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

• Main Authors: Danilov, S., Mehlmann, C., Fofonova, V.
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: arXiv 2021
• Subjects: Numerical Analysis math.NA; FOS Mathematics; Sea ice
• Online Access: https://dx.doi.org/10.48550/arxiv.2106.13641; https://arxiv.org/abs/2106.13641

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.