Preface Acknowledgements 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 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 conditionsfor convection-diffusion 2.12 Summary and concluding remarks References 3 The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow 3.1 Introduction 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 Babuska-Brezzi (BB) restrictions 3.7 A single-step version 3.8 Boundary conditions 3.9 The performance of two-step and one-step algorithms on an inviscid problem 3.10 Concluding remarks References 4 Incompressible Newtonian laminar flows 4.1 Introduction and the basic equations 4.2 Use of the CBS algorithm for incompressible flows 4.3 Adaptive mesh refinement 4.4 Adaptive mesh generation for transient problems 4.5 Slow flows - mixed and penalty formulations 4.6 Concluding remarks References 5 Incompressible non-Newtonian flows 5.1 Introduction 5.2 Non-Newtonian flows - metal and polymer forming 5.3 Viscoelastic flows 5.4 Direct displacement approach to transient metal forming 5.5 Concluding remarks References 6 Free surface and buoyancy driven flows 6.1 Introduction 6.2 Free surface flows 6.3 Buoyancy driven flows 6.4 Concluding remarks References 7 Compressible high-speed gas flow 7.1 Introduction 7.2 The governing equations 7.3 Boundary conditions.- subsonic and Suoersonic fl0w 7.4 Numerical approximations and the CBS algorithm 7.5 Shock capture 7.6 Variable smoothing 7.7 Some preliminary examples for the Euler equation 7.8 Adaptive refinement and shock capture in Euler problems 7.9 Three-dimensional inviscid examples in steady state 7.10 Transient two- and three-dimensional problems 7.11 Viscous problems in two dimensions 7.12 Three-dimensional viscous problems …… 8 Turbulent flows 9 Generalized flow through porous media 10 Shallow water problems 11 Long and medium waves 12 Short waves 13 Computer implementation of the CBS algorithm Appendix Author index Subject index
鄂公網(wǎng)安備 42010302001612號(hào) 