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  3. High-Order Methods for Incompressible Fluid Flow
  • Cited by 477
  • M. O. Deville, École Polytechnique Fédérale de Lausanne, P. F. Fischer, Argonne National Laboratory, Illinois, E. H. Mund, Université Libre de Bruxelles and Université Catholique de Louvain
Publisher:
Cambridge University Press
Online publication date:
August 2009
Print publication year:
2002
Online ISBN:
9780511546792
DOI:
https://doi.org/10.1017/CBO9780511546792
Subjects:
Mathematics, Computational Science, Geometry and Topology, Numerical Analysis and Computational Science
Series:
Cambridge Monographs on Applied and Computational Mathematics (9)
Information

Book description

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.

Reviews

'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.’

Source: 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.’

Source: Zeitschrift für Angewandte Mathematik und Mechanik

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