INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2001; 35: 281–297 A level set technique applied to unsteady free surface flows A. Iafrati* ,1 , A. Di Mascio and E. F. Campana Istituto Nazionale per Studi ed Esperienze di Architettura Naale (INSEAN), Via di Vallerano 139, 00128 Rome, Italy SUMMARY An unsteady Navier – Stokes solver for incompressible fluid is coupled with a level set approach to describe free surface motions. The two-phase flow of air and water is approximated by the flow of a single fluid whose properties, such as density and viscosity, change across the interface. The free surface location is captured as the zero level of a distance function convected by the flow field. To validate the numerical procedure, two classical two-dimensional free surface problems in hydrodynamics, namely the oscillating flow in a tank and the waves generated by the flow over a bottom bump, are studied in non-breaking conditions, and the results are compared with those obtained with other numerical approaches. To check the capability of the method in dealing with complex free surface configurations, the breaking regime produced by the flow over a high bump is analyzed. The analysis covers the successive stages of the breaking phenomenon: the steep wave evolution, the falling jet, the splash-up and the air entrainment. In all phases, numerical results qualitatively agree with the experimental observa- tions. Finally, to investigate a flow in which viscous effects are relevant, the numerical scheme is applied to study the wavy flow past a submerged hydrofoil. Copyright © 2001 John Wiley & Sons, Ltd. KEY WORDS: free surface flow; level set; two-phase flow; wave breaking 1. INTRODUCTION Several important phenomena occurring in naval hydrodynamics, such as wave breaking, cavitation and ventilation, cannot be properly faced with standard numerical techniques. As an example, suitable models based on simplified assumptions [1] are usually employed to prevent the occurrence of complex topological configurations of the air – water interface [2]. Historically, the first attempt to treat flows with complex interface was made by Harlow and Welch [3], who developed the marker and cell (MAC) method. In this method, the interface is reconstructed by following massless interface particles that move with the local fluid velocity. * Correspondence to: INSEAN, Via di Vallerano 139, 00128 Rome, Italy. Tel.: +39 6 50299296; Fax: +39 6 5070619. 1 E-mail: a.iafrati@mail.insean.it Copyright © 2001 John Wiley & Sons, Ltd. Receied July 1999 Reised January 2000