On discretizing sea-ice dynamics on triangular meshes using vertex, cell or edge velocities. (February 2022)

• Record Type: Journal Article
• Authors: Danilov, S.; Mehlmann, C.; Fofonova, V.
• Is Part Of: Ocean modelling. Volume 170(2022)
• Publication Date: 2022-02
• Subjects: Triangular meshes -- Sea ice dynamics -- Viscous plastic rheology -- Finite elements -- Computational modes; Oceanography -- Periodicals; Océanographie -- Périodiques; Oceanography; Periodicals; 551.46
• DOI: 10.1016/j.ocemod.2021.101937
• Languages: English
• ISSNs: 1463-5003

Abstract

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 discretizations based on cell and edge velocities may suffer from non-trivial kernels in the strain rate or stress divergence operators and need either special strain rate computations for cell velocities, or stabilization 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. Highlights: Cell and edge sea ice velocities on triangular meshes ensure more accurate stress divergence than the vertex velocities. Discretizations of sea ice dynamics based on cell and edge velocities maintain numerical modes. These discretizations may support kernels in discrete operators, and may need stabilization to suppress them. Numerical modes are characterized by large negative eigenvalues of stress divergence operator. They have implications for stability of explicit methods such as Elastic Viscous Plastic method.