Finite Element Methods for Viscous Incompressible Flows

1st Edition

A Guide to Theory, Practice, and Algorithms

Authors: Max Gunzburger
Hardcover ISBN: 9780123073501
eBook ISBN: 9780323139823
Imprint: Academic Press
Published Date: 28th September 1989
Page Count: 288
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Table of Contents

Discretization of the Primitive Variable Formulation: A Primitive Variable Formulation. The Finite Element Problem and the Div-Stability Condition. Finite Element Spaces. Alternate Weak Forms, Boundary Conditions and Numerical Integration. Penalty Methods. Solution of the Discrete Equations: Newton's Method and Other Iterative Methods. Solving the Linear Systems. Solution Methods for Large Reynolds Numbers. Time Dependent Problems: A Weak Formulation and Spatial Discretizations. Time Discretizations. The Streamfunction-Vorticity Formulation: Algorithms for the Streamfunction-Vorticity Equations. Solution Techniques for Multiply Connected Domains. The Streamfunction Formulation: Algorithms for Determining Streamfunction Approximations. Eigenvalue Problems Connected with Stability Studies for Viscous Flows: Energy Stability Analysis of Viscous Flows. Linearized Stability Analysis of Stationary Viscous Flows. Exterior Problems: Truncated Domain-Artificial Boundary Condition Methods. Nonlinear Constitutive Relations: A Ladyzhenskaya Model and Algebraic Turbulence Models. Bingham Fluids. Electromagnetically or Thermally Coupled Flows: Flows of Liquid Metals. The Boussinesq Equations. Remarks on Some Topics That Have Not Been Considered: Problems, Formulations, Algorithms, and Other Issues That Have Not Been Considered. Bibliography. Glossary of Symbols. Index.


In this book, the author examines mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. The principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing, useful algorithms are also discussed. Although rigorous results are stated, no detailed proofs are supplied; rather, the intention is to present these results so that they can serve as a guide for the selection and, in certain respects, the implementation of algorithms.


Mathematicians, engineers, and others involved in practical computations.


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© Academic Press 1989
Academic Press
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@qu:"An excellent guide and can be strongly recommended." @source:--ZENTRALBLATI FUR MATHEMATIK @qu:"Due to the style chosen, the book is easy to read and should also be accessible for engineers who want to know about the variety of rigorous results has succeeded in his goal as formulated in the preface: in writing a book for those who want to get a quick taste of the main points and of the mathematical results available without delving into details." @source:--MATHEMATICAL REVIEWS @qu:"The book is written for the middle ground; the audience that can readily apply the material includes the applied mathematician and the theoretically disposed engineer who seek to use finite element methods for actual flowfield computations." @source:--SIAM REVIEW

About the Authors

Max Gunzburger Author

Affiliations and Expertise

Carnegie-Mellon University