Pieter Wesseling (auth.)9783540678533, 3540678530
The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state-of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary mathematical analysis. Attention is given to difficulties arising from geometric complexity of the flow domain and of nonuniform structured boundary-fitted grids. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. Numerical analysis of the shallow-water equations is included. The theory of hyperbolic conservation laws is treated. Godunov’s order barrier and how to overcome it by means of slope-limited schemes is discussed. An introduction is given to efficient iterative solution methods, using Krylov subspace and multigrid acceleration. Many pointers are given to current literature, to help the reader to quickly reach the current research frontier. |
Table of contents :
Front Matter….Pages I-XII
The basic equation of fluid dynamics….Pages 1-52
Partial differential equations: analytic aspects….Pages 53-80
Finite volume and finite difference discretization on nonuniform grids….Pages 81-109
The stationary convection-diffusion equation….Pages 111-161
The nonstationary convection-diffusion equation….Pages 163-226
The incompressible Navier-Stokes equations….Pages 227-262
Iterative methods….Pages 263-303
The shallow-water equations….Pages 305-338
Scalar conservation laws….Pages 339-396
The Euler equations in one space dimension….Pages 397-466
Discretization in general domains….Pages 467-502
Numerical solution of the Euler equations in general domains….Pages 503-530
Numerical solution of the Navier-Stokes equations in general domains….Pages 531-566
Unified methods for computing incompressible and compressible flow….Pages 567-601
Back Matter….Pages 603-644 |
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