A dynamical core based on a discontinuous Galerkin method for higher-order finite-element sea ice modeling

Abstract

The ability of numerical sea ice models to reproduce localized deformation features associated with fracture processes is key for an accurate representation of the ice dynamics and of dynamically coupled physical processes in the Arctic and Antarctic. Equally key is the capacity of these models to minimize the numerical diffusion stemming from the advection of these features to ensure that the associated strong gradients persist in time, without the need to unphysically re-inject energy for re-localization. To control diffusion and improve the approximation quality, we present a new numerical core for the dynamics of sea ice that is based on higher-order finite-element discretizations for the momentum equation and higher-order discontinuous Galerkin methods for the advection. The mathematical properties of this core are discussed, and a detailed description of an efficient shared-memory parallel implementation is given. In addition, we present different numerical tests and apply the new framework to a benchmark problem to quantify the advantages of the higher-order discretization. These tests are based on Hibler's viscous–plastic sea ice model, but the implementation of the developed framework in the context of other physical models reproducing a strong localization of the deformation is possible.