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

D. B. Ingham, M. A. Kelmanson (Autoren)

Buch | Softcover

IV, 173 Seiten

1984 | 1. Softcover reprint of the original 1st ed. 1984
Springer Berlin (Verlag)
978-3-540-13646-0 (ISBN)

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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.

Content.- 1 - General Introduction.- 2 - An Integral Equation Method for the Solution of Singular Slow Flow Problems.- 3 - Modified Integral Equation Solution of Viscous Flows Near Sharp Corners.- 4 - Solution of Nonlinear Elliptic Equations with Boundary Singularities by an Integral Equation Method.- 5 - Boundary Integral Equation Solution of Viscous Flows with Free Surfaces.- 6 - A Boundary Integral Equation Method for the Study of Slow Flow in Bearings with Arbitrary Geometrics.- 7 - General Conclusions.

Erscheint lt. Verlag	1.8.1984
Reihe/Serie	Lecture Notes in Engineering
Zusatzinfo	IV, 173 p.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 244 mm
Gewicht	321 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Optik
	Technik
Schlagworte	Bipotentialgleichung • boundary • Boundary value problem • BVP • fluid mechanics • Geometry • Integral • Integralverfahren • Mechanics • Nichtlineare elliptische Differentialgleichung • Randwertproblem • Singularität (Math.) • Viskose Strömung
ISBN-10	3-540-13646-0 / 3540136460
ISBN-13	978-3-540-13646-0 / 9783540136460
Zustand	Neuware