有限元方法流体力学 第6版PDF|Epub|txt|kindle电子书版本网盘下载

有限元方法流体力学 第6版PDF格式电子书版下载

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1 Introduction to the equations of fluid dynamics and the finite element approximation1

1.1 General remarks and classification of fluid dynamics problems discussed in this book1

1.2 The governing equations of fluid dynamics4

1.3 Inviscid，incompressible flow11

1.4 Incompressible（or nearly incompressible）flows13

1.5 Numerical solutions：weak forms，weighted residual and finite element approximation14

1.6 Concluding remarks26

References27

2 Convection dominated problems-finite element approximations to the convection-diffusion-reaction equation28

2.1 Introduction28

2.2 The steady-state problem in one dimension31

2.3 The steady-state problem in two（or three）dimensions45

2.4 Steady state-concluding remarks49

2.5 Transients-introductory remarks50

2.6 Characteristic-based methods53

2.7 Taylor-Galerkin procedures for scalar variables65

2.8 Steady-state condition66

2.9 Non-linear waves and shocks66

2.10 Treatment of pure convection70

2.11 Boundary conditions for convection-diffusion72

2.12 Summary and concluding remarks73

References74

3 The characteristic-based split（CBS）algorithm.A general procedure for compressible and incompressible flow79

3.1 Introduction79

3.2 Non-dimensional form of the governing equations81

3.3 Characteristic-based split（CBS）algorithm82

3.4 Explicit，semi-implicit and nearly implicit forms92

3.5 Artificial compressibility and dual time stepping95

3.6 ’Circumvention’of the Babu？ka-Brezzi（BB）restrictions97

3.7 A single-step version98

3.8 Boundary conditions100

3.9 The performance of two-step and one-step algorithms on an inviscid problem103

3.10 Concluding remarks104

References105

4 Incompressible Newtonian laminar flows110

4.1 Introduction and the basic equations110

4.2 Use of the CBS algorithm for incompressible flows112

4.3 Adaptive mesh refinement123

4.4 Adaptive mesh generation for transient problems131

4.5 Slow flows-mixed and penalty formulations131

4.6 Concluding remarks136

References136

5 Incompressible non-Newtonian flows141

5.1 Introduction141

5.2 Non-Newtonian flows-metal and polymer forming141

5.3 Viscoelastic flows154

5.4 Direct displacement approach to transient metal forming163

5.5 Concluding remarks165

References166

6 Free surface and buoyancy driven flows170

6.1 Introduction170

6.2 Free surface flows170

6.3 Buoyancy driven flows189

6.4 Concluding remarks191

References193

7 Compressible high-speed gas flow197

7.1 Introduction197

7.2 The governing equations198

7.3 Boundary conditions-subsonic and supersonic flow199

7.4 Numerical approximations and the CBS algorithm202

7.5 Shock capture203

7.6 Variable smoothing205

7.7 Some preliminary examples for the Euler equation206

7.8 Adaptive refinement and shock capture in Euler problems212

7.9 Three-dimensional inviscid examples in steady state217

7.10 Transient two-and three-dimensional problems226

7.11 Viscous problems in two dimensions227

7.12 Three-dimensional viscous problems240

7.13 Boundary layer-inviscid Euler solution coupling241

7.14 Concluding remarks242

References242

8 Turbulent flows248

8.1 Introduction248

8.2 Treatment of incompressible turbulent flows251

8.3 Treatment of compressible flows264

8.4 Large eddy simulation267

8.5 Detached Eddy Simulation（DES）270

8.6 Direct Numerical Simulation（DNS）270

8.7 Concluding remarks271

References271

9 Generalized flow through porous media274

9.1 Introduction274

9.2 A generalized porous medium flow approach275

9.3 Discretization procedure279

9.4 Non-isothermal flows282

9.5 Forced convection282

9.6 Natural convection284

9.7 Concluding remarks288

References289

10 Shallow water problems292

10.1 Introduction292

10.2 The basis of the shallow water equations293

10.3 Numerical approximation297

10.4 Examples of application298

10.5 Drying areas310

10.6 Shallow water transport311

10.7 Concluding remarks313

References314

11 Long and medium waves317

11.1 Introduction and equations317

11.2 Waves in closed domains-finite element models318

11.3 Difficulties in modelling surface waves320

11.4 Bed friction and other effects320

11.5 The short-wave problem320

11.6 Waves in unbounded domains（exterior surface wave problems）321

11.7 Unbounded problems324

11.8 Local Non-Reflecting Boundary Conditions（NRBCs）324

11.9 Infinite elements327

11.10 Mapped periodic（unconjugated）infinite elements327

11.11 Ellipsoidal type infinite elements of Burnett and Holford328

11.12 Wave envelope（or conjugated）infinite elements330

11.13 Accuracy of infinite elements332

11.14 Trefftz type infinite elements332

11.15 Convection and wave refraction333

11.16 Transient problems335

11.17 Linking to exterior solutions（or DtN mapping）336

11.18 Three-dimensional effects in surface waves338

11.19 Concluding remarks344

References344

12 Short waves349

12.1 Introduction349

12.2 Background349

12.3 Errors in wave modelling351

12.4 Recent developments in short wave modelling351

12.5 Transient solution of electromagnetic scattering problems352

12.6 Finite elements incorporating wave shapes352

12.7 Refraction364

12.8 Spectral finite elements for waves372

12.9 Discontinuous Galerkin finite elements（DGFE）374

12.10 Concluding remarks378

References378

13 Computer implementation of the CBS algorithm382

13.1 Introduction382

13.2 The data input module383

13.3 Solution module384

13.4 Output module387

References387

Appendix A Non-conservative form of Navier-Stokes equations389

Appendix B Self-adjoint differential equations391

Appendix C Postprocessing392

Appendix D Integration formulae395

Appendix E Convection-diffusion equations：vector-valued variables397

Appendix F Edge-based finite element formulation405

Appendix G Multigrid method407

Appendix H Boundary layer-inviscid flow coupling409

Appendix I Mass-weighted averaged turbulence transport equations413

Author index417

Subject index427