Bergmann, M.

Bosi, U.

Parisot, M.

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Boussinesq/Navier Stokes two way coupling for the simulationof wave energy convertersUmberto Bosi∗, Michel Bergmann∗ and Martin Parisot∗∗Centre de Recherche INRIA Bordeaux Sud-Ouest200 Avenue de la Vieille Tour, 33405 Talence, Francee-mail: umberto.bosi@inria.fr,ABSTRACTThe standard approach when studying and simulating the interaction between waves and floatingstructures is to use a single mathematical model in the whole numerical domain. This bringsto a trade off between the precision of the simulation and the computational speed to solve themodel: where high fidelity models can be used only for small computational domains as theyare computationally heavy, simpler and more efficient models will lose potentially importantinformation. The choice of the model becomes of key importance, especially for wave energyconverters (WEC) as an accurate description of the wave dynamics will lead to better estimatedresults for the converter. However, choosing a high fidelity model will limit the simulation toonly one WEC, making the study of energy farms challenging.To overcome these limitations, we propose a hybrid approach that aims to mix a low perfor-mance, high fidelity Navier Stokes (NS) model [1] with the faster performances of asymptoticmodels such as Boussinesq (B) models [2, 3]. Given the computational cost, NS is be usedonly on a local scale: the domain will surround the floating structure to capture at best thewave/structure interaction, which may involve strong nonlinearities, overtopping and complexWEC displacements. Afar from the structure, asymptotic models are enough to properly de-scribe wave propagation and weakly nonlinear waves. The Boussinesq models approximate theEuler wave equation by integrating it vertically thus reducing the original problem to a lowerdimension one (R3 → R2), resulting in efficient models that take into account weakly nonlin-ear effects and non-hydrostatic kinematics. The B domain does not contain the WEC as theintegrated 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 where theexact solution is superimposed to the simulation solution on a small layer thanks to a relaxationof the model [4]. This relaxation layer is used here to transfer the waves generated in the globaldomain to the local one [5]. Moreover, this approach can be easily expanded to propagate wavesfrom the local NS domain back to the B domain resulting in a two way coupling between models.This work will present the resulting coupled system that permits a precise description on the localscale of the wave energy converter while remaining efficient over the larger propagation domain.It is also easily scalable to accommodate multiple NS domains for each WEC, potentially up tofull wave energy farms with a reduced use of computational power. Preliminary results of thecoupling will be presented.REFERENCES[1] Bergmann, M., Carlino, M. G., Iollo, A., & Telib, H. (2022). ADER scheme for incom-pressible Navier-Stokes equations on Overset grids with a compact transmission condition.Journal of Computational Physics, 467, 111414.[2] Bosi, U., Engsig-Karup, A. P., Eskilsson, C., & Ricchiuto, M. (2019). A spectral/hp elementdepth-integrated model for nonlinear wave–body interaction. Computer Methods in AppliedMechanics and Engineering, 348, 222-249.2[3] Parisot, M. (2019). Entropy-satisfying scheme for a hierarchy of dispersive reduced modelsof free surface flow. https://doi.org/10.1002/fld.4766.[4] Appelö, D., Hagstrom, T., & Kreiss, G. (2006). Perfectly matched layers for hyperbolic sys-tems: General formulation, well-posedness, and stability. SIAM Journal on Applied Math-ematics, 67(1), 1–23. https://doi.org/10.1137/050639107[5] Aliyar, S., Ducrozet, G., Bouscasse, B., Bonnefoy, F., Sriram, V., Ferrant, P. (2022). Nu-merical coupling strategy using HOS-OpenFOAM-MoorDyn for OC3 Hywind SPAR typeplatform. Ocean Engineering, 263. https://doi.org/10.1016/j.oceaneng.2022.112206

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

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

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