A general method for calculating three-dimensional laminar and turbulent boundary layers on ship hulls

A general method for representing the flow properties in the three-dimensional boundary layers around ship hulls of arbitrary shape is described. It makes use of an efficient two-point finite-diffirence schem to solve the boundary-layer equations and includes an algebraic eddy-viscosity representaion of the Reynolds-stress ternsor. The numericzal method contains novel and desirable features and allows the calculation of flows in which the circumferential velocity component contains regions of flow reversal across the boundary layer. The inviscid pressure distribution is determined with the Douglas-Neumann method which, if necessary, can conveniently allow for the boundary-layer displacement surface. To allow its application to ships, and particularly to those with double-elliptic and flat-bottomed hulls, a non-orthogonal coordinate system has been developed and is shown to be economical, precise and comparatively easy to use. Present calculations relate to zero Froude number but they can be extended to include the effects of a water wave and local regions of flow separation which may stem from bulbous-bow geometries.