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Lecture Notes in Engineering

Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems

Authors: Ingham, D. B., Kelmanson, M. A.

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About this book

Harmonic and biharmonic boundary value problems (BVP) arising in physical situations in fluid mechanics are, in general, intractable by analytic techniques. In the last decade there has been a rapid increase in the application of integral equation techniques for the numerical solution of such problems [1,2,3]. One such method is the boundary integral equation method (BIE) which is based on Green's Formula [4] and enables one to reformulate certain BVP as integral equations. The reformulation has the effect of reducing the dimension of the problem by one. Because discretisation occurs only on the boundary in the BIE the system of equations generated by a BIE is considerably smaller than that generated by an equivalent finite difference (FD) or finite element (FE) approximation [5]. Application of the BIE in the field of fluid mechanics has in the past been limited almost entirely to the solution of harmonic problems concerning potential flows around selected geometries [3,6,7]. Little work seems to have been done on direct integral equation solution of viscous flow problems. Coleman [8] solves the biharmonic equation describing slow flow between two semi infinite parallel plates using a complex variable approach but does not consider the effects of singularities arising in the solution domain. Since the vorticity at any singularity becomes unbounded then the methods presented in [8] cannot achieve accurate results throughout the entire flow field.

Table of contents (7 chapters)

  • General Introduction

    Ingham, Derek B. (et al.)

    Pages 1-17

  • An Integral Equation Method for the Solution of Singular Slow Flow Problems

    Ingham, Derek B. (et al.)

    Pages 19-51

  • Modified Integral Equation Solution of Viscous Flows Near Sharp Corners

    Ingham, Derek B. (et al.)

    Pages 53-87

  • Solution of Nonlinear Elliptic Equations with Boundary Singularities by an Integral Equation Method

    Ingham, Derek B. (et al.)

    Pages 89-113

  • Boundary Integral Equation Solution of Viscous Flows with Free Surfaces

    Ingham, Derek B. (et al.)

    Pages 115-143

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-642-82330-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $149.99
price for USA in USD
  • ISBN 978-3-540-13646-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems
Authors
Series Title
Lecture Notes in Engineering
Series Volume
7
Copyright
1984
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin, Heidelberg
eBook ISBN
978-3-642-82330-5
DOI
10.1007/978-3-642-82330-5
Softcover ISBN
978-3-540-13646-0
Series ISSN
0176-5035
Edition Number
1
Number of Pages
IV, 173
Topics