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

  • Book
  • © 1984

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Authors:
  1. Derek B. Ingham

    1. Department of Applied Mathematical Studies, University of Leeds, Leeds, England

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  2. Mark A. Kelmanson

    1. Department of Applied Mathematical Studies, University of Leeds, Leeds, England

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Engineering (LNENG, volume 7)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-IV
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  2. General Introduction

    • Derek B. Ingham, Mark A. Kelmanson
    Pages 1-17

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

    • Derek B. Ingham, Mark A. Kelmanson
    Pages 19-51

  4. Modified Integral Equation Solution of Viscous Flows Near Sharp Corners

    • Derek B. Ingham, Mark A. Kelmanson
    Pages 53-87

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

    • Derek B. Ingham, Mark A. Kelmanson
    Pages 89-113

  6. Boundary Integral Equation Solution of Viscous Flows with Free Surfaces

    • Derek B. Ingham, Mark A. Kelmanson
    Pages 115-143

  7. A Boundary Integral Equation Method for the Study of Slow Flow in Bearings with Arbitrary Geometries

    • Derek B. Ingham, Mark A. Kelmanson
    Pages 145-167

  8. General Conclusions and Discussion for Further Work

    • Derek B. Ingham, Mark A. Kelmanson
    Pages 169-173
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Keywords

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.

Authors and Affiliations

  • Department of Applied Mathematical Studies, University of Leeds, Leeds, England

    Derek B. Ingham, Mark A. Kelmanson

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