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arXiv · 2608.26810

A Discontinuous Galerkin discretization for the sea ice dynamics

Emma Lagracie·Thomas Richter
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Abstract

Sea ice dynamics plays a crucial role in the Earth's climate system, making it an important component of weather and climate prediction models. Its numerical simulation remains challenging, however, as it exhibits complex mechanical behaviors due to a nonlinear ice rheology and interactions with external physical forcings. In particular, sea ice presents linear kinematic features (LKFs), i.e., narrow bands of intense deformation associated with processes such as lead opening or pressure-ridge formation. Accurately representing these features is necessary as they affect thermodynamics and ocean-atmosphere exchange. Yet their number, localization, and structure are highly sensitive to spatial resolution and to the chosen discretization of the sea ice velocity. In this work, we investigate the spatial discretization of Hibler's viscous plastic sea-ice model using a fully discontinuous Galerkin (DG) representation of all variables, including the velocity field. The ability of DG elements to represent discontinuities while having high order local polynomial approximation makes them well suited for resolving the complex ice deformation features, and insuring robustness towards mesh-induced numerical artefacts. We assess the fully DG method using an established sea ice dynamics benchmark and compare the obtained sea ice deformation with state-of-the-art discretizations. Additionally, we study the theoretical convergence of the modified Elastic-Viscous-Plastic (mEVP) formulation as a pseudo-time iterative solver for the viscous-plastic (VP) momentum equations. We prove the convergence of the underlying continuous pseudo-time dynamical system towards the viscous plastic formal limit, thereby providing a theoretical foundation for the use of mEVP as an iterative solver for Hibler's VP model.

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Emma Lagracie, Thomas Richter. 2026-08-27. A Discontinuous Galerkin discretization for the sea ice dynamics. https://arxiv.org/abs/2608.26810

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