General remarks and classification of fluid mechanics problems ... 2.6 Characteristic-based methods. 2.7 ... Numerical approximations and the CBS algorithm ... Steady-state field problems - heat conduction, electric and magnetic potential,. 8.
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
1 4 10 12 12
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
13 13 15 26 30 32 35 47 48 48 52 59 59
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
64 64 67 76 78 80 81
viii Contents
3.7 3.8
The performance of two- and single-step algorithms on an inviscid problem Concluding remarks References
85 87 87
4
Incompressible laminar flow - newtonian and non-newtonian fluids 91 4.1 Introduction and the basic equations 91 4.2 Inviscid, incompressible flow (potential flow) 93 4.3 Use of the CBS algorithm for incompressible or nearly incompressible flows 97 4.4 Boundary-exit conditions i00 4.5 Adaptive mesh refinement 102 4.6 Adaptive mesh generation for transient problems 113 4.7 Importance of stabilizing convective terms 113 4.8 Slow flows - mixed and penalty formulations 113 4.9 Non-newtonian flows - metal and polymer forming 118 4.10 Direct displacement approach to transient metal forming 132 4.1 1 Concluding remarks 133 References 134
Compressible high-speed gas flow 6.1 Introduction 6.2 The governing equations Boundary conditions - subsonic and supersonic flow 6.3 6.4 Numerical approximations and the CBS algorithm Shock capture 6.5 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
Shallow-water problems 7.1 Introduction The basis of the shallow-water equations 7.2 7.3 Numerical approximation
218 218 219 223
Contents ix 7.4 7.5 7.6
Examples of application Drying areas Shallow-water transport References
224 236 237 239
8
Waves Introduction and equations 8.1 8.2 Waves in closed domains - finite element models 8.3 Difficulties in modelling surface waves 8.4 Bed friction and other effects 8.5 The short-wave problem 8.6 Waves in unbounded domains (exterior surface wave problems) Unbounded problems 8.7 8.8 Boundary dampers 8.9 Linking to exterior solutions 8.10 Infinite elements 8.11 Mapped periodic infinite elements 8.12 Ellipsoidal type infinite elements of Burnett and Holford 8.13 Wave envelope infinite elements 8.14 Accuracy of infinite elements 8.15 Transient problems 8.16 Three-dimensional effects in surface waves References
Computer implementation of the CBS algorithm 9.1 Introduction 9.2 The data input module 9.3 Solution module 9.4 Output module 9.5 Possible extensions to CBSflow References
274 274 275 278 289 289 289
Appendix A: Non-conservative form of Navier-Stokes equations
29 1
Appendix B: Discontinuous Galerkin methods in the solution of the convection-diffusion equation
293
Appendix C: Edge-based finite element formulation
298
Appendix D: Multigrid methods
300
Appendix E: Boundary layer-inviscid flow coupling
302
Author index
307
Subject index
315
Volume 1: The basis 1. Some preliminaries: the standard discrete system 2. A direct approach to problems in elasticity 3. Generalization of the finite element concepts. Galerkin-weighted residual and variational approaches 4. Plane stress and plane strain 5. Axisymmetric stress analysis 6. Three-dimensional stress analysis 7. Steady-state field problems - heat conduction, electric and magnetic potential, fluid flow, etc 8. ‘Standard’ and ‘hierarchical’ element shape functions: some general families of Co continuity 9. Mapped elements and numerical integration - ‘infinite’ and ‘singularity’ elements 10. The patch test, reduced integration, and non-conforming elements 1 1. Mixed formulation and constraints - complete field methods 12. Incompressible problems, mixed methods and other procedures of solution 13. Mixed formulation and constraints - incomplete (hybrid) field methods, boundary/Trefftz methods 14. Errors, recovery processes and error estimates 15. Adaptive finite element refinement 16. Point-based approximations; element-free Galerkin - and other meshless methods 17. The time dimension - semi-discretization of field and dynamic problems and analytical solution procedures 18. The time dimension - discrete approximation in time 19. Coupled systems 20. Computer procedures for finite element analysis Appendix A. Matrix algebra Appendix B. Tensor-indicia1 notation in the approximation of elasticity problems Appendix C. Basic equations of displacement analysis Appendix D. Some integration formulae for a triangle Appendix E. Some integration formulae for a tetrahedron Appendix F. Some vector algebra Appendix G. Integration by parts Appendix H. Solutions exact at nodes Appendix I. Matrix diagonalization or lumping
Volume 2: Solid and structural mechanics 1. 2. 3. 4.
