On discretizing sea-ice dynamics on triangular meshes using vertex, cell or edge velocities

TL;DR

This paper compares different discretization methods for sea-ice dynamics on triangular meshes, analyzing their mathematical properties and stability issues, and proposes solutions for improving numerical stability.

Contribution

It introduces new strain rate computations for cell-based discretization and analyzes the stability implications of different velocity placements.

Findings

Cell and edge velocity discretizations better capture linear kinematic features.

Kernel removal techniques improve strain rate computations.

Spurious stress divergence branches affect stability but not physical accuracy.

Abstract

Discretization of the equations of Viscous Plastic and Elastic Viscous Plastic (EVP) sea ice dynamics on triangular meshes can be done by placing discrete velocities at vertices, cells or edges. Since there are more cells and edges than vertices, the cell- and edge-based discretizations simulate more linear kinematic features at the same mesh than the vertex discretization. However, the discretization based on cell and edge velocities suffer from kernels in the strain rate or stress divergence operators and need either special strain rate computations as proposed here for cell velocities, or stabilization as proposed earlier for edge velocities. An elementary Fourier analysis clarifies how kernels are removed, and also shows that cell and edge velocity placement leads to spurious branches of stress divergence operator with large negative eigenvalues. Although spurious branches correspond to fast decay and are not expected to distort sea ice dynamics, they demand either smaller internal time steps or higher stability parameters in explicit EVP-like methods.