Numerical analysis of various artificial damping schemes in a three-dimensional numerical wave tank

Abstract

Various artificial damping schemes for progressive water waves were evaluated in a three-dimensional numerical wave tank (3D NWT). Five types of damping schemes were applied to the end of a computational domain and their damping capabilities were compared to find an optimum artificial damping scheme. The 3D NWT was based on a nine-node, bi-quadratic, higher-order boundary element method (HOBEM). A semi-Lagrangian approach known as the Mixed-Eulerian–Lagrangian (MEL) method was used to capture the nonlinear free surface fluctuation. A Runge–Kutta fourth-order time integration scheme was used for time marching to produce a time history of water surface elevations. For efficient damping performance, four different ramping functions were introduced and applied to the damping coefficients, and their influences were evaluated in order to select an optimal ramping shape along the artificial damping zone. The conservation of total energy in the computational domain was ensured to verify wave dissipation in the artificial damping zone. The wave elevations at different locations in the damping zone were also compared in order to appraise the damping capabilities of the respective damping schemes. The optimal numerical damping scheme associated with a proper damping shape over a range of damping zones was proposed for an efficient numerical beach.