有限元法（第3卷）

內(nèi)容概要

這是一套在國際上頗具權(quán)威性的經(jīng)典著作(共3卷)，由有限元法的創(chuàng)始人zienkiewicz教授和美國加州大學TayIor教授合作撰寫。本書初版于1967年，以后經(jīng)過多次修訂再版，深受力學界和工程界科技人員的歡迎。本套書的特點是理論可靠，內(nèi)容全面，既有基礎(chǔ)理論，又有其具體應(yīng)用。適用于計算力學、力學、土木、水利、機械、航天航空等領(lǐng)域的專家、教授、工程技術(shù)人員和研究生。

書籍目錄

PreJace to Volume1 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   References2 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  References3 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  References4 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  References5 Free surfaces, buoyancy and tucbulent incompressible flows  5.1 Introduction  5.2 Free surface flows  5.3 Buoyancy driven flows  5.4 Turbulent flows  References6 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  References7 Shallow-water problems  7.1 Introduction  7.2 The basis of the shallow-water equations  7.3 Numerical approximation  ……8 Waves9 Computer implementation of the CBS algorithmAppendix A:Non-conservative form of Navier-Stokes equationsAppendix B:Discontinuous Galerkin methods in the solution of the convection-diffusion equationAppendix C:Edge-based finite element formulationAppendix D:Multigrid methodsAppendix E:Boundary layer-inviscid flow couplingAuthor indexSubject index

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