5. 6. 7. 8. 9.
10. 1 1. 12. 13.
General problems in solid mechanics and non-linearity Solution of non-linear algebraic equations Inelastic materials Plate bending approximation: thin (Kirchhoff) plates and C , continuity requirements ‘Thick’ Reissner-Mindlin plates - irreducible and mixed formulations Shells as an assembly of flat elements Axisymmetric shells Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions Semi-analytical finite element processes - use of orthogonal functions and ‘finite strip’ methods Geometrically non-linear problems - finite deformation Non-linear structural problems - large displacement and instability Pseudo-rigid and rigid-flexible bodies Computer procedures for finite element analysis Appendix A: Invariants of second-order tensors
Not only does this give us a vector space structure on Tx but it makes ^U an isomorphism. We will make use of this isomorphism later, so it is worth summarizing ...
Passing data to Excel 2007 application . ... Simple 12-bit digitizing system . ... The simple device driver for the parallel port . .... Configuring IIS and ASP. NET .
effect of power arcs should be considered in the design of metal fittings. ..... bonded to the core, then it shall be removed and the remaining core thoroughly ...
Dimensions, interior and exterior, 14 .... The Mark IV series of the British Ford Zephyr and Zodiac models were ... Compact six-cylinder 249Scc (2 S-litre) engine arranged in 60 degrees ... Iically operated disc brakes are fitted on all wheels and a
Advantages and disadvantages of FRP composite ... 2.6. Applications of FRP strengthening. 36. 2.7 ... Fatigue of long span plated 2.3m beams using FRP plates.
Milestones in the life of François Malkovsky. 13. Seeking a new dance. 23. “To dance” by Malkovsky. 29. A “harmonious” dance: the logic of harmony. 31.
22 1. 223. 226. 229. Singular elements by mapping for fracture mechanics, etc. 234 ... Incompressible materials, mixed methods and other procedures of solution.
Jul 10, 2010 - The following text is a piece of my forthcoming book (updated with respect to .... violated without this arousing much discussion (§§Erreur ! Source du renvoi introuvable.,Erreur ! Source du renvoi introuvable.). We have seen that ..
Axiom Event dec : â e e' : Event, {e = e'}+{e = e'}. Definition Object := Var + Event. Values. Parameter Val : Set. Axiom Val dec : â x y : Val, {x = y}+{x = y}.
superclass is the generalized class, while the subclasses are specified classes. ..... Listed are the core metadata elements required to identify a dataset, typically for ..... Figure A.11 defines metadata about the portrayal catalogue(s) used to dis
Toggle Low. Lid must be closed and locked for this to be enabled. Speed Spin. Note: The basket must be empty for this function. 011. Toggle Mid. Lid must be ...
Simple thermostat system . ... Measuring temperature with the DS1722 digital sensor . ..... Simple remote control system using FM transmitter and receiver .
any sufficiently regular one-scale function u(x) and two-scale function v(Ëx,y), .... spectrum for an N-cantilevers array, we suggest to operate a truncation in the mode list so that to retain a simple infinity of ...... spond to the Tellegen theore
Annex J (informative) Multilingual support for free text metadata element. .... determining data fitness for use, data access, data transfer, and use of digital data); .... superclass is the generalized class, while the subclasses are specified class
The most natural configuration for an audio system in the automobile places the ... electrical environment in an automobile is one that is inherently noisy and filled .... Aux Out: Auxiliary output to provide conditioned signal for another amp. 10.
audio.mp3â]. Want to know what somebody is called? You have three main ways to do that: You can ask: â« Comment s'appelle-t-il/elle? What is his/her name?
here, generalises the Theorem of Schinzel, in what concerns the number n .... a projective space Pn and defined over some algebraically closed field K, the .... We are ready now to define the height of an algebraic number α. ...... we form the row .
approximately 3000V. ... When repackaging main control assembly in anti-static bag, observe above instructions. ...... the following notes to identify the switch(es).
Jun 8, 2013 - This book covers the fundamental theory and techniques for digital video ..... absorption function of the camera be denoted by ac(λ), then the light intensity ..... in designing the color TV system is that it must be compatible with th
