NDLI: Time-dependent conformal mapping of doubly-connected regions

Content Provider	Springer Nature Link
Author	Bridges, T. J. Turner, M. R.
Copyright Year	2015
Abstract	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 (J. Comput. Phys. 196:53–87, 14) and it is shown that correct calculation of the conformal modulus is essential in order to obtain agreement between the two methods.
Ending Page	972
Page Count	26
Starting Page	947
File Format	PDF
ISSN	10197168
e-ISSN	15729044
Journal	Advances in Computational Mathematics
Issue Number	4
Volume Number	42
Language	English
Publisher	Springer US
Publisher Date	2016-02-15
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fluid mechanics Visualization Computational Mathematics and Numerical Analysis Functions of a complex variable Conformal mapping Mathematical and Computational Biology Sloshing Hilbert-Garrick transformation Mathematical Modeling and Industrial Mathematics Computational Science and Engineering
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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