Modelling of Wave-structure Interaction for Cylindrical Structures using a Spectral Element Multigrid Method

Description

The need for advanced time-domain simulators for improved offshore engineering analysis are growing with the continued improvement in computational ressources. In line with this trend, we consider a fully nonlinear potential flow (FNPF) model discretised with a stabilised Galerkin Spectral Element Method [5] addressing the stability problems and lack of progress made for this type of modelling approach since the work of Robertson & Sherwin (1999) [11]. A recent review of the Spectral Element Method is given in [12]. In a recent study a SEM-based fully nonlinear potential flow model referred to as the FNPF-SEMmodel [4] was developed and then validated in a blindtest experiment [10] against experimental measurements for focusing waves interacting with a fixed FPSO structure. In this work, we consider a standard benchmark problem for cylindrical structures due to McCamy & Fuchs (1954) [9], with an objective to evaluate a new extension of this solver with a p-multigrid method with the aim to enable scalable O(n) complexity in work effort. Recently, the first proof of an efficient geometric p-multigrid method was demonstrated in 2D and in 3D[8], and in this work we provide some additional results based on refined developments of the algorithms with the aim of demonstrating the practical feasibility of using this new SEMbased solver for 3D analysis. Our main objective is to handle the wave propagation problem as well as the curvilinear features of offshore structures such as cylindrical structures within a single FNPF solver. In particular, the new FNPF-SEM p-multigrid solver makes it possible to address both wave propagation and wave-structure problems within a single solver. The p-multigrid method is designed to exploit the p-type convergence property in solving the Laplace problem, and by avoiding h-type convergence property it is possible to handle the representation of structural bodies with curvilinear features without refining the underlying mesh-topology. In this sense, this work contributes to demonstrating that the spectral element method is a technology that is useful for engineering analysis. It comes with the ability to represent offshore structures that can also be handled with methods such as HOBEM [7], however, SEM comes with sparse matrices after global assembly in the discrete problem, and therefore provides more efficient and better scalability than boundary element methods that comes with dense operators and much higher costs to achieve asymptotic scalability. By using a FNPF formulation it is possible to predict the horizontal and vertical hydrodynamic forces for marine structures placed offshore, and account for the nonlinear effects that are significant when standard frequency domain analysis falls short and time domain solutions may be used instead.

Period	7 Apr 2019 → 10 Apr 2019
Event title	34th International Workshop on Floating Bodies And Water Waves
Event type	Conference
Conference number	34th
Location	New Castle, Australia, New South WalesShow on map
Degree of Recognition	International