Boussinesq/Navier Stokes Two Way Coupling for the Simulation of Water Wave/Structure Interaction

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

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Wave/structure interactions are often simulated using a single mathematical model in the numerical domain. However this approach leads to one major trade off between efficiency and precision. We propose an alternative strategy: splitting the numerical domain in a small local subdomain to handle the structure dynamic and a global one dedicated to the propagation of the waves and subsequently couple them to take advantage of either precision or efficiency. In particular, the local domain is solved by the Navier Stokes (NS) equations that can capture the strongly nonlinear effects present close to the structure. The global domain does not contain the structures and it's dedicated to wave propagation by asymptotic models, such as Boussinsesq models (B) that can efficiently simulate weakly nonlinear waves. The coupling strategy between the two models is inspired by the perfectly matched layer method where the exact solution is superimposed to the computed solution on a small layer thanks to a relaxation of the equations. The relaxation layer here works as a connection between the two models: the NS and B velocities values are exchanged between the domains using an explicit scheme that relaxes the computed solution of one model towards the other. Since waves are expected to propagate reciprocally between the global and the local domain, this method allows to have a two way coupling between models using multiple relaxing layers per domain. Preliminary results will also be presented in the framework of marine energy. Systems such as wave energy farm provides an ideal test case for model coupling where the floating converters are simulated by a NS local domain and the wave propagation by a global B domain.