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

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 mor...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Danilov, S, Mehlmann, C, Fofonova, V
Format: Article
Language:English
Subjects:
Apexes
Decay rate
Discretization
Divergence
Dynamic stability
Eigenvalues
Finite element method
Fourier analysis
Graph theory
Kernels
Kinematics
Sea ice
Strain rate
Velocity
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2106.13641