The Finite Element Method for Fluid Dynamics book cover

The Finite Element Method for Fluid Dynamics

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.

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

Hardbound, 400 Pages

Imprint: Butterworth Heinemann

ISBN: 978-0-7506-6322-9


  • "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


  • 1 Introduction to the equations of fluid dynamics and the finite elementapproximation1.1 General remarks and classification of fluid dynamics problems discussed in this book1.2 The governing equations of fluid dynamics1.3 Inviscid, incompressible flow1.4 Incompressible (or nearly incompressible) flows1.5 Numerical solutions: weak forms, weighted residual and finite element approximation 1.6 Concluding remarks1.7 ExercisesReferences2 Convection dominated problems – finite element approximations to the convection–diffusion-reaction equation2.1 Introduction2.2 The steady-state problem in one dimension2.3 The steady-state problem in two (or three) dimensions2.4 Steady state -- concluding remarks2.5 Transients -- introductory remarks2.6 Characteristic-based methods2.7 Taylor--Galerkin procedures for scalar variables2.8 Steady-state condition2.9 Non-linear waves and shocks2.10 Treatment of pure convection2.11 Boundary conditions for convection--diffusion2.12 Summary and concluding remarks2.13 ExercisesReferences3 The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow3.1 Introductionviii Contents3.2 Non-dimensional form of the governing equations3.3 Characteristic-based split (CBS) algorithm3.4 Explicit, semi-implicit and nearly implicit forms3.5 Artificial compressibility and dual time stepping3.6 ‘Circumvention’ of the Babu¡ska--Brezzi (BB) restrictions3.7 A single-step version3.8 Boundary conditions3.9 The performance of two and single step algorithms on an inviscid problem3.10 Concluding remarksReferences4 Incompressible Newtonian laminar flows4.1 Introduction and the basic equations4.2 Use of the CBS algorithm for incompressible flows4.3 Adaptive mesh refinement4.4 Adaptive mesh generation for transient problems4.5 Slow flows -- mixed and penalty formulations4.6 Concluding remarksReferences5 Incompressible non-Newtonian flows5.1 Introduction5.2 Non-Newtonian flows - metal and polymer forming5.3 Viscoelastic flows5.4 Direct displacement approach to transient metal forming5.5 Concluding remarksReferences6 Free surface and buoyancy driven flows6.1 Introduction6.2 Free surface flows6.3 Buoyancy driven flows6.4 Concluding remarksReferences 7 Compressible high-speed gas flow7.1 Introduction7.2 The governing equations7.3 Boundary conditions -- subsonic and supersonic flow7.4 Numerical approximations and the CBS algorithm7.5 Shock capture7.6 Variable smoothing7.7 Some preliminary examples for the Euler equation7.8 Adaptive refinement and shock capture inEuler problems7.9 Three-dimensional inviscid examples in steady state7.10 Transient two- and three-dimensional problems Contents ix7.11 Viscous problems in two dimensions 7.12 Three-dimensional viscous problems 7.13 Boundary layer--inviscid Euler solution coupling7.14 Concluding remarksReferences8 Turbulent flows8.1 Introduction8.2 Treatment of incompressible turbulent flows8.3 Treatment of compressible flows8.4 Large eddy simulation8.5 Detached Eddy Simulation (DES) and MonotonicallyIntegrated LES (MILES)8.6 Direct Numerical Simulation (DNS)8.7 SummaryReferences9 Flow through porous media9.1 Introduction9.2 A generalized porous medium flow approach9.3 Discretization procedure9.4 Non-isothermal flows9.5 Forced convection9.6 Natural convection9.7 SummaryReferences10 Shallow water problems10.1 Introduction10.2 The basis of the shallow water equations10.3 Numerical approximation10.4 Examples of application10.5 Drying areas10.6 Shallow water transport10.7 Concluding remarksReferences11 Long and medium waves11.1 Introduction and equations11.2 Waves in closed domains - finite element models11.3 Difficulties in modelling surface waves11.4 Bed friction and other effects 11.5 The short-wave problem11.6 Waves in unbounded domains (exterior surface wave problems)11.7 Unbounded problems11.8 Local Non-Reflecting Boundary Conditions (NRBCs)11.9 Infinite elements11.10 Mapped periodic (unconjugated) infinite elementsx Contents11.11 Ellipsoidal type infinite elements of Burnett and Holford11.12 Wave envelope (or conjugated) infinite elements11.13 Accuracy of infinite elements11.14 Trefftz type infinite elements11.15 Convection and wave refraction11.16 Transient problems11.17 Linking to exterior solutions (or DtN mapping)11.18 Three-dimensional effects in surface waves11.19 Concluding remarksReferences12 Short waves12.1 Introduction12.2 Background12.3 Errors in wave modelling12.4 Recent developments in short wave modelling12.5 Transient solution of electromagnetic scattering problems12.6 Finite elements incorporating wave shapes12.7 Refraction12.8 Spectral finite elements for waves12.9 Discontinuous Galerkin finite elements (DGFE)12.10 Concluding remarksReferences13 Computer implementation of the CBS algorithm13.1 Introduction13.2 The data input module13.3 Solution module13.4 Output moduleReferencesAppendix A Non-conservative form of Navier–Stokes equationsAppendix B Self-adjoint differential equationsAppendix C PostprocessingAppendix D Integration formulaeAppendix E Convection–diffusion equations: vector-valued variablesAppendix F Edge-based finite element formulationAppendix G Multigrid methodAppendix H Boundary layer–inviscid flow couplingAppendix I Mass-weighted averaged turbulence transport equationsAuthor IndexSubject Index


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