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. 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 topics, as well as 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 indispensable resource for professionals and researchers in various fields of science, chemical, mechanical, biomechanical, civil and aerospace engineering.

C. Pozrikidis has held positions as Professor of Fluid Mechanics and Chemical Engineering. He is well known for his contributions in fluid mechanics and biomechanics, applied mathematics and scientific computing. He has published numerous research papers and is the author of eight books and the editor of two contributed volumes.

Preface Note to the Instructor Note to the Reader 1 Kinematic structure of a flow 2 Kinematic analysis of a flow 3 Stresses, the equation of motion, and vorticity transport 4 Hydrostatics 5 Exact solutions 6 Flow at low Reynolds numbers 7 Irrotational flow 8 Boundary-layer analysis 9 Hydrodynamic stability 10 Boundary-integral methods for potential flow 11 Vortex motion 12 Finite-difference methods for convection-diffusion 13 Finite-difference methods for incompressible Newtonian flow A Mathematical supplement B Primer of numerical methods C FDLIB software library D User Guide of directory 08 stab of FDLIB on hydrodynamic stab References Index