海冰动力学数值方法研究进展

在海冰动力学数值模拟和预测研究中,人们将海冰视为连续介质分别建立了欧拉坐标下的有限差分（FD）方法、拉格朗日坐标下的光滑质点流体动力学（SPH）方法、欧拉和拉格朗日坐标相结合的质点网格法（PIC）,近年来又发展了基于非连续介质的颗粒流（GF）方法。对以上几种海冰动力学数值方法的特点和适用性进行了讨论,结果表明：FD、PIC和SPH方法可适用于中长期海冰动力学数值模拟,但SPH方法的计算效率需进一步提高;GF方法在不同尺度下的海冰动力学数值模拟中的计算精度均有很强的适用性,但目前较适用于小尺度下海冰动力学基本特性的数值试验研究,计算时效还不能满足实际海冰数值模拟和预测的要求。为进一步提高海冰动力学模拟的精度和适用性,在不同时空尺度下分别发展与其相适应的数值方法是必要的。

ADVANCES IN NUMERICAL METHODS FOR SEA ICE DYNAMICS

In the study of sea ice rheological behavior under different temporal and spatial scales, a series of numerical methods have been developed in the past several decades. Nowadays, there are mainly four methods applied commonly, which are Finite Different (FD) method, Particle-In-Cell (PIC), Smoothed Particle Hydrodynamics (SPH) and granular flow (GF) method. The Eulerian FD method is the most widely applied method for its high computational efficiency and stability in the polar and Marginal Ice Zone (MIZ) at large scale. It was also applied into other seas at meso-scale, such as Bohai Sea, Baltic Sea. Some new schemes, such as Line Successive Over-Relaxation (LSOR) and Alternative Direction Implicit (ADI), were adopted into the FD method to improve its computational precision. The most shortcoming of FD method is the obvious numerical diffusion in solving momentum and continuity equations, especially at the ice edge. To remedy this problem, the coupled Lagrangian and Eulerian PIC approach was established for sea ice dynamics at large and meso scales. In the PIC method, the sea ice in fixed cells is divided into a series ice particle. The ice mass in cells is adjusted with the drifting of Lagrangian particles, and the particle velocity is interpolated from Eulerian cells. In the Lagrangian SPH method, the Gaussian kernel function is used to integrate the ice parameters from discrete particles to continuous field, and the sea ice rehology can be described precisely with the drifting, deformation of ice particles. In the three methods above, Hibler's Viscous plastic constitutive law was used generally. In the GF method, the sea ice is simulated as discrete medium instead of the continuous medium assumed in other methods. The viscous-elastic-plastic law was established to model the interaction among ice particles, and the dynamics processes of ice ridging, rafting and breakup can be simulated at small scales. But the biggest cost of this increased accuracy is a significant increase in computational time when compared with other methods, especially in its application at large and meso scales. Thus, different numerical methods for the different demands for scale, precision or efficiency accordingly. Meanwhile, with the modification of existing methods, other new numerical methods, such as Arbitrary-Lagrangian-Eulerian (ALE), should be developed. Moreover, the study of numerical methods for sea ice dynamics should be coupled with other sea ice problems, such as constitutive law and thermodynamics, to improve the computational precision and efficiency comprehensively.