海冰动力学数值模拟中改进的PIC方法

为了准确地模拟海冰的动力过程,需要建立精确有效的数值方法。本文结合质点网格法(PIC)和光滑质点流体动力学方法(SPH)发展了一种改进的PIC方法。该方法在欧拉坐标下对海冰动量方程进行差分计算,在拉格朗日坐标下进行海冰质点位移、厚度和密集度计算,并采用Gauss函数进行欧拉网格点与拉格朗日质点间海冰参数的交互插值。采用改进的PIC方法对规则区域内的海冰堆积过程进行了数值试验,对渤海海冰的动力过程进行了72小时数值模拟。计算结果均表明改进的PIC方法具有计算量小,计算结果平稳精确的优点,可很好地适用于海冰动力作用过程的数值模拟。

Modified PIC method for numerical simulation of sea ice dynamics

The effective numerical method is very important to model the sea ice dynamic process accurately.In this paper,a modified Particle-In-Cell(PIC) method for sea ice dynamics,coupling the finite different(FD) method and Smoothed Particle Hydrodynamics(SPH),is presented.In this method, the ice cover is,firstly,scattered into a series of Lagrangian ice particles, which have their own size,thickness,concentration and velocity.The ice thickness and concentration at Eulerian grid positions are interpolated using Gaussian interpolating function from their surrounding ice particles.The momentum equation of sea ice dynamics is solved with FD approach to obtain the Eulerian cell velocity,which is used to estimate the velocity of each Lagragian ice particle with Gaussian function also.The thickness and concentration of ice particle are calculated with their mass density and smooth length,which are adjusted from their movement and current location.With this modified PIC method,the numerical simulations of ice ridging in an idealized rectangular basin and ice dynamics in Bohai Sea are carried out,and the simulating results are compared well with the analytical solution and observed data on site.