Analysed and Fractal Singlle Point Method for Solving Hydraulic Problems in Ocean Engineering

ABSTRACT This paper presents two kinds of Single Point Method (SPM), i. e. analysed SPM and fractal SPM, and decides the analysed solution and fractal distribution on any solitary point for problems in ocean engineering. The analysed SPM is according to the optimization method of weighted residuals for solitary point, and gives the hydraulic equation's solution for any solitary point (point solution) which is suitable only for that solitary point. As the solution for solitary point is being development independently, it does not need to consider the compatibility with other points, but total boundary conditions and the supplementary derived residual equations and derived boundary equation which were got by running the derivative operations to the differential equation and boundary conditions should be taken into account. The fractal SPM is according to multifactor variable dimension fractals, and decides the fractal distribution of some physical quantities on any solitary point for hydraulic problem. It is differentiated from the existing fractal method (contains one factor and the fractal dimension is a constant) by that the different factors (characteristic scales) correspond with different fractal distribution and for different fractal distributions the fractal dimension Di are the function of characteristic scale Ri.