A NEW POTENTIAL / RANSE APPROACH FOR WATER WAVE DIFFRACTION Pierre Ferrant, Lionel Gentaz, David Le Touzé Division Hydrodynamique Navale, Laboratoire de Mécanique des Fluides, Ecole Centrale de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes Cedex 03, France e-mail : Pierre.Ferrant@ec-nantes.fr, Lionel.Gentaz@ec-nantes.fr, David.Letouze@ec-nantes.fr Abstract This paper is devoted to the numerical simulation of water diffraction in viscous flow. An original approach using a diffracted flow defined as the difference between total and incident flows is followed. The incident flow is defined explicitly using nonlinear potential flow theory; Navier-Stokes equations and nonlinear free surface boundary conditions are solved for the diffracted flow only. This procedure, which is very efficient in terms of computing time and accuracy, was primarily developed by Ferrant (1996) for 3D non linear wave-body interactions in potential theory. INTRODUCTION Today Numerical Wave Tanks (NWTs) have become efficient tools for coastal or ocean engineering problems. First NWTs were based on the potential flow theory, following the Mixed Euler-Lagrange Method introduced by Longuet- Higgins and Cokelet (1976). Potential flow nonlinear NWTs were developed by Cointe (1989) in 2D or Beck (1994) in 3D, among many others. Alternative models based on RANS (Reynolds-Averaged Navier-Stokes) Equations with finite difference or finite volume methods may be developed, allowing vorticity and viscous effects occurring in wave-body interaction problems to be modeled. In such methods, the interface can be updated by different manners : the free surface capturing principle has been used by Harlow & Welch (1965) or Miyata (1986) with the Marker and Cell (MAC) method or Hirt & Nichols (1981) and many others with the Volume of Fluid (VOF) method. Examples of interface tracking methods may be found in Daubert & Cahouet (1984) or Yeung & Ananthakrishnan (1994) Wave generation and absorption are of course of primary importance in such numerical simulations. Wave generation is usually performed by the simulation of a wavemaker on the upstream boundary of the wave tank, which is equivalent to the prescription of a wave kinematics on this boundary. The generation of waves by a pressure patch (see Armenio and Favretto 1997) acting over a narrow area of the free surface is advantageous because the upstream boundary can be used for wave damping. This damping can be achieved by implementing an open boundary condition (Orlanski 1976) or by modifying free surface boundary conditions ( see e.g. Clément (1996) for the absorption in potential NWT’s). However wave generation and wave damping remain an issue in NWTs based on RANS equations. In RANSE NWT’s a fine grid (more than 50 nodes per wavelength) is necessary for a correct simulation of wave propagation, without damping or dispersive effect, leading to large CPU. Moreover wave reflections on the body or on the downstream boundary and consecutively on the upstream boundary are going to affect the incoming wave train: as a consequence, the useable duration of the simulation (for computation of hydrodynamic loads on the structure for example) is usually limited. In this paper a new formulation is proposed which suppresses these limitations by modifying the initial problem in order to solve the diffracted flow only. This approach was previously used for potential flow model in 2D (Schønberg & Chaplin 2001) or 3D cases (Ferrant 1996). It consists in splitting all unknowns of the problem (potential and free surface elevation) in a sum of an incident term and a diffracted term. The incident terms are described explicitly. Here splitting of unknowns will be applied to a 2D viscous flow solver (Gentaz et al. 2000) whose main properties are described hereafter. The case of a regular wave train on a submerged square body is studied to demonstrate the viability of the proposed approach.