First results of the study of a two-dimensional numerical wave tank in viscous fluid are presented in this paper. Navier-Stokes equations are solved by an original fully-coupled solver to compute unsteady, incompressible free surface flows in viscous fluid by second order finite difference schemes. Exact non-linear free surface boundary conditions and moving grid technique are used. Generation and propagation of waves in a tank are simulated. A numerical damping method has been used for wave absorption at the outlet boundary. First comparisons with experiments show a good agreement for waves with an moderate steepness.
Over the last two decades several numerical methods to compute two-dimensional non-linear and unsteady free surface flows have appeared in the literature. We will especially focus in numerical wave tanks with or without body in or at the surface of the fluid domain. In this case it consists in computing free surface flow with a wavemaker at one lateral boundary and an absorption mechanism at the other boundary in order to let the waves exit the flume without significant reflection. Concerning the potential flow theory methods based on the Mixed Euler-Lagrange (MEL) approach first proposed by Longuet-Higgins and Cokelet (1976) have been used by many authors. Classical hydrodynamic problems have been successfully treated in this way : interaction between opposite direction waves, simulation of plunging wave breaking (Dommermuth et al., 1988), interaction of monochromatic waves or solitary wave With an immersed body. One of the most serious hindrances in the numerical simulation of wave tank is absorption of the incident waves at the outflow boundary. In potential flow efficient absorption methods have been developed like numerical beach method or active absorption. The first one called numerical beach or sponge layer consists in adding dissipative terms to the free surface boundary conditions in a short zone located at the end of the flume.
