulation has become a viable substitute, and occasionally the only alternative, to physical experimentation.The new approach has motivated the writing of texts and monographs from a new perspective that incorporates numerical and computer programming aspects as an integral part of the curicullum: methods, concepts, and ideas should be presented in a unified fashion that motivates and underlines the necessity of the new elements, but does not compromise the rigour of the classical approach and does not oversimplify.

Interfacing fundamental concepts and practical methods of scientific computing can be done on different levels distinguished by the texture of the weaving. In one approach, theory and implementation are kept complementary and presented in a sequential fashion. In a second approach, the coupling involves two intermediate steps: deriving computational methods and simulation algorithms immediately following problem formulations; and translating equations into computer code instructions. The author of this book appreciates the advantages of the second approach and advocates its usage as a means of enhanced learning: scientific programming offers a powerfull venue for developing analytical skills and physical insight.

## Contents

**Preface**

**1. Fluid motion: Introduction to kinematics**

1.1 Fluids and solids

1.2 Fluid parcels and flow kinematics

1.3 Coordinates, velocity, and acceleration

1.4 Fluid velocity and streamlines

1.5 Material surfaces and elementary motions

1.6 Point particles and their trajectories

1.7 Function interpolation

**2. Fluid motion: More on kinematics**

2.1 Fundamental modes of fluid parcel motion

2.2 Fluid parcel expansion

2.3 Fluid parcel rotation and vorticity

2.4 Fluid parcel deformation

2.5 Numerical differentiation

2.6 Areal and volumetric flow rate

2.7 Mass flow rate, mass conservation, and the continuity equation

2.8 Properties of point particles

2.9 Incompressible fluids and stream functions

2.10 Kinematic conditions at boundaries

**3. Flow computation based on kinematics**

3.1 Flow classification based on kinematics

3.2 Irrotational flows and the velocity potential

3.3 Finite-difference methods

3.4 Linear solvers

3.5 Two-dimensional point sources and point-source dipoles

3.6 Three-dimensional point sources and point-source dipoles

3.7 Point vortices and line vortices

**4. Forces developing in a fluid**

4.1 Body forces and surface forces

4.2 Traction and the stress tensor

4.3 Traction jump across a fluid interface

4.4 Stresses in a fluid at rest

4.5 Viscous and Newtonian fluids

4.6 Simple non-Newtonian fluids

4.7 Stresses in polar coordinates

4.8 Condition on the tangential boundary velocity

4.9 Wall stresses in Newtonian fluids

**5. Hydrostatics**

5.1 Equilibrium of pressure and body forces

5.2 Force exerted on immersed surfaces

5.3 Archimedes' principle

5.4 Shapes of two-dimensional interfaces

5.5 A semi-infinite interface attached to an inclined plate

5.6 Meniscus between two parallel plates

5.7 A two-dimensional drop on a horizontal plane

5.8 Axisymmetric interfacial shapes

**6. Equation of motion and vorticity transport**

6.1 Newton's second law for the motion of a fluid parcel

6.2 Integral momentum balance

6.3 Cauchy's equation of motion

6.4 Euler's and Bernoulli's equations

6.5 The Navier-Stokes equation

6.6 Vorticity transport

6.7 Dynamic similitude, the Reynolds number, and dimensionless numbers in fluid dynamics

**7. Channel, tube, and film flows**

7.1 Steady flow in a two-dimensional channel

7.2 Steady film flow down an inclined plane

7.3 Steady flow in a circular or annular tube

7.4 Steady flow in tubes with various cross-sections

7.5 Steady swirling flow

7.6 Transient flow in a channel

7.7 Oscillatory flow in a channel

7.8 Transient and oscillatory flow in a circular tube

**8. Finite-difference methods**

8.1 Choice of governing equations

8.2 Unidirectional flow; velocity/pressure formulation

8.3 Unidirectional flow; velocity/vorticity formulation

8.4 Unidirectional flow; stream function/vorticity formulation

8.5 Two-dimensional flow; stream function/vorticity formulation

8.6 Velocity/pressure formulation

8.7 Operator splitting and solenoidal projection

**9. Flows at low Reynolds numbers**

9.1 Lubrication flows in narrow channels

9.2 Film flow on a horizontal wall or down a plane wall

9.3 Two-layer flow in a channel

9.4 Flow due to the motion of a sphere

9.5 Point forces and point sources in Stokes flow

9.6 Two-dimensional flow

9.7 Flow near corners

**10. Flows at high Reynolds numbers**

10.1 Changes in the structure of a flow with increasing Reynolds number

10.2 Prandtl boundary layer analysis

10.3 Boundary layer on a flat surface

10.4 Von Karman's momentum integral method

10.5 Instability of shear flows

10.6 Turbulent motion

10.7 Analysis of turbulent motion

**11. Vortex motion**

11.1 Vorticity and circulation in two-dimensional flow

11.2 Motion of point vortices

11.3 Two-dimensional flow with distributed vorticity

11.4 Vorticity, circulation, and three-dimensional flow induced by vorticity

11.5 Axisymmetric flow induced by vorticity

11.6 Vortex motion in three-dimensional flow

**12. Aerodynamics**

12.1 General features of flow past an aircraft

12.2 Airfoils and the Kutta-Joukowski condition

12.3 Vortex panels

12.4 Vortex panel method

12.5 Vortex sheet representation

12.6 Point-source-dipole panels

12.7 Point-source panels and Green's third identity

**References**

**FDLIB**

**FDLIB Directories**

**Subject Index**