Numerical simulation of ship stern flows with a space-marching Navier-Stokes method

When a ship is viewed from some distance while it steadily advances on a straight course through still water, the aesthetically appealing wave pattern, trailing with the ship, is usually the most apparent flow disturbance. Below the water surface, however, largely invisible for the human observer, additional turmoil is created. In spite of the small viscosity of water, a motion is imparted to a substantial amount of fluid because of the no-slip condition on the hull surface. Related to this imparted motion is the viscous drag of the hull, nearly always the dominant contribution to the hull resistance. The propulsor of the ship, mounted behind the stern and thus operating in the ship-disturbed flow field, adds considerably to the complexity of the water motion in overcoming both the viscous and the wave-making resistance.
The flow phenomena touched upon above are at the basis of some classical problems of hydrodynamic ship design. For example: the minimisation of the ship's resistance under certain hull-geometric constraints; the design and the analysis of the propulsor, usually a screw propeller; the improvement of the performance of the hull and the propeller as two interacting bodies, with regard not only to the propulsive efficiency but also to the suppression of cavitation, vibrations and noise. The idealised environmental condition of the water being at rest until the ship arrives to disturb it is herein considered to yield a representative average of what happens in a wind-disturbed sea.
In dealing with these problems, naval architects have, for more than a century, relied primarily on experiments with small scale models of the ship under investigation; the role of computational methods has been comparatively modest. This cannot be attributed to the lack of an accurate mathematical description of the flow. On the contrary, fluid mechanics is a branch of physics with a completely satisfactory theoretical model, consisting of the so-called Navier-Stokes equations. As a matter of fact, these equations were established even before the time that systematic ship model experiments were initiated. The minor role of computational techniques is rather due to the intrinsic complexity of the equations, prohibiting analytical solution while requiring for numerical solution much greater computer power than currently available. At present, only approximate forms of the Navier-Stokes 2 Numerical simulation ofship stern flows equations can be solved in practical applications.