Stavros Kontos from DTU Mechanical Engineering defends his PhD,
Robust Numerical Methods for Nonlinear Wave-Structure Interaction in a Moving Frame of Reference,
Wednesday, 16th of November, 2016 at 14:00. The defence takes place at DTU Lyngby, in Building 341, Auditorium 22. Professor Harry B. Bingham is principal supervisor, Associate Professor Allan P. Engsig-Karup and Dr. Ole Lindberg are co-supervisors.
Abstract:
This project is focused on improving the state of the art for predicting the interaction between nonlinear ocean waves and marine structures. To achieve this goal, a flexible order finite difference potential fl ow solver has been extended to calculate for fully nonlinear wave-structure interaction problems at forward speed.
The model utilises the e ciency of nite dierence methods on structured grids and exploits the fl exibility of a novel Immersed Boundary Method (IBM) based on Weighted Least Squares (WLS) for the approximation of the no-fl ux boundary condition on the body surface. As a result, the grid generation is very simple and the need for regridding when considering moving body problems is avoided.
The temporal oscillations related to the IBM method and moving boundaries are minimized by suffi cient spatial resolution and an increased time-step size.
The time-dependant physical domain is mapped to a time-invariant computational domain with a sigma transformation. For a smooth and continuous transformation a C2 continuous free surface is required over the entire domain. Thus, an arti ficial free surface that respects this property is created in the interior of the body using a seventh order polynomial. The forward speed problem is formulated in a moving coordinate system attached to the mean position of the body. Robust approximations for all combinations of forward speed and wave velocity are obtained by expressing the free surface boundary conditions in Hamilton-Jacobi form and using a Weighted Essentially Non-Oscillatory (WENO) scheme for the convective derivatives. The linear WENO weights are derived with a new procedure that is suitable for numerical implementation and avoids the limitations of existing tabulated WENO coffie cients.
Furthermore, a simplifi ed smoothness indicator that performs as well as the tabulated versions is proposed. Explicit high-order Runge-Kutta time integration and a Lax-Friedrichs-type numerical flux complete the scheme. The solver was tested on the two-dimensional zero speed wave radiation problem and the steady forward speed problem with satisfactory results and thus, the proof of concept for extending the methodology to three dimensions is established.