A comparison between the parabolic and partially-parabolic solution procedures for three-dimensional turbulent flows around ships' hulls

Abstract

This paper is concerned with the prediction of three-dimensional turbulent flows around bodies of arbitrary shape, with particular emphasis on a ship's hull. Two solution methods are compared employing a non-orthogonal coordinate system, in which the surface of the body is arranged to coincide with a coordinate surface. The velocity components are solved for the axial, radial and circumferential components in the cylindrical-polar system from which the non-orthogonal coordinates are derived. The partial-differential equations governing the flows under consideration are solved by two finite-difference methods for three-dimensional, parabolic 1 and partially-parabolic 2 flows. Turbulence is accounted for through a two-equation model of turbulence developed by Harlow and Nakayama 3 and modelled by Launder and Spalding. 4 Solutions are presented for flow around a ship's hull which demonstrate the potential of the present methods.