低密集度浮碎冰数值生成方法研究

Numerical generation method of broken ice at low concentration

合理的浮碎冰初始分布是数值模拟极地船舶碎冰阻力的关键,目前主要通过Voronoi图得到初始的浮碎冰分布,但该方法得到的浮碎冰直径呈正态分布与实际观测结果不一致。本文将Voronoi图方法、概率理论等有机结合,推导出量化浮碎冰直径的公式,之后通过分离轴定理将数值重叠的浮碎冰进行分离,形成给定密集度下浮碎冰的生成方法,使浮碎冰直径满足指数分布规律,为浮碎冰场的数值建模提供合理的输入。在验证方法有效性的同时,开展了相关变量对浮碎冰分布特性的影响研究。数值研究结果表明:浮碎冰直径经过量化后,随机点数对浮碎冰的数值生成结果基本没有影响;当δ=0.1时,浮碎冰的数值生成结果的离散度最小;参数β是影响浮碎冰分布概率密度函数的一个重要参数,β的取值应根据不同海域进行选取。

The reasonable distribution of broken ices has a significant effect on the resistance simulation of polar ships.The initial distribution of broken ices was mainly obtained by Voronoi diagram method in most previous studies,but the diameters of the broken ices obtained followed normal distribution,which were inconsistent with the observation results.To overcome this difficulty,Voronoi diagram method and probability theory were combined to derive the formula for quantifying the diameters of broken ices.Through the separation axis theorem,the overlapped broken ices were separated.Therefore,the diameter distribution of broken ices obtained by the novel generation method satisfies the exponential function,which provides reasonable input for the numerical modeling of broken ice field.Moreover,the influence of relevant variables on the distribution characteristics of broken ices has been studied.The numerical results show that random points have little effect on the numerical results of broken ices.There is a minimum discreteness of the numerical results whileδis equal to 0.1.The probability density function of broken ices is affected by parameterβsignificantly,whose value should be selected according to sea zones.