Abstract
A new sea ice dynamical core, the Discrete Element Model for Sea Ice (DEMSI), is under development for use in coupled Earth system models. DEMSI is based on the discrete element method, which models collections of ice floes as interacting Lagrangian particles. In basin-scale sea ice simulations the Lagrangian motion results in significant convergence and ridging, which requires periodic remapping of sea ice variables from a deformed particle configuration back to an undeformed initial distribution. At the resolution required for Earth system models we cannot resolve individual sea ice floes, so we adopt the sub-gridscale thickness distribution used in continuum sea ice models. This choice leads to a series of hierarchical tracers depending on ice fractional area or concentration that must be remapped consistently. The circular discrete elements employed in DEMSI help improve the computational efficiency at the cost of increased complexity in the effective element area definitions for sea ice cover that are required for the accurate enforcement of conservation. An additional challenge is the accurate remapping of element values along the ice edge, the location of which varies due to the Lagrangian motion of the particles. In this paper we describe a particle-to-particle remapping approach based on well-established geometric remapping ideas that enforces conservation, bounds-preservation, and compatibility between associated tracer quantities, while also robustly managing remapping at the ice edge. One element of the remapping algorithm is a novel optimization-based flux correction that enforces concentration bounds in the case of non-uniform motion. We demonstrate the accuracy and utility of the algorithm in a series of numerical test cases.
Highlights
Sea ice, the frozen surface of the ocean at high latitudes, forms an important component of the Earth climate system
At the resolution required for Earth system models we cannot resolve individual sea ice floes, so we adopt the sub-gridscale thickness distribution used in continuum sea ice models
The circular discrete elements employed in Discrete Element Model for Sea Ice (DEMSI) help improve the computational efficiency at the cost of increased complexity in the effective element area definitions for sea ice cover that are required for the accurate enforcement of conservation
Summary
The frozen surface of the ocean at high latitudes, forms an important component of the Earth climate system. In the work of Hopkins (2004), the authors represented the ridging process through a remapping scheme of overlapping converging neighboring elements. Elements with arbitrarily small radii, introduce computational challenges with regard 40 to efficient contact searching, time step size, and contact model formulation (Hopkins, 2004; Shire et al, 2020) Both these considerations, require long duration DEM simulations of sea ice deformation to periodically perform a remapping of the model elements to an undeformed distribution. Collision detection between circular elements, on the other hand, is much less computationally expensive since for circular elements only a comparison between the element separation and the element radii is needed to determine if a collision has occurred In this regard, in the work which follows, we explore how to represent sea ice in a Hopkins (2004)-like DEM model using more computationally efficient circular elements. 70 and achieves second-order accuracy, tracer compatibility, conservation, and bounds preservation
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