求解零航速物体水动力的简单Green函数方法

频率域中求解零航速物体水动力的简单Green函数方法的基本原理是将流场分成内场和外场,外场中的速度势通过特征函数展开写成解析表达式,内场周界上的速度势则利用边界积分方程求解,但选用的Green函数是简单的,即无界域中点源的速度势。这意味着在内场的整个周界都要布置奇点。内外场速度势在它们的交界面上用代入法连接。简单Green函数方法已成功地应用于二维、三维物体的一阶和二阶辐射、绕射问题,结果表明该方法具有很多方面的优越性。

The Simple Green''''s Function Technique for Calculating the Hydrodynamic Forces Acting on a Body Without Forward Speed

As an efficient numerical tool the simple Green's function technique is demonstrated in this paper for calculating the hydrodynamic problems of a body without forward speed. The fundamental characteristic of the method is to divide the fluid region around the body into an inner region, described by an integral equation, and an outer region where the velocity potential is described by an expansion of eigenfunctions with unknown coefficients. The potentials of the two regions are then matched on the radiation boundaries using a simple substitution procedure. The potential and therefore the hydrodynamic pressure forces on the body are obtained by solving the integral equation for inner region taking a simple function, i. e., the potential of point source in an unbounded fluid, as the Green's function.The simple Green's function technique has been successfully utilized to solve the 1st and 2nd order radiation and diffraction problems for two or three dimensional bodies. It is shown that the method is superior from a computational point of view.