Boussinesq/Navier Stokes Two Way Coupling for the Simulation of Wave Energy Converters

  • Bosi, Umberto (INRIA Bordeaux Sud Ouest)
  • Bergmann, Michel (INRIA Bordeaux Sud Ouest)
  • Parisot, Martin (INRIA Bordeaux Sud Ouest)

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The standard approach when studying and simulating the interaction between waves and floating structures is to use a single mathematical model in the whole numerical domain. This brings to a trade off between precision and the computational speed: where high fidelity models can be used only for small domains as they are computationally heavy, simpler and more efficient models will lose potentially important information. The choice of the model becomes of key importance, especially for wave energy converters (WEC) as a high fidelity description of the dynamics will lead to better computed results for the converter it will be limited to only one WEC, making the study of energy farms challenging. We propose a hybrid approach that aims to mix a Navier Stokes (NS) model with asymptotic Boussinesq (B) models. Given the computational cost, NS is used only on a local scale: the domain will surround the floating structure to capture the strongly nonlinear wave/structure interaction and the complex WEC displacements. Afar from the structure, B models are enough to properly describe wave propagation and weakly nonlinear waves. Those models approximate the Euler wave equation by integrating it vertically thus reducing the original problem to a lower dimension one (R3 → R2), resulting in efficient models that take into account weakly nonlinear effects and non-hydrostatic kinematics. The B domain does not contain the WEC as the integrated nature of the model is not adapted to handle free floating structures. The coupling between the two models is inspired by the perfectly match layer method, however here the relaxation layer is used here to transfer the waves generated in the global domain to the local one. This approach can be easily expanded to propagate waves from the local domain to the propagation resulting in a two way coupling between models. This work will present the resulting coupled system that permits a precise description on the local scale of the wave energy converter while remaining efficient over a larger domain. It is also easily scalable to accommodate multiple NS domains for each WEC, potentially up to energy farms with reduced computational power. Preliminary results of the coupling will be presented.