Allan Engsig-Karup: Modelling wave-structure interaction in complex geometries using a high-order Boussinesq model

In a recent Ph.D. project the possibility of applying the Discontinuous Galerkin spectral/hp element method for the next generation of Boussinesq-type models has been investigated. These numerical methods have reached a level of maturity that turns them into an attractive alternative to the existing Boussinesq-type models, which traditionally have been based on finite difference methods in structured domains. In particular, we seek to take advantage of the geometrical flexibility of spectral/hp finite element methods to enable us to solve wave problems in increasingly complex environments. A nodal discontinuous Galerkin finite element method (DG-FEM) is used for the spatial discretization to solve a recently derived set of high-order Boussinesq-type equations [1] in complex and curvilinear geometries, and thereby amends the application range of previous numerical models. The new Boussinesq method allows for the accurate description of fully nonlinear and dispersive water waves in both shallow and deep waters, and to demonstrate and investigate the applicability of the model both linear and nonlinear test cases have been considered where water waves interact with bottom-mounted fully reflecting structures. References [1] Madsen, P. A., Bingham, H. B. and Liu, H. 2002 A new Boussinesq method for fully nonlinear waves from shallow to deep water. J. Fluid Mech. 462, pp. 1-30.

Dr. Allan Engsig-Karup is at Coastal, Maritime and Structural Engineering Technical University of Denmark (DTU) Lyngby, Denmark.