High-Order Methods for Incompressible Fluid Flow

This book covers the development of high-order numerical methods for the simulation of incompressible fluid flows in complex domains.

M. O. Deville (Author), P. F. Fischer (Author), E. H. Mund (Author)

9780521453097, Cambridge University Press

Hardback, published 15 August 2002

528 pages, 104 b/w illus.
23.7 x 15.8 x 3.8 cm, 0.944 kg

'… 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

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 attention given to enforcement of incompressibility. 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. Computer scientists, engineers and applied mathematicians interested in developing software for solving flow problems will find this book a valuable reference.

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.

Subject Areas: Fluid mechanics [PHDF], Applied mathematics [PBW], Numerical analysis [PBKS]