Efficient computation of steady, 3D water-wave patterns

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 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 boudary condition. As test cases we cosider gravity-wave patterns due to 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, and the mesh widths. In all experiments, our focus is on the convergence behavior of the free-surface iteration process.