An unstructured CD-grid variational formulation for sea ice dynamics

Abstract

We present a new unstructured CD-grid formulation of the elastic-viscous-plastic rheology, where the velocity unknowns are co-located at the edges. Our framework of choice is the Model for Prediction Across Scales (MPAS) within E3SM, the climate model of the U.S. Department of Energy, although our approach is general and could be applied to other models as well. The mesh cells in our analysis have n sides, with n greater than or equal to three. Given an initial mesh, we compute the divergence of the stress using a sub-grid, which introduces two separate sets of cells that may differ in shape or be equal depending on the initial topology of the initial mesh. The proposed approach is of higher order compared to the existing B-grid discretization of MPAS-Seaice, and does not need stabilization as other CD-grid formulations on unstructured grids. Our new methodology will contribute to transitioning the dynamics of MPAS-Seaice to a CD-grid mesh, facilitating improved coupling with MPAS-Ocean and reducing numerical errors associated with interpolation.