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Computing Three-Dimensional Flexural-Gravity Water Waves

Banff International Research Station for Mathematical Innovation and Discovery

The goal of this work is to build on previous results by Parau et al. [1, 2, 3, 4] and produce a more efficient and accurate method for computing solutions to Euler's equations for water waves underneath an ice sheet in three dimensions. As was previously done, we solve the equations via a numerically implemented boundary integral equations method and utilize some high performance computing techniques. In this talk, we give details of the current methods and compare solutions for different models of the ice sheet. This is a joint work with Emilian Parau, Jean-Marc Vanden-Broeck and Paul Milewski. <br/> <br/> References: <ol> <li> E. I. Parau, and J.-M. Vanden-Broeck Nonlinear two- and three-dimensional free surface flows due to moving disturbances. Eur. J. Mech. B Fluid, Vol 21 (2002), pp. 643-656. </li> <li> E. I. Parau, J.-M. Vanden-Broeck and M. J. Cooker Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems. Physics of Fluids, Vol 17 (2005), pp. 1-9. </li> <li> E. I. Parau, J.-M. Vanden-Broeck and M. J. Cooker Nonlinear three- dimensional gravity-capillary solitary waves. J. Fluid Mech., Vol 536 (2005), pp. 99-105. </li> <li> E. I. Parau, and J.-M. Vanden-Broeck Three-dimensional waves beneath an ice sheet due to a steadily moving pressure. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., Vol 369 (2011), pp. 2973-2988. </li> </ol>

Mathematics; Fluid mechanics; Partial differential equations; Fluid dynamics

video/mp4

Author affiliation: UCL

2017-05-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61519

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/