## 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

INTRODUCTION TO MECHANICS OF CONTINUA | 1 |

VI | 9 |

General Principles | 16 |

Constitutive Laws | 26 |

DYNAMICS OF INVISCID FLUIDS | 51 |

Irrotational Flows of Incompressible Inviscid Fluids | 59 |

Principles of the Wing Profiles Theory | 70 |

Conformal Mapping | 79 |

The Cauchy Problem for Ordinary Differential Equations | 207 |

FINITEDIFFERENCE METHODS | 247 |

Discretization of the Partial Differential Equations | 253 |

Burgers Equation Without Shock | 277 |

Elliptic Equations | 295 |

Compact Finite Differences | 320 |

Coordinate Transformation | 335 |

FINITE ELEMENT AND BOUNDARY ELEMENT | 345 |

Almost Potential Fluid Flow | 92 |

Unsteady Irrotational Flows Generated by the Motion | 100 |

Notions on the Steady Compressible Barotropic Flows | 110 |

Mach Lines Weak Discontinuity Surfaces | 123 |

VISCOUS INCOMPRESSIBLE FLUID DYNAMICS | 133 |

Equivalent Formulations for the NavierStokes | 140 |

Vlli | 157 |

Plaque | 191 |

INTRODUCTION TO NUMERICAL SOLUTIONS | 197 |

### 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

accuracy algorithm approximation boundary conditions boundary layer calculated Cauchy problem circulation coefficients complex potential components computational domain conformal mapping conservation constant continuity equation continuum contour coordinates corresponding curve defined denote depends derivative determined discretization error Euler Euler equations Euler system exact solution example Figure finite differences finite differences method finite element method finite volume finite volume method fluid flow formulas Fourier given grad gradp gradv grid points incompressible initial conditions integral inviscid fluid iterations Let us consider linear mass MATLAB matrix motion Navier-Stokes equations nodes numerical solution obtain Obviously panel parameters particles piecewise plane polynomial pressure remark respectively result Reynolds number satisfies scalar scheme second order shock solve space spatial steady step Stokes stream function surface tensor theorem thermodynamic tion torsor transformation unique unknown functions variables vector velocity potential viscous vortex sheet vorticity wave zero