A level set approach for the numerical simulation of high Reynolds number turbulent ows with a free surface is presented. The algorithm is based on a general pseudo-compressible Reynolds Averaged Navier{Stokes Equations (RANSE) solver, already used in conjunction with a surface-fitting approach for the numerical simulation of steady ows past ship hulls. The RANSE solver is coupled with a non-standard level set approach, the original algorithm having been modified in order to gain increased resolution in the nearby of the free surface. To this end, only the liquid phase is simulated; the level set function is used only as a tracking device to locate the actual position of the free surface. Moreover, the solution in the air region is extrapolated in a way that ensures second order accuracy also in the free surface region. Some numerical results for the ow around a submerged profile and two ship hulls are shown.


Numerical simulation of free surface turbulent ows is a goal of paramount importance for the design and optimization of ship hulls. The results of many efforts dedicated to this topic, done in the past years by many research groups around the world, are summarized, for instance, in the proceedings of the workshop held in Gothenburg (Larson et al., 2000). As it can be seen in these proceedings, most of the computations where performed by means of surface fitting approaches, i.e. with algorithms where the grid moves to fit the actual position of the free surface. Moreover, when dealing with unsteady practical problems, like for instance a ship maneuvering in waves, the topology of the multi-block grid can change in time, and it can turn out to be impossible to handle problems with large geometrical changes of the domain occupied by the water.

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