Reduced Order Modelling for Wave-Structure Modelling

In offshore engineering, the simulation of ocean waves and their interaction with structures has become more prominent. High-fidelity simulations of these problems are costly and burden the computational resources. To address this issue, we investigate proper orthogonal decomposition (POD) [1] based reduced-order modelling for wave structure interaction problems of relevance for offshore engineering. The POD method is based on generating a low-dimensional and much more efficient reduced order model representing the full order model based on a set of governing equations, e.g., describing fully nonlinear potential flow [2]. Therefore, significant time and cost savings can be achieved through using POD for the Laplace problem as demonstrated already for dispersive and nonlinear water wave modelling [3]. In this talk, we present our latest progress on developing reduced order models based on temporal discretizations using explicit Runge-Kutta methods and the spatial discretizations with the spectral element method (SEM) that supports unstructured meshes allowing for the handling of the wave propagation problem as well as the geometries of complex structures [4,5]. The results of several numerical tests used as benchmark problems are presented, illuminating that acceleration of more than two orders of magnitude is possible.