Yyanis graduated from the University of Oxford in 2017 with an MMath in Mathematics, with a broad interest in applications. He has undertaken summer projects on topics in fluid dynamics at Oxford and Perm Krai, Russia, and has written undergraduate and Master’s theses on the topics of Thermohaline circulation oceanography and the Stokes wave. Outside of mathematics, Yyanis enjoys sports (occasionally seriously but mainly frivolously), films, and music.

Research project title:
Numerical and analytical approaches using complex ray theory and exponential asymptotics in 3D wave-structure interactions

Supervisor(s):
Philippe Trinh, Paul Milewski

Project description:
Despite significant advances in computational hardware and numerical algorithms, the simulation of fully nonlinear three-dimensional free-surface flows around blunt-bodied objects remains particularly limited. On account of the processing power required, most modern desktop (and in some cases high-performance) computations still require the use of simplifying geometrical assumptions and coarse meshes on the order of a hundred points per spatial dimension. In contrast, numerical simulations of comparable two-dimensional flows can be routinely done with O(1000) grid points in the spatial dimension. There continues to be a need for the analytical theories that can provide explicit asymptotic descriptions of the flow properties, particularly for the use of efficient hybrid numerical-analytical approaches. Recently, there has been success in developing new asymptotic techniques for studying linear wave-structure flows in three-dimensions. These techniques are based on the use of exponential asymptotics applied to low-speed hydrodynamical flows. Yyanis’s research develops new analytical and numerical techniques related to the area of complex ray theory and asymptotic analysis, to extend these ideas to nonlinear problems.