SEMINAR “Contemporary Analysis and Partial Differential Equations” (10.04.2023)

SEMINAR “Contemporary Analysis and Partial Differential Equations” (10.04.2023)





Yuriy Semenov

Institute of Hydromechanics of the NAS of Ukraine, Ukraine

Nonlinear 2D Problems of Free Surface/Interface Flows

Monday, 10 April 2023 at 13:00

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The mechanics of flexure-gravity waves are both challenging and exciting. In the last decade, this topic has received much attention due to ice melting in the Arctic Regions and opening new routs for ships. Most of the studies are based on linear theories, while the nonlinear effects play an important role in the comprehensive physical understanding of the phenomena. The development of the nonlinear theory of the flexural-gravity waves requires advanced analytical tools for solving fluid/structure interaction problems. In this seminar talk, we focus our attention on the methodology for solving fluid/structure interaction problems involving free-surface and interface flows with an elastic sheet on the liquid surface. We consider methodology development from the classical hodograph method to the advanced integral hodograph method which was successfully applied for solving water-entry problems, and free surface problems for high-speed planning hulls and hydrofoil crafts. We show how the boundary-value problem can be reduced to a system of integral equations, which are then solved numerically. Special attention will be given to analysing the classical problem of flexural-gravity waves generated by an obstruction on the bottom of the channel. The existence of the solution and the interface shape for both sub and super-critical flow regions will be discussed.

Seminar video report

Supplementary materials: Presentation

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