A numerical method to solve the m-terms of a submerged body with forward speed

Duan, W.Y. and Price, W.G. (2002) A numerical method to solve the m-terms of a submerged body with forward speed. International Journal for Numerical Methods in Fluids, 40 (5), 655-667. (doi:10.1002/fld.367).

Abstract

To model mathematically the problem of a rigid body moving below the free surface, a control surface surrounding the body is introduced. The linear free surface condition of the steady waves created by the moving body is satisfied. To describe the fluid flow outside this surface a potential integral equation is constructed using the Kelvin wave Green function whereas inside the surface, a source integral equation is developed adopting a simple Green function. Source strengths are determined by matching the two integral equations through continuity conditions applied to velocity potential and its normal derivatives along the control surface. After solving for the induced fluid velocity on the body surface and the control surface, an integral equation is derived involving a mixed distribution of sources and dipoles using a simple Green function and one component of the fluid velocity. The normal derivatives of the fluid velocity on the body surface, namely the m-terms, are then solved by this matching integral equation method (MIEM). Numerical results are presented for two elliptical sections moving at a prescribed Froude number and submerged depth and a sensitivity analysis undertaken to assess the influence of these parameters. Furthermore, comparisons are performed to analyse the impact of different assumptions adopted in the derivation of the m-terms. It is found that the present method is easy to use in a panel method with satisfactory numerical precision.

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