A unified spectral/hp element depth-integrated Boussinesq model for nonlinear wave-floating body interaction

Umberto Bosi 1
1 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : The wave energy sector relies heavily on mathematical modelling and simulation of the interactions between waves and floating bodies. In this work, we have developed a medium-fidelity wave-body interaction model for the simulation of truncated surface piercing structures operating in heave motion, such as point absorbers wave energy converters (WECs). The motivation of the work lies in the present approach to wave-body interaction. The standard approach is to use models based on linear potential flow (LPF). LPF models are based on the small amplitude/ small motion assumption and, while highly computational efficient, cannot account for nonlinear hydrodynamic effects (except for Morison-type drag). Nonlinear effects are particularly important for WEC operating in resonance, or in nearshore regions where wave transformations are expected. More recently, Reynolds Averaged Navier-Stokes (RANS) simulations have been employed for modelling WECs. RANS is a complete and accurate model but computationally very costly. At present RANS models are therefore unsuited for the optimization of single devices, not to mention energy farms. Thus, we propose a numerical model based built on Boussinesq-type equations to include wave-wave interaction as well as finite body motion in a computationally efficient formulation. Boussinesq-type equations are depth-integrated wave models and are standard engineering tool for numerical simulation of propagation of nonlinear wave in shallow water and coastal areas. Thanks to the elimination of the vertical dimension and the avoidance of a time-dependent computational the resulting model is very computational efficient. Jiang (Jiang, 2001) proposed a unified Boussinesq model, decomposing the problem into free surface and body domains. Notably, in Jiang’s methodology also the body domain is modeled by a depth-integrated approach –hence the term unified. As all models based on Boussinesq-type equations, the model is limited to shallow and intermediate depth regimes. We consider the Madsen and Sørensen model, an enhanced Boussinesq model, for the propagation of waves. We employ a spectral/hp finite element method (SEM) to discretize the governing equations. The continuous SEM is used inside each domain and flux-based coupling conditions are derived from the discontinuous Galerkin method. The use of SEM give support for the use of adaptive meshes for geometric flexibility and high-order accurate approximations makes the scheme computationally efficient. In this thesis, we present 1D results for the propagation and interaction of waves with floating structures. The 1D model is verified using manufactured solutions. The model is then validated against published results for wave-body interaction. The hydrostatic cases (forced motion and decay test) are compared to analytical and semi-analytical solutions (Lannes, 2017), while the non-hydrostatic tests (fixed pontoon and freely heaving bodies) are compared to RANS reference solutions. The model is easily extended to handle multiple bodies and a proof-of-concept result is presented. Finally, we implement the latching technique, a method to control the movement of the body such that the response to the wave movement is improved. The model is extended to two horizontal dimensions and verified and validated against manufactured solutions and RANS simulations. The model is found to have a good accuracy both in one and two dimensions and is relevant for applications of waves interacting with wave energy devices. The model can be extended to simulate more complex cases such as WEC farms/arrays or include power generation systems to the device.
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Umberto Bosi. A unified spectral/hp element depth-integrated Boussinesq model for nonlinear wave-floating body interaction. Modeling and Simulation. Université de Bordeaux, 2019. English. ⟨NNT : 2019BORD0084⟩. ⟨tel-02297587⟩

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