Numerical methods for the computation of stationary free surfaces is the subject of much current research in computational engineering. The present report is directed towards free surfaces in maritime engineering. Of interest here are the long steady waves generated by hovercraft and ships, the gravity waves. In the present report an existing 2D iterative method for the computation of stationary gravity-wave solutions is extended to 3D, numerically investigated, and improved. The method employs the so-called quasi free-surface boundary condition. As test cases we consider gravity-wave patterns due to hovercraft-type pressure perturbations imposed at the free surface of a steady, uniform horizontal flow. The effects are studied of the distance of the imposed pressure distribution to the far-field boundary, the magnitude of the imposed pressure perturbation, the mesh widths, as well as the presence of a no-slip boundary intersecting the free surface. In all experiments, our focus is on the convergence behavior of the free-surface iteration process.

Free boundary problems (msc 35R35), Navier-Stokes equations (msc 76D05), Waves (msc 76D33)
Life Sciences (theme 5), Energy (theme 4)
CWI
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Lewis, M.R, & Koren, B. (2002). Efficient computation of steady, 3D water-wave patterns, application to hovercraft-type flows. Modelling, Analysis and Simulation [MAS]. CWI.