[PDF] Boundary Integral And Singularity Methods For Linearized Viscous Flow eBook

Author : C. Pozrikidis
Publisher : Cambridge University Press
Page : 276 pages
File Size : 38,93 MB
Release : 1992-02-28
Category : Mathematics
ISBN : 9780521406932

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In addition to theory, this study focuses on practical application and computer implementation in a coherent introduction to boundary integrals, boundary element and singularity methods for steady and unsteady flow at zero Reynolds numbers.

Author : D. B. Ingham
Publisher : Springer Science & Business Media
Page : 165 pages
File Size : 11,1 MB
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 3642823300

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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.

Author : P.K. Banerjee
Publisher : CRC Press
Page : 368 pages
File Size : 34,43 MB
Release : 1990-05-31
Category : Science
ISBN : 1482296551

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This volume demonstrates that boundary element methods are both elegant and efficient in their application to time dependent time harmonic problems in engineering and therefore worthy of considerable development.

Author : Robert A. Brown
Publisher : Springer Science & Business Media
Page : 122 pages
File Size : 29,34 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461384133

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It is increasingly the case that models of natural phenomena and materials processing systems involve viscous flows with free surfaces. These free boundaries are interfaces of the fluid with either second immiscible fluids or else deformable solid boundaries. The deformation can be due to mechanical displacement or as is the case here, due to phase transformation; the solid can melt or freeze. This volume highlights a broad range of subjects on interfacial phenomena. There is an overview of the mathematical description of viscous free-surface flows, a description of the current understanding of mathematical issues that arise in these models and a discussion of high-order-accuracy boundary-integral methods for the solution of viscous free surface flows. There is the mathematical analysis of particular flows: long-wave instabilities in viscous-film flows, analysis of long-wave instabilities leading to Marangoni convection, and de§ scriptions of the interaction of convection with morphological stability during directional solidification. This book is geared toward anyone with an interest in free-boundary problems, from mathematical analysts to material scientists; it will be useful to applied mathematicians, physicists, and engineers alike.

Author : Mirela Kohr
Publisher : WIT Press (UK)
Page : 456 pages
File Size : 23,6 MB
Release : 2004
Category : Science
ISBN :

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This book presents the fundamental mathematical theory of, and reviews state-of-the-art advances in, low Reynolds number viscous incompressible flow. The authors devote much of the text to the development of boundary integral methods for slow viscous flow pointing out new and important results.

Author : Vladimir Kompiš
Publisher : Springer
Page : 231 pages
File Size : 23,83 MB
Release : 2014-05-04
Category : Technology & Engineering
ISBN : 3709125480

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The book outlines special approaches using singular and non-singular, multi-domain and meshless BEM formulations, hybrid- and reciprocity-based FEM for the solution of linear and non-linear problems of solid and fluid mechanics and for the acoustic fluid-structure interaction. Use of Trefftz functions and other regularization approaches to boundary integral equations (BIE), boundary contour and boundary node solution of BIE, sensitivity analysis, shape optimization, error analysis and adaptivity, stress and displacement derivatives in non-linear problems smoothing using Trefftz polynomials and other special numerical approaches are included. Applications to problems such as noise radiation from rolling bodies, acoustic radiation in closed and infinite domains, 3D dynamic piezoelectricity, Stefan problems and coupled problems are included.