## Basics of Fluid Mechanics and Introduction to Computational Fluid DynamicsThe present book – through the topics and the problems approach – aims at filling a gap, a real need in our literature concerning CFD (Computational Fluid Dynamics). Our presentation results from a large documentation and focuses on reviewing the present day most important numerical and computational methods in CFD. Many theoreticians and experts in the field have expressed their - terest in and need for such an enterprise. This was the motivation for carrying out our study and writing this book. It contains an important systematic collection of numerical working instruments in Fluid Dyn- ics. Our current approach to CFD started ten years ago when the Univ- sity of Paris XI suggested a collaboration in the field of spectral methods for fluid dynamics. Soon after – preeminently studying the numerical approaches to Navier–Stokes nonlinearities – we completed a number of research projects which we presented at the most important inter- tional conferences in the field, to gratifying appreciation. An important qualitative step in our work was provided by the dev- opment of a computational basis and by access to a number of expert softwares. This fact allowed us to generate effective working programs for most of the problems and examples presented in the book, an - pect which was not taken into account in most similar studies that have already appeared all over the world. |

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### Contents

1 | |

16 | |

Constitutive Laws | 26 |

vi | 43 |

Shock Waves | 49 |

x | 68 |

5 | 79 |

Almost Potential Fluid Flow | 92 |

INTRODUCTION TO NUMERICAL SOLUTIONS | 196 |

FINITEDIFFERENCE METHODS | 247 |

Elliptic Equations | 295 |

FINITE ELEMENT AND BOUNDARY ELEMENT | 345 |

LeastSquares Finite Element Method LSFEM | 356 |

THE FINITE VOLUME METHOD | 397 |

SPECTRAL METHODS | 439 |

Appendix | 483 |

### Other editions - View all

Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics Titus Petrila,Damian Trif No preview available - 2008 |

Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics Titus Petrila,Damian Trif No preview available - 2014 |

### Common terms and phrases

advection airfoil algorithm approximation axis boundary conditions boundary layer calculated Cauchy problem characteristic choose coefficients complex potential components compressible computational domain conformal mapping constant continuity contour coordinates corresponding curves defined denote depends determined Dirichlet discretization elliptic equa error Euler Euler system exact solution example Figure finite differences method finite element method fluid flow formulas given grid points incompressible fluid incompressible fluid flow infinity initial conditions integral inviscid fluid iterations Let us consider linear Mach MATLAB matrix mesh Navier–Stokes equations Navier–Stokes system nodes nondimensionalized nonlinear numerical solution obstacle obtain Obviously order derivatives panel parameters partial differential equation perturbation physical domain plane polynomial pressure remark respectively result Reynolds number satisfies scheme second order shock wave solve space spatial derivative stability steady step Stokes stream function supersonic Suppose surface tensor theorem tion transformation uniform unique unknown function variables vector velocity potential viscous vortex sheets vorticity wave number zero