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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.

Tabla de contenidos provista por Syndetics

• Preface(p. xi)
• Acknowledgements(p. xiii)
• 1 Introduction to the equations of fluid dynamics and the finite element approximation(p. 1)
• 1.1 General remarks and classification of fluid dynamics problems discussed in this book(p. 1)
• 1.2 The governing equations of fluid dynamics(p. 4)
• 1.3 Inviscid, incompressible flow(p. 11)
• 1.4 Incompressible (or nearly incompressible) flows(p. 13)
• 1.5 Numerical solutions: weak forms, weighted residual and finite element approximation(p. 14)
• 1.6 Concluding remarks(p. 26)
• References(p. 27)
• 2 Convection dominated problems - finite element approximations to the convection-diffusion-reaction equation(p. 28)
• 2.1 Introduction(p. 28)
• 2.2 The steady-state problem in one dimension(p. 31)
• 2.3 The steady-state problem in two (or three) dimensions(p. 45)
• 2.4 Steady state - concluding remarks(p. 49)
• 2.5 Transients - introductory remarks(p. 50)
• 2.6 Characteristic-based methods(p. 53)
• 2.7 Taylor-Galerkin procedures for scalar variables(p. 65)
• 2.8 Steady-state condition(p. 66)
• 2.9 Non-linear waves and shocks(p. 66)
• 2.10 Treatment of pure convection(p. 70)
• 2.11 Boundary conditions for convection-diffusion(p. 72)
• 2.12 Summary and concluding remarks(p. 73)
• References(p. 74)
• 3 The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow(p. 79)
• 3.1 Introduction(p. 79)
• 3.2 Non-dimensional form of the governing equations(p. 81)
• 3.3 Characteristic-based split (CBS) algorithm(p. 82)
• 3.4 Explicit, semi-implicit and nearly implicit forms(p. 92)
• 3.5 Artificial compressibility and dual time stepping(p. 95)
• 3.6 'Circumvention' of the Babuska-Brezzi (BB) restrictions(p. 97)
• 3.7 A single-step version(p. 98)
• 3.8 Boundary conditions(p. 100)
• 3.9 The performance of two-step and one-step algorithms on an inviscid problem(p. 103)
• 3.10 Concluding remarks(p. 104)
• References(p. 105)
• 4 Incompressible Newtonian laminar flows(p. 110)
• 4.1 Introduction and the basic equations(p. 110)
• 4.2 Use of the CBS algorithm for incompressible flows(p. 112)
• 4.3 Adaptive mesh refinement(p. 123)
• 4.4 Adaptive mesh generation for transient problems(p. 131)
• 4.5 Slow flows - mixed and penalty formulations(p. 131)
• 4.6 Concluding remarks(p. 136)
• References(p. 136)
• 5 Incompressible non-Newtonian flows(p. 141)
• 5.1 Introduction(p. 141)
• 5.2 Non-Newtonian flows - metal and polymer forming(p. 141)
• 5.3 Viscoelastic flows(p. 154)
• 5.4 Direct displacement approach to transient metal forming(p. 163)
• 5.5 Concluding remarks(p. 165)
• References(p. 166)
• 6 Free surface and buoyancy driven flows(p. 170)
• 6.1 Introduction(p. 170)
• 6.2 Free surface flows(p. 170)
• 6.3 Buoyancy driven flows(p. 189)
• 6.4 Concluding remarks(p. 191)
• References(p. 193)
• 7 Compressible high-speed gas flow(p. 197)
• 7.1 Introduction(p. 197)
• 7.2 The governing equations(p. 198)
• 7.3 Boundary conditions - subsonic and supersonic flow(p. 199)
• 7.4 Numerical approximations and the CBS algorithm(p. 202)
• 7.5 Shock capture(p. 203)
• 7.6 Variable smoothing(p. 205)
• 7.7 Some preliminary examples for the Euler equation(p. 206)
• 7.8 Adaptive refinement and shock capture in Euler problems(p. 212)
• 7.9 Three-dimensional inviscid examples in steady state(p. 217)
• 7.10 Transient two- and three-dimensional problems(p. 226)
• 7.11 Viscous problems in two dimensions(p. 227)
• 7.12 Three-dimensional viscous problems(p. 240)
• 7.13 Boundary layer-inviscid Euler solution coupling(p. 241)
• 7.14 Concluding remarks(p. 242)
• References(p. 242)
• 8 Turbulent flows(p. 248)
• 8.1 Introduction(p. 248)
