## Computational Fluid DynamicsIncreasingly, computational fluid dynamics (CFD) techniques are being used to study and solve complex fluid flow and heat transfer problems. This comprehensive book ranges from elementary concepts for the beginner to state-of-the-art CFD for the practitioner. It begins with CFD preliminaries, in which the basic principles of finite difference (FD), finite element (FE), and finite volume (FV) methods are discussed and illustrated through examples, with step-by-step hand calculations. Then, FD and FE methods respectively are covered, including both historical developments and recent contributions. The next section is devoted to structured and unstructured grids, adaptive methods, computing techniques, and parallel processing. Finally, the author describes a variety of practical applications to problems in turbulence, reacting flows and combustion, acoustics, combined mode radiative heat transfer, multiphase flows, electromagnetic fields, and relativistic astrophysical flows. Students and practitioners - particularly in mechanical, aerospace, chemical, and civil engineering - will use this authoritative text to learn about and apply numerical techniques to the solution of fluid dynamics problems. |

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### Contents

Governing Equations | 29 |

PART TWO FINITE DIFFERENCE METHODS | 43 |

Solution Methods of Finite Difference Equations | 63 |

Incompressible Viscous Flows via Finite Difference Methods | 106 |

Compressible Flows via Finite Difference Methods | 120 |

Finite Volume Methods via Finite Difference Methods | 218 |

PART THREE FINITE ELEMENT METHODS | 241 |

Finite Element Interpolation Functions | 262 |

Adaptive Methods | 607 |

Computing Techniques | 644 |

References | 674 |

Applications to Chemically Reactive Flows and Combustion | 724 |

Applications to Acoustics | 796 |

Applications to Combined Mode Radiative Heat Transfer | 841 |

Applications to Multiphase Flows | 902 |

Applications to Electromagnetic Flows | 927 |

Linear Problems | 309 |

Nonlinear ProblemsConvectionDominated Flows | 347 |

Incompressible Viscous Flows via Finite Element Methods | 399 |

Compressible Flows via Finite Element Methods | 418 |

Miscellaneous Weighted Residual Methods | 462 |

Interaction | 486 |

Relationships between Finite Differences and Finite Elements | 509 |

PART FOUR AUTOMATIC GRID GENERATION ADAPTIVE METHODS | 531 |

Unstructured Grid Generation | 581 |

Applications to Relativistic Astrophysical Flows | 955 |

Astrophysical Flows | 967 |

Appendix A ThreeDimensional Flux Jacobians | 979 |

Appendix B Gaussian Quadrature | 985 |

Two Phase Flow Source Term Jacobians for Surface Tension | 993 |

Relativistic Astrophysical Flow Metrics Christoffel Symbols | 999 |

1007 | |

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### Common terms and phrases

algorithm applied approximations boundary layer Chapter Comp compressible conservation variables control surfaces control volume convection convergence coordinates differential equation diffusion test functions Dirichlet boundary conditions domain eigenvalues elliptic error Euler equations exact solution explicit FDV parameters finite difference equations finite element equations finite element methods finite volume methods flowfield fluid dynamics flux formulation Galerkin methods geometries given governing equations gradients grid hyperbolic implicit scheme incompressible flows integration interpolation functions inviscid Jacobian Lax-Wendroff linear Mach number matrix mesh Meth Navier-Stokes system Neumann boundary conditions nodal nonlinear numerical diffusion numerical diffusion test obtain one-dimensional order accuracy order upwind schemes parabolic Petrov-Galerkin physical polynomials pressure problems quadratic quadrilateral Reynolds number second order Section shown in Figure solved step supersonic system of equations Taylor series test functions three-dimensional triangle triangular element turbulent two-dimensional unstructured grids variation parameters vector velocity viscosity