# Computation of Steady Viscous Flow Near a Ship’s Stern

• M. Hoekstra
Chapter
Part of the Notes on Numerical Fluid Mechanics book series (volume 17)

## Summary

We consider the problem of computing the steady incompressible viscous flow past the rear part of a ship when free surface effects can be neglected. First some alternative approaches are reviewed which have emanated from different views on how to deal with the pressure in the primitive variable formulation of the Navier-Stokes equations. Then a particular solution method is described. The underlying mathematical model is a slightly reduced form of the Navier-Stokes equations: a main stream direction is identified and diffusion effects in this direction are neglected. The equations are solved in a multiple-sweep space-marching process. Multiple sweeps (global relaxation) are needed to allow the pressure to have influence on the upstream flow field. In each sweep the step-by-step evaluation of the solution is governed by an incomplete factorisation scheme. With this scheme a simultaneous solution is obtained in planes approximately perpendicular to the main stream direction. The performance of the method may be judged from some results of application. The proposed numerical solution to a classical problem in ship hydrodynamics is expected to be of great significance in future ship design studies.

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