Introduction to
Theoretical and Computational Fluid Dynamics

C. Pozrikidis

Oxford University Press

Second Edition, 2011

1243 pages

ISBN-10: 0199752079, ISBN-13: 978-0199752072


This book is accompanied by the software library FDLIB

Preface and Table of Contents

Why this book?

This book discusses the fundamental principles and equations governing the motion of incompressible Newtonian fluids, and simultaneously introduces analytical and numerical methods for solving a broad range of pertinent problems. Sample topics include an in-depth discussion of kinematics, elements of differential geometry of lines and surfaces, vortex dynamics, properties and computation of interfacial shapes in hydrostatics, exact solutions, flow at low Reynolds numbers, interfacial flows, hydrodynamic stability, boundary-layer analysis, vortex motion, boundary-integral methods for potential and Stokes flow, principles of computational fluid dynamics (CFD), and finite-difference methods for Navier--Stokes flow. The discourse includes classical and original formulations and derivations accompanied by solved and unsolved problems that illustrate the theoretical results and explain the implementation of the numerical methods. Appendices provide a wealth of information and establish the necessary mathematical and numerical framework. A unique and comprehensive synthesis of the essential aspects of the discipline, this volume serves as an ideal textbook in several graduate courses on theoretical and computational fluid dynamics, applied mathematics, and scientific computing. The material is an indispensible resource for professionals and researchers in various fields of science and engineering, including physics; chemical, mechanical, biomechanical, civil and aerospace engineering; applied mathematics; and scientific computing.

Why is this book special?

• What distinguishes this book from a typical text on fluid mechanics is that the discourse is carried into the realm of numerical methods and into the discipline of computational fluid dynamics (CFD).

• What distinguishes this book from a typical text on computational fluid dynamics is that a full discussion of the theory with minimal external references is provided, and no experience in computational fluid dynamics or knowledge of its terminology is assumed.

• Appendices provide a wealth of information and establish the necessary mathematical and numerical framework.

What is new in the second Edition?

The Second Edition considerably extends the contents of the First Edition to include contemporary topics and some new and original material. Clarifications, further explanations, detailed proofs, original derivations, and solved problems have been added in numerous places. Chapter 1 on kinematics, Chapter 8 on hydrodynamic stability, and Chapter 11 on vortex methods have been considerably expanded. Numerous schematic depictions and graphs have been included as visual guides to illustrate the results of theoretical derivations. Expanded appendices containing useful background material have been added for easy reference. These additions underscore the intended purpose of the Second Edition as a teaching, research, and reference resource.


  1. Page 24:
    Table 1.3.1(d): Right-hand side of expression for ar: The first partial derivative should be with respect to r (Thanks to Xiangxi Meng (Zoey)).
  2. Section 3.2.2: This section contains a couple of typos. Please replace with the much improved and extended section energy balances and transport.
  3. Page 466:
    Equation (6.10.7): Please revise the left-hand side to read: IjS (Thanks to Brian Wood).
  4. Page 1017:
    Equation (A.4.8): Please cross out the "dot u" at the very end. (Thanks to Shane Taylor).