High-Order Methods for Incompressible Fluid Flow

ISBN-13: 9780521453097 / Angielski / Twarda / 2002 / 528 str.

E. H. Mund; P. F. Fischer; M. O. Deville

Opis

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications.

Recenzje

'… strongly recommended for engineers, computer scientists, and applied mathematicians who are interested in the numerical simulation of flow problems with high accuracy.' Zeitschrift für Angewandte Mathematik und Mechanik

Spis treści

Preface; 1. Fluid mechanics and computation: an introduction; 2. Approximation methods for elliptic problems; 3. Parabolic and hyperbolic problems; 4. Mutidimensional problems; 5. Steady Stokes and Navier-Stokes equations; 6. Unsteady Stokes and Navier-Stokes equations; 7. Domain decomposition; 8. Vector and parallel implementations; Appendix A. Preliminary mathematical concepts; Appendix B. Orthogonal polynomials and discrete transforms.