Particle-in-cell and finite difference approaches for the study of marginal ice zone problems

Abstract

Eulerian Finite Difference (FD) and quasi-Lagrangian Particle-In-Cell (PIC) approaches are applied in the present paper to study Marginal Ice Zone (MIZ) problems. The elliptical, viscous-plastic, rheological model of Hibler (Hibler, W.D. III, 1979. A dynamic thermodynamic sea ice model. J. Phys. Oceanogr., Vol. 9, pp. 815–846) was used. The numerical implementation of the equations governing the ice motion is described in detail. A Successive Over-Relaxation (SOR) scheme is employed for the FD and PIC methods in solving the momentum equation. Following Zhang and Hibler (Zhang, J., Hibler, W.D. III, 1997. On an efficient numerical method for modeling sea ice dynamics. J. Geophys. Res., Vol. 102, pp. 8691–8702), a pseudo time stepping procedure was used to update the bulk and shear viscosities, and the other velocity dependent terms, while maintaining the ice strength and the old time step velocity appearing in the inertia term ∂ v /∂ t unchanged. By performing these pseudo time step iterations, it was possible to (1) ensure that the stresses corresponded to the elliptical yield criterion during plastic deformation, and (2) improve the accuracy of the velocity field and hence, the nonlinear terms involving velocities. Two geometrical configurations were examined: a straight MIZ in which the coast was modeled by a straight rigid boundary; and a MIZ in which the coast was considered to be a straight corner-shaped solid boundary. Special attention was given to the implementation of the boundary conditions for ice–water interfaces. This is an important element in MIZ problems where one can find complex moving ice–water interfaces, which are not usually observed in the Arctic basin. A simple way to calculate the ice compactness, which is particularly useful for the PIC method, is described. The present numerical results obtained from both the FD and the PIC methods are in general agreement. In particular, results obtained from these two approaches for the straight MIZ are almost identical. However, the PIC method has the advantage of providing an exact location of the free edge of the ice. It also appears to provide a more accurate and trouble-free means to predict deformations within the ice fields.