Solving the linear radiation problem in 3D using the spectral element method

  • Visbech, Jens (Technical University of Denmark (DTU), Department of Applied Mathematics and Computer Science)
  • Engsig-Karup, Allan Peter (Technical University of Denmark (DTU), Department of Applied Mathematics and Computer Science)
  • Bingham, Harry (Technical University of Denmark (DTU), Department of Civil and Mechanical Engineering)

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Linear impulsive formulations are widely used for modeling interactions between ocean waves and floating offshore structures. The basic principle of these types of formulations is to force the floating body with a velocity impulse and study the resulting force on the body based on potential flow theory [5], thus neglecting viscous forces and assuming that the flow is incompressible. The set of governing equations, stated in terms of potential flow equations with a free surface, can be discretized using -- in principle any -- numerical methods. In this talk, we present our work on a higher-order Galerkin-based spectral element method (SEM), that provides a basis for efficient modeling of wave propagation and wave-structure modeling taking into account complex geometries, e.g. see [1,4]. In [2] and [3] results of the first 2D SEM-based model for solving the linear radiation potential through impulsive formulations were presented. In this work, we present a 3D extension of this work by showing the results of simulations of various floating structures with varying geometrical complexity. This includes using higher-order elements to represent curved boundaries, analysis of stability, convergence, and scalability.