Nonlinear Waves Seminar - Matthew Turner
| Event Description: Matthew Turner, Department of Mathematics, University of Surrey Time-dependent conformal mappings with applications to nonlinear sloshing problems In this talk we examine 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. Results of this theory are applied to 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, such as the free surface evolution. Ìý We also present results 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)Ìý and it is shown that correct calculation of the conformal modulus is essential in order to obtain agreement between the two methods. |
| Location Information: ÌýÌý() 1111 Engineering DR Boulder, CO Room:Ìý226: Applied Math Conference Room |
| Contact Information: Name: Ian Cunningham Phone: 303-492-4668 Email: amassist@colorado.edu |