PreJace to Volume 1 Introduction and the equations of fluid dynamics 1.1 General remarks and classification of fluid mechanics problems discussed in this book 1.2 The governing equations of fluid dynamics 1.3 Incompressible (or nearly incompressible) flows 1.4 Concluding remarks References 2 Convection dominated problems - finite element approximations to the convection-diffusion 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 Vector-valued variables 2.11 Summary and concluding remarks References 3 A general algorithm for compressible and incompressible flows - the characteristic-based split (CBS) algorithm 3.1 Introduction 3.2 Characteristic-based split (CBS) algorithm 3.3 Explicit, semi-implicit and nearly implicit forms 3.4 Circumventing' the Babuska-Brezzi (BB) restrictions 3.5 A single-step version 3.6 Boundary conditions 3.7 The performance of two- and single-step algorithms on an inviscid problem 3.8 Concluding remarks References 4 Incompressible laminar flow - newtonian and non-newtonian fluids 4.1 Introduction and the basic equations 4.2 Inviscid, incompressible flow (potential flow) 4.3 Use of the CBS algorithm for incompressible or nearly incompressible flows 4.4 Boundary-exit conditions 4.5 Adaptive mesh refinement 4.6 Adaptive mesh generation for transient problems 4.7 Importance of stabilizing convective terms 4.8 Slow flows - mixed and penalty formulations 4.9 Non-newtonian flows - metal and polymer forming 4.10 Direct displacement approach to transient metal forming 4.11 Concluding remarks References 5 Free surfaces, buoyancy and tucbulent incompressible flows 5.1 Introduction 5.2 Free surface flows 5.3 Buoyancy driven flows 5.4 Turbulent flows References 6 Compressible high-speed gas flow 6.1 Introduction 6.2 The governing equations 6.3 Boundary conditions - subsonic and supersonic flow 6.4 Numerical approximations and the CBS algorithm 6.5 Shock capture 6.6 Some preliminary examples for the Euler equation 6.7 Adaptive refinement and shock capture in Euler problems 6.8 Three-dimensional inviscid examples in steady state 6.9 Transient two and three-dimensional problems 6.10 Viscous problems in two dimensions 6.11 Three-dimensional viscous problems 6.12 Boundary layer-inviscid Euler solution coupling 6.13 Concluding remarks References 7 Shallow-water problems 7.1 Introduction 7.2 The basis of the shallow-water equations 7.3 Numerical approximation …… 8 Waves 9 Computer implementation of the CBS algorithm Appendix A:Non-conservative form of Navier-Stokes equations Appendix B:Discontinuous Galerkin methods in the solution of the convection-diffusion equation Appendix C:Edge-based finite element formulation Appendix D:Multigrid methods Appendix E:Boundary layer-inviscid flow coupling Author index Subject index
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