Accuracy of viscous resistance computations for ships including free surface effects

The European 6^th-framework project VIRTUE aims at advancing the use of CFD in ship design. Workpackage 1 of this project considers the prediction of steady flow around the hull, resistance and propulsion; the field in which the use of CFD is most widespread. Several CFD codes are able to predict the viscous flow and wake field accurately today. However, the predicted resistance and its components are often not so accurate. As results of the CFD Workshop Tokyo 2005 and several other experiences show, in particular the viscous pressure resistance (Cvp) may vary a lot between different methods and often shows substantial grid dependence and large sensitivity to modelling and discretization details.
It is shown that for double-body flow computations the implementation of the symmetry conditions at the still water plane indeed has a large effect on that resistance component.
We used two types of implementations for the symmetry boundary conditions: a direct approach that discretizes directly the symmetry conditions themselves using 1^st – 3^st order discretization, indicated by O1 – O3; and an indirect one (IND) that sets the normal velocity component zero and that solves the continuity equation and the momentum equations tangential to the symmetry plane for points in this plane, taking the symmetry conditions into account in the coefficients of the discretised equations. As Fig.1 shows, for the O2 formulation Cvp increases by 50% from fine to coarse grid, and its scale effect decreases by 50%. A drastic improvement of the numerical accuracy of Cvp is obtained in our RANS code by adopting the IND formulation, in which the resistance and scale effect estimate is much less sensitive to grid density. The present paper reports ongoing work in which similar studies are done for viscous flow computations including free-surface effects. The next section describes the method used.