• 8.2 Treatment of incompressible turbulent flows(p. 251)
• 8.3 Treatment of compressible flows(p. 264)
• 8.4 Large eddy simulation(p. 267)
• 8.5 Detached Eddy Simulation (DES)(p. 270)
• 8.6 Direct Numerical Simulation (DNS)(p. 270)
• 8.7 Concluding remarks(p. 271)
• References(p. 271)
• 9 Generalized flow through porous media(p. 274)
• 9.1 Introduction(p. 274)
• 9.2 A generalized porous medium flow approach(p. 275)
• 9.3 Discretization procedure(p. 279)
• 9.4 Non-isothermal flows(p. 282)
• 9.5 Forced convection(p. 282)
• 9.6 Natural convection(p. 284)
• 9.7 Concluding remarks(p. 288)
• References(p. 289)
• 10 Shallow water problems(p. 292)
• 10.1 Introduction(p. 292)
• 10.2 The basis of the shallow water equations(p. 293)
• 10.3 Numerical approximation(p. 297)
• 10.4 Examples of application(p. 298)
• 10.5 Drying areas(p. 310)
• 10.6 Shallow water transport(p. 311)
• 10.7 Concluding remarks(p. 313)
• References(p. 314)
• 11 Long and medium waves(p. 317)
• 11.1 Introduction and equations(p. 317)
• 11.2 Waves in closed domains - finite element models(p. 318)
• 11.3 Difficulties in modelling surface waves(p. 320)
• 11.4 Bed friction and other effects(p. 320)
• 11.5 The short-wave problem(p. 320)
• 11.6 Waves in unbounded domains (exterior surface wave problems)(p. 321)
• 11.7 Unbounded problems(p. 324)
• 11.8 Local Non-Reflecting Boundary Conditions (NRBCs)(p. 324)
• 11.9 Infinite elements(p. 327)
• 11.10 Mapped periodic (unconjugated) infinite elements(p. 327)
• 11.11 Ellipsoidal type infinite elements of Burnett and Holford(p. 328)
• 11.12 Wave envelope (or conjugated) infinite elements(p. 330)
• 11.13 Accuracy of infinite elements(p. 332)
• 11.14 Trefftz type infinite elements(p. 332)
• 11.15 Convection and wave refraction(p. 333)
• 11.16 Transient problems(p. 335)
• 11.17 Linking to exterior solutions (or DtN mapping)(p. 336)
• 11.18 Three-dimensional effects in surface waves(p. 338)
• 11.19 Concluding remarks(p. 344)
• References(p. 344)
• 12 Short waves(p. 349)
• 12.1 Introduction(p. 349)
• 12.2 Background(p. 349)
• 12.3 Errors in wave modelling(p. 351)
• 12.4 Recent developments in short wave modelling(p. 351)
• 12.5 Transient solution of electromagnetic scattering problems(p. 352)
• 12.6 Finite elements incorporating wave shapes(p. 352)
• 12.7 Refraction(p. 364)
• 12.8 Spectral finite elements for waves(p. 372)
• 12.9 Discontinuous Galerkin finite elements (DGFE)(p. 374)
• 12.10 Concluding remarks(p. 378)
• References(p. 378)
• 13 Computer implementation of the CBS algorithm(p. 382)
• 13.1 Introduction(p. 382)
• 13.2 The data input module(p. 383)
• 13.3 Solution module(p. 384)
• 13.4 Output module(p. 387)
• References(p. 387)
• Appendix A Non-conservative form of Navier-Stokes equations(p. 389)
• Appendix B Self-adjoint differential equations(p. 391)
• Appendix C Postprocessing(p. 392)
• Appendix D Integration formulae(p. 395)
• Appendix E Convection-diffusion equations: vector-valued variables(p. 397)
• Appendix F Edge-based finite element formulation(p. 405)
• Appendix G Multigrid method(p. 407)
• Appendix H Boundary layer-inviscid flow coupling(p. 409)
• Appendix I Mass-weighted averaged turbulence transport equations(p. 413)
• Author index(p. 417)
• Subject index(p. 427)

Notas de autor provistas por Syndetics

O.C.Zienkiewicz is Professor Emeritus at the Civil and Computational Engineering Centre, University of Wales Swansea, UK, and holds the UNESCO Chair of Numerical Methods in Engineering at the Technical University of Catalunya, Barcelona, Spain
R.L. Taylor is a Professor in the Graduate School, Department of Civil and Environmental Engineering at the University of California, Berkeley, USA
P. Nithiarasu is Senior Lecturer at the School of Engineering, University of Wales Swansea, UK