Conformal contour dynamics in bounded domains |
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| Authors: | Irene Gned Haysam Telib Luca Zannetti |
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| Institution: | 1. Instituto de Física Fundamental (IFF–CSIC), Serrano 123, 28006 Madrid, Spain;2. Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom;1. Dipartimento di Matematica ”F. Brioschi”, Politecnico di Milano, P.zza L. da Vinci, 32, 20133–Milano, Italy;2. Dipartimento di Matematica ”F. Enriques”, Università di Milano, Via C. Saldini 50, 20133–Milano, Italy;3. Department of Mathematics and Informatics, University of Sofia, J. Bourchier Bldg., 5, 1164–Sofia, Bulgaria;1. Instituto de Física Fundamental (IFF-CSIC), Serrano 123, 28006 Madrid, Spain;2. Department of Chemistry, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom;3. Instituto Superior de Tecnologías y Ciencias Aplicadas, Ave. Salvador Allende y Luaces, Quinta de Los Molinos, Plaza, La Habana 10600, Cuba;1. Institut de Mathématiques de Jussieu – Paris Rive Gauche, Campus des Grands Moulins, Bâtiment Sophie Germain, 75013 Paris, France;2. Courant Institute of Mathematical Sciences, 251 Mercer St, New York, NY 10012, United States |
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| Abstract: | A contour dynamics algorithm is presented for vortex patches in unbounded domains and in simply connected bounded domains. It is based on conformal mapping and spectral analysis. The inside and outside of a vortex patch are analytically mapped onto the inside and outside of the unit circles of two different complex planes. The flow field is determined by matching the inner and outer flows on the patch boundary. Following the Legras and Zeitlin conformal dynamics concept, the time evolution of the patch boundary is expressed by means of the time derivatives of the mapping functions. The presence of a bounding wall, which can be permeable and movable, is considered. The geometry and dynamics of the patch and the flow velocity on the bounding wall are represented by Fourier series; by assuming their coefficients as control parameters, the proposed formulation can be appealing for optimization and control purposes. Two numerical examples of the proposed technique are presented. |
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