ERCIM News No.45 - April 2001 [contents]

### Efficient Computation of Ship Waves

by Piet Hemker

A new solution method for the efficient computation of water waves around a ship was developed at CWI, in close cooperation with the Dutch maritime research institute, MARIN.

The ability to predict the behaviour of flows is essential in many engineering applications, such as ship hydrodynamics. Although the physical laws describing fluid flow and their mathematical formulation (the full Navier-Stokes equations) are well understood for more than a century, due to its tremendous complexity the most accurate mathematical model is still unmanageable for engineering purposes. Therefore, those concerned with practical fluid-mechanics problems have always considered more tractable models. For practical computations by means of a computer, the unknown functions are approximated by tabular values, and the fluid-flow problem then translates into the problem of solving a very large system of equations in which the tabular values are the unknowns. This technique is called ‘discrete approximation’. The approximation becomes increasingly accurate as the tabulation becomes finer.

On the other hand, however, the system of equations grows correspondingly and becomes more difficult to handle.The large system of equations is solved to arbitrary accuracy by a computer in an iterative (ie, cyclic) process. Although the rapid development of computers has allowed the treatment of increasingly larger systems, it still remains a challenge (and a practical necessity) to obtain, within a given computational effort, better accuracy for more complex flow problems.

 One challenge in the hydrodynamic design of ships is to find the optimal shape of the ship hull satisfying prior requirements of use, economy, safety, etc. CFD computations have led to improvements of the hull shape, so that the high amplitude of the long waves made by the ship could be strongly reduced. (Photo courtesy MARIN.)

One of the flow problems that have recently become tractable is: free-surface viscous flow in three dimensions, eg, waving water flow around a ship hull. Here the problem is to determine both the (viscous) flow and the shape of the wavy water surface. Previously, only simpler models could be applied, and the surface and the flow problem were treated separately: either the wavy surface of an inviscid fluid-flow, or a viscous fluid-flow below a flat water surface was determined. However, simultaneous treatment is required to obtain more reliable results. The essential problem was the inefficiency of the available iterative methods for the viscous free-surface flow problem. As a consequence, in practice the accuracy of the approximation was limited, and the more sophisticated model gave less accurate results. Hence, an essentially more efficient iterative method had to be developed. The new method was shown to be efficient for a test problem. Since October, computations for actual ship flows are in progress.