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Time-dependent conformal mapping of doubly-connected regions

Turner, Matthew and Bridges, Thomas (2015) Time-dependent conformal mapping of doubly-connected regions Advances in Computational Mathematics, 42 (4). pp. 947-972.


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This paper examines two key features of time-dependent conformal mappings in doubly-connected regions, the evolution of the conformal modulus Q(t) and the boundary transformation generalizing the Hilbert transform. It also applies the theory to an unsteady free surface flow. Focusing on inviscid, incompressible, irrotational fluid sloshing in a rectangular vessel, it is shown that the explicit calculation of the conformal modulus is essential to correctly predict features of the flow. Results are also presented for fully dynamic simulations which use a time-dependent conformal mapping and the Garrick generalization of the Hilbert transform to map the physical domain to a time-dependent rectangle in the computational domain. The results of this new approach are compared to the complementary numerical scheme of Frandsen (2004) (J. Comp. Phys. 196, 53-87) and it is shown that correct calculation of the conformal modulus is essential in order to obtain agreement between the two methods.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 17 December 2015
DOI : 10.1007/s10444-015-9448-6
Copyright Disclaimer : © The Author(s) 2016. This article is published with open access at The final publication is available at Springer via
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 04 Feb 2016 11:04
Last Modified : 16 Jan 2019 17:01

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