Combined Eulerian-Lagrangian or Pseudo-Lagrangian Descriptions of Waves Caused by an Advancing Free Surface Disturbance

We develop a new methodology for the numerical modeling of nonlinear free surface waves, caused by an advancing free surface disturbance, based on combining Lagrangian and Eulerian, or pseudoLagrangian, methods for the time updating of free surface geometry and motion. We solve potential flow equations with a threedimensional (3D) higher-order Boundary Element Method (BEM; Grilli et al., 2000, 2001; and Sung and Grilli, 2005, for some more recent extensions). Specifically, the Lagrangian and Eulerian methods are combined in order to exploit their respective advantages. The full Lagrangian updating is very accurate for highly nonlinear waves, and the Eulerian or pseudo-Lagrangian methods yield smaller computational times because they allow using a shorter domain, particularly for the forward speed problem of an advancing disturbance on or below the free surface. As a validation application, we compute 3D nonlinear waves caused by a moving pressure patch. Numerical results show that the present methodology works quite well and gives reasonable wave resistance for numerical examples, as compared with theory, and other computations based on full Lagrangian and pseudoLagrangian methods.