Description
Book SynopsisHigh-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 app
Trade Review'This interesting book presents the range of certain mathematical, engineering as well as computer science topics that are the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. The present book is an excellent advanced textbook and a valuable reference on high-order methods applied to incompressible fluid flow problems. It is warmly recommended to computer scientists, engineers, and applied mathematicians interested in developing software for solving flow problems. It is also recommended to graduate students that have a background in fluid mechanics and numerical methods.' Mirela Kohr, Faculty of Mathematics
'The book is clearly written, with a good distribution of helpful figures and some pseudo-code to help unravel certain aspects of the algorithms … overall this book makes a strong contribution which enhances the available literature on this topic and endeavours to make spectral element methods more accessible to the general practitioner.' Classical and Quantum Gravity
'… 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
Table of ContentsPreface; 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.
