## The Finite Element Method for Fluid DynamicsDealing with general problems in fluid mechanics, convection diffusion, compressible and incompressible laminar and turbulent flow, shallow water flows and waves, this is the leading text and reference for engineers working with fluid dynamics in fields including aerospace engineering, vehicle design, thermal engineering and many other engineering applications. The new edition is a complete fluids text and reference in its own right. Along with its companion volumes it forms part of the indispensable Finite Element Method series.New material in this edition includes sub-grid scale modelling; artificial compressibility; full new chapters on turbulent flows, free surface flows and porous medium flows; expanded shallow water flows plus long, medium and short waves; and advances in parallel computing. * A complete, stand-alone reference on fluid mechanics applications of the FEM for mechanical, aeronautical, automotive, marine, chemical and civil engineers. * Extensive new coverage of turbulent flow and free surface treatments * Accompanied by downloadable FEM source code |

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### Contents

1 | |

28 | |

Chapter 3 The characteristicbased split CBS algorithm A general procedure for compressible and incompressible flow | 79 |

Chapter 4 Incompressible Newtonian laminar flows | 110 |

Chapter 5 Incompressible nonNewtonian flows | 141 |

Chapter 6 Free surface and buoyancy driven flows | 170 |

Chapter 7 Compressible highspeed gas flow | 197 |

Chapter 8 Turbulent flows | 248 |

Appendix A Nonconservative form of NavierStokes equations | 389 |

Appendix B Selfadjoint differential equations | 391 |

Appendix C Postprocessing | 392 |

Appendix D Integration formulae | 395 |

vectorvalued variables | 397 |

Appendix F Edgebased finite element formulation | 405 |

Appendix G Multigrid method | 407 |

Appendix H Boundary layerinviscid flow coupling | 409 |

Chapter 9 Generalized flow through porous media | 274 |

Chapter 10 Shallow water problems | 292 |

Chapter 11 Long and medium waves | 317 |

Chapter 12 Shortwaves | 349 |

Chapter 13 Computer implementation of the CBS algorithm | 382 |

Appendix I Massweighted averaged turbulence transport equations | 413 |

417 | |

427 | |

Color Plate Section | 437 |

### Common terms and phrases

acoustic adaptive analysis approximation artiﬁcial Bettess boundary conditions boundary layer calculation CBS algorithm Chapter coefﬁcient Comp compressible Computer Methods convection deﬁned density deviatoric difﬁculties diffusion discussed domain error Euler Euler equations example ﬁeld ﬁne ﬁnite difference Finite element Finite element analysis Finite Element Method ﬁrst flow past ﬂow problems ﬂuid dynamics ﬂuid mechanics formulation Galerkin method Helmholtz equation incompressible ﬂow inﬁnite elements integration International Journal inviscid iteration Journal for Numerical linear Mach number Mech mesh Meth Methods in Applied Methods in Engineering Methods in Fluids Morgan Nithiarasu nodal nodes non-dimensional Numerical Methods O.C. Zienkiewicz obtained Peraire Petrov—Galerkin plane wave porous porous medium procedure reference reﬁnement Reynolds number scalar scheme shallow water shallow water equations shape functions shock shown in Fig solid mechanics solved speciﬁed steady-state step transient unstructured grid unstructured mesh values variable velocity viscoelastic viscosity wave equation zero