Dealing with general problems in fluid mechanics, convection diffusion, compressible and incompressible laminar and turbulent flow, shallow water flows and waves, this is the leading text and reference for engineers working with fluid dynamics in fields including aerospace engineering, vehicle design, thermal engineering and many other engineering applications. The new edition is a complete fluids text and reference in its own right. Along with its companion volumes it forms part of the indispensable Finite Element Method series. New material in this edition includes sub-grid scale modelling; artificial compressibility; full new chapters on turbulent flows, free surface flows and porous medium flows; expanded shallow water flows plus long, medium and short waves; and advances in parallel computing.

Key Features

* A complete, stand-alone reference on fluid mechanics applications of the FEM for mechanical, aeronautical, automotive, marine, chemical and civil engineers. * Extensive new coverage of turbulent flow and free surface treatments * Accompanied by downloadable FEM source code


Practicing engineers, senior students and researchers in mechanical, automotive, aeronautical and civil engineering. Key topic for applied mathematicians and engineering software developers.

Table of Contents

1 Introduction to the equations of fluid dynamics and the finite element approximation 1.1 General remarks and classification of fluid dynamics problems discussed in this book 1.2 The governing equations of fluid dynamics 1.3 Inviscid, incompressible flow 1.4 Incompressible (or nearly incompressible) flows 1.5 Numerical solutions: weak forms, weighted residual and finite element approximation 1.6 Concluding remarks 1.7 Exercises References 2 Convection dominated problems – finite element approximations to the convection–diffusion-reaction equation 2.1 Introduction 2.2 The steady-state problem in one dimension 2.3 The steady-state problem in two (or three) dimensions 2.4 Steady state -- concluding remarks 2.5 Transients -- introductory remarks 2.6 Characteristic-based methods 2.7 Taylor--Galerkin procedures for scalar variables 2.8 Steady-state condition 2.9 Non-linear waves and shocks 2.10 Treatment of pure convection 2.11 Boundary conditions for convection--diffusion 2.12 Summary and concluding remarks 2.13 Exercises References 3 The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow 3.1 Introduction viii Contents 3.2 Non-dimensional form of the governing equations 3.3 Characteristic-based split (CBS) algorithm 3.4 Explicit, semi-implicit and nearly implicit forms 3.5 Artificial compressibility and dual time stepping 3.6 ‘Circumvention’ of the Babu¡ska--Brezzi (BB) restrictions 3.7 A single-step version


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It is very difficult to write a book which covers the entire finite element field. ..The authors have made a splendid attempt at a very difficult task. The books remain a tremendous bargain...and are an invaluable guide to the entire field of finite elements. If you are serious about working on finite elements you cannot do without this book. - Mathematics Today, August 2001. "...the publication of the first edition was an epoch making is written by...the greatest theorist of the subject. If you are serious about finite elements, this is a book that you simply cannot afford to be without." - International Journal of Numerical Methods in Engineering. "..the pre-eminent reference work on finite element analysis." - Applied Mechanical Review "...a very good book...presentation is first class...will be of great assistance to all engineers and scientists interested in the method...a very commendable piece of work." - Journal of the British Society for Strain Measurement