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This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.
Book Synopsis Singular Integral Equations and Discrete Vortices by : I. K. Lifanov
Download or read book Singular Integral Equations and Discrete Vortices written by I. K. Lifanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.
Method of Discrete Vortices presents a mathematical substantiation and in-depth description of numerical methods for solving singular integral equations with one-dimensional and multiple Cauchy integrals. The book also presents the fundamentals of the theory of singular equations and numerical methods as applied to solving problems in such branches of mechanics as aerodynamics, elasticity, and electrodynamics.
Book Synopsis Method of Discrete Vortices by : S. M. Belotserkovsky
Download or read book Method of Discrete Vortices written by S. M. Belotserkovsky and published by CRC Press. This book was released on 1992-12-31 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Method of Discrete Vortices presents a mathematical substantiation and in-depth description of numerical methods for solving singular integral equations with one-dimensional and multiple Cauchy integrals. The book also presents the fundamentals of the theory of singular equations and numerical methods as applied to solving problems in such branches of mechanics as aerodynamics, elasticity, and electrodynamics.
Book Synopsis An Introduction to the Discrete Vortex Method by : D. J. Maull
Download or read book An Introduction to the Discrete Vortex Method written by D. J. Maull and published by . This book was released on 1979 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
Book Synopsis Vortex Methods by : Georges-Henri Cottet
Download or read book Vortex Methods written by Georges-Henri Cottet and published by Cambridge University Press. This book was released on 2008-04-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
Book Synopsis A Discrete-Vortex Method for Studying the Wing Rock of Delta Wings by : Thomas G. Gainer
Download or read book A Discrete-Vortex Method for Studying the Wing Rock of Delta Wings written by Thomas G. Gainer and published by . This book was released on 2002 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis and Application of the Discrete Vortex Method by : Marie Dillon Dahleh
Download or read book Analysis and Application of the Discrete Vortex Method written by Marie Dillon Dahleh and published by . This book was released on 1990 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Understanding vortex dynamics is the key to understanding much of fluid dynamics. For this reason, many researchers, using a great variety of different approaches--analytical, computational, and experimental--have studied the dynamics of vorticity. The AMS-SIAM Summer Seminar on Vortex Dynamics and Vortex Methods, held in June 1990 at the University of Washington in Seattle, brought together experts with a broad range of viewpoints and areas of specialization. This volume contains the proceedings from that seminar. The focus here is on the numerical computation of high Reynolds number incompressible flows. Also included is a smaller selection of important experimental results and analytic treatments. Many of the articles contain valuable introductory and survey material as well as open problems. Readers will appreciate this volume for its coverage of a wide variety of numerical, analytical, and experimental tools and for its treatment of interesting important discoveries made with these tools.
Book Synopsis Vortex Dynamics and Vortex Methods by : Christopher Radcliff Anderson
Download or read book Vortex Dynamics and Vortex Methods written by Christopher Radcliff Anderson and published by American Mathematical Soc.. This book was released on 1991-12-23 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding vortex dynamics is the key to understanding much of fluid dynamics. For this reason, many researchers, using a great variety of different approaches--analytical, computational, and experimental--have studied the dynamics of vorticity. The AMS-SIAM Summer Seminar on Vortex Dynamics and Vortex Methods, held in June 1990 at the University of Washington in Seattle, brought together experts with a broad range of viewpoints and areas of specialization. This volume contains the proceedings from that seminar. The focus here is on the numerical computation of high Reynolds number incompressible flows. Also included is a smaller selection of important experimental results and analytic treatments. Many of the articles contain valuable introductory and survey material as well as open problems. Readers will appreciate this volume for its coverage of a wide variety of numerical, analytical, and experimental tools and for its treatment of interesting important discoveries made with these tools.
Book Synopsis Discrete Vortex Method for Two-dimensional Flow Past Bodies Ofarbitrary Shape Undergoing Prescribed Rotary and Translationalmotion by : J. Honore Walther
Download or read book Discrete Vortex Method for Two-dimensional Flow Past Bodies Ofarbitrary Shape Undergoing Prescribed Rotary and Translationalmotion written by J. Honore Walther and published by . This book was released on 1994 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Discrete Vortex Method Analysis Tool for Control of Flows with Trapped Vortices by : Abdessalem Bouferrouk
Download or read book A Discrete Vortex Method Analysis Tool for Control of Flows with Trapped Vortices written by Abdessalem Bouferrouk and published by . This book was released on 2007 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discrete Vortex Method and Turbulence by : S. M. Belotserkovsky
Download or read book Discrete Vortex Method and Turbulence written by S. M. Belotserkovsky and published by . This book was released on 1994 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
