## Numerical Methods for Fluid Dynamics: With Applications to GeophysicsThis scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean |

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### Contents

1 | |

Chapter
2 Ordinary Differential Equations | 35 |

Chapter
3 FiniteDifference Approximations for OneDimensional Transport | 89 |

Chapter
4 Beyond OneDimensional Transport | 147 |

Chapter
5 Conservation Laws and FiniteVolume Methods | 202 |

Chapter
6 SeriesExpansion Methods | 281 |

Chapter
7 SemiLagrangian Methods | 357 |

Chapter
8 Physically Insignificant Fast Waves | 392 |

Chapter
9 Nonreflecting Boundary Conditions | 453 |

Appendix
A Numerical Miscellany | 496 |

501 | |

511 | |

### Other editions - View all

Numerical Methods for Fluid Dynamics: With Applications to Geophysics Dale R. Durran No preview available - 2012 |

Numerical Methods for Fluid Dynamics: With Applications to Geophysics Dale R. Durran No preview available - 2010 |

Numerical Methods for Fluid Dynamics: With Applications to Geophysics Dale R. Durran No preview available - 2010 |

### Common terms and phrases

ˇ ˇ ˇ Ä x Ä accuracy Adams–Bashforth advection equation algorithm amplification factor amplitude boundary condition Boussinesq coefficients conservation law convergence coordinate Courant number damping defined difference differencing differential–difference diffusion discussed in Sect dispersion relation domain evaluated expansion functions finite finite-difference approximation finite-difference scheme finite-element first-order flow fluid flux flux-limited formula Fourier fourth-order Galerkin method gravity waves grid points group velocity horizontal hyperbolic implicit initial condition integration interpolation interval limit linear matrix mesh nC1j nodes nonlinear numerical approximation numerical solution obtained one-dimensional ordinary differential equations oscillation partial differential equations perturbations phase speed physical polynomial preceding equation problem propagation Rossby waves Runge–Kutta methods satisfy second-order semi-implicit semi-Lagrangian shallow-water shown in Fig simulation spatial derivatives spectral method spherical harmonics stable time step Suppose third-order tion tracer trajectory transform trapezoidal true solution truncation error two-dimensional unstable upstream values vertical wave number wavelengths zero