Dr. Stéphane Popinet

National Institute of Water and Atmospheric Research (NIWA), Wellington/NZ

and Université Pierre et Marie Curie, Paris

Applications in marine and coastal engineering, flood hazard prevention and oceanatmosphere interactions require the description of free surface dynamics on a wide range of scales: from centimetres to thousands of kilometres. Simulation of unsteady free-surface flows has proved to be one of the most challenging disciplines of computational research.

Robust numerical descriptions of these problems can be facilitated through a hierarchy of theoretical approximations of the unsteady underlying equations of motion. Spatial scales can vary by orders-of-magnitude within these models.

Space and time adaptive approaches have been developed within the Gerris Flow Solver (http://gfs.sf.net). I will show how such approaches can help solve these problems efficiently.

Applications include:

• small-scale Navier-Stokes simulations of air/water interaction;
• medium-scale nonlinear shallow-water models of tsunamis;
• vessel- and obstacle-generated waves;
• large-scale spectral wave forecasting.