| Preface |
| Acknowledgements |
| Introduction to the equations of fluid dynamics and the finite element approximation / 1： |
| General remarks and classification of fluid dynamics problems discussed in this book / 1.1： |
| The governing equations of fluid dynamics / 1.2： |
| Inviscid, incompressible flow / 1.3： |
| Incompressible (or nearly incompressible) flows / 1.4： |
| Numerical solutions: weak forms, weighted residual and finite element approximation / 1.5： |
| Concluding remarks / 1.6： |
| References |
| Convection dominated problems - finite element approximations to the convection-diffusion-reaction equation / 2： |
| Introduction / 2.1： |
| The steady-state problem in one dimension / 2.2： |
| The steady-state problem in two (or three) dimensions / 2.3： |
| Steady state - concluding remarks / 2.4： |
| Transients - introductory remarks / 2.5： |
| Characteristic-based methods / 2.6： |
| Taylor-Galerkin procedures for scalar variables / 2.7： |
| Steady-state condition / 2.8： |
| Non-linear waves and shocks / 2.9： |
| Treatment of pure convection / 2.10： |
| Boundary conditions for convection-diffusion / 2.11： |
| Summary and concluding remarks / 2.12： |
| The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow / 3： |
| Non-dimensional form of the governing equations / 3.1： |
| Characteristic-based split (CBS) algorithm / 3.3： |
| Explicit, semi-implicit and nearly implicit forms / 3.4： |
| Artificial compressibility and dual time stepping / 3.5： |
| 'Circumvention' of the Babuska-Brezzi (BB) restrictions / 3.6： |
| A single-step version / 3.7： |
| Boundary conditions / 3.8： |
| The performance of two-step and one-step algorithms on an inviscid problem / 3.9： |
| Incompressible Newtonian laminar flows / 3.10： |
| Introduction and the basic equations / 4.1： |
| Use of the CBS algorithm for incompressible flows / 4.2： |
| Adaptive mesh refinement / 4.3： |
| Adaptive mesh generation for transient problems / 4.4： |
| Slow flows - mixed and penalty formulations / 4.5： |
| Incompressible non-Newtonian flows / 4.6： |
| Non-Newtonian flows - metal and polymer forming / 5.1： |
| Viscoelastic flows / 5.3： |
| Direct displacement approach to transient metal forming / 5.4： |
| Free surface and buoyancy driven flows / 5.5： |
| Free surface flows / 6.1： |
| Buoyancy driven flows / 6.3： |
| Compressible high-speed gas flow / 6.4： |
| The governing equations / 7.1： |
| Boundary conditions - subsonic and supersonic flow / 7.3： |
| Numerical approximations and the CBS algorithm / 7.4： |
| Shock capture / 7.5： |
| Variable smoothing / 7.6： |
| Some preliminary examples for the Euler equation / 7.7： |
| Adaptive refinement and shock capture in Euler problems / 7.8： |
| Three-dimensional inviscid examples in steady state / 7.9： |
| Transient two- and three-dimensional problems / 7.10： |
| Viscous problems in two dimensions / 7.11： |
| Three-dimensional viscous problems / 7.12： |
| Boundary layer-inviscid Euler solution coupling / 7.13： |
| Turbulent flows / 7.14： |
| Treatment of incompressible turbulent flows / 8.1： |
| Treatment of compressible flows / 8.3： |
| Large eddy simulation / 8.4： |
| Detached Eddy Simulation (DES) / 8.5： |
| Direct Numerical Simulation (DNS) / 8.6： |
| Generalized flow through porous media / 8.7： |
| A generalized porous medium flow approach / 9.1： |
| Discretization procedure / 9.3： |
| Non-isothermal flows / 9.4： |
| Forced convection / 9.5： |
| Natural convection / 9.6： |
| Shallow water problems / 9.7： |
| The basis of the shallow water equations / 10.1： |
| Numerical approximation / 10.3： |
| Examples of application / 10.4： |
| Drying areas / 10.5： |
| Shallow water transport / 10.6： |
| Long and medium waves / 10.7： |
| Introduction and equations / 11.1： |
| Waves in closed domains - finite element models / 11.2： |
| Difficulties in modelling surface waves / 11.3： |
| Bed friction and other effects / 11.4： |
| The short-wave problem / 11.5： |
| Waves in unbounded domains (exterior surface wave problems) / 11.6： |
| Unbounded problems / 11.7： |
| Local Non-Reflecting Boundary Conditions (NRBCs) / 11.8： |
| Infinite elements / 11.9： |
| Mapped periodic (unconjugated) infinite elements / 11.10： |
| Ellipsoidal type infinite elements of Burnett and Holford / 11.11： |
| Wave envelope (or conjugated) infinite elements / 11.12： |
| Accuracy of infinite elements / 11.13： |
| Trefftz type infinite elements / 11.14： |
| Convection and wave refraction / 11.15： |
| Transient problems / 11.16： |
| Linking to exterior solutions (or DtN mapping) / 11.17： |
| Three-dimensional effects in surface waves / 11.18： |
| Short waves / 11.19： |
| Background / 12.1： |
| Errors in wave modelling / 12.3： |
| Recent developments in short wave modelling / 12.4： |
| Transient solution of electromagnetic scattering problems / 12.5： |
| Finite elements incorporating wave shapes / 12.6： |
| Refraction / 12.7： |
| Spectral finite elements for waves / 12.8： |
| Discontinuous Galerkin finite elements (DGFE) / 12.9： |
| Computer implementation of the CBS algorithm / 12.10： |
| The data input module / 13.1： |
| Solution module / 13.3： |
| Output module / 13.4： |
| Non-conservative form of Navier-Stokes equations / Appendix A： |
| Self-adjoint differential equations / Appendix B： |
| Postprocessing / Appendix C： |
| Integration formulae / Appendix D： |
| Convection-diffusion equations: vector-valued variables / Appendix E： |
| Edge-based finite element formulation / Appendix F： |
| Multigrid method / Appendix G： |
| Boundary layer-inviscid flow coupling / Appendix H： |
| Mass-weighted averaged turbulence transport equations / Appendix I： |
| Author index |
| Subject index |
| Preface |
| Acknowledgements |
| Introduction to the equations of fluid dynamics and the finite element approximation / 1： |
図書
