Analysis of dissipation operators that damp spurious modes while maintaining discrete approximate geostrophic equilibriums for the B-grid staggered scheme on triangular meshes
Do, Minh-Hieu; Nguyen, Van-Thanh; Omnes, Pascal (2023), Analysis of dissipation operators that damp spurious modes while maintaining discrete approximate geostrophic equilibriums for the B-grid staggered scheme on triangular meshes, Journal of Computational Physics, 489. 10.1016/j.jcp.2023.112261
Type
Article accepté pour publication ou publiéDate
2023Journal name
Journal of Computational PhysicsVolume
489Publisher
Elsevier
Publication identifier
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Show full item recordAuthor(s)
Do, Minh-HieuCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Nguyen, Van-Thanh
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Omnes, Pascal
Laboratoire Analyse, Géométrie et Applications [LAGA]
Abstract (EN)
By analyzing the discrete steady states of the Godunov scheme applied to the linear wave equation with Coriolis source term, we show that such a collocated scheme does not preserve discrete geostrophic equilibriums (GE) on triangular meshes. To overcome this difficulty, we propose a staggered strategy which computes the pressure field at the vertices of the triangles and the velocity field at the cell centers (the so-called triangular B-grids). We analyze a family of methods covering triangular variants of the Low Froude (LF) scheme [1], the Apparent Topography (AT) scheme [2, 3], as well as a new modification of it. The LF scheme simply deletes the numerical diffusion terms in the pressure equation in order to capture a discrete version of the GE. In the AT scheme, the numerical diffusion on the pressure equation is kept but in such a way that it does not impact the discrete GE. However, since the AT scheme cannot be proved to be stable through energy estimates and does not preserve the space which is orthogonal to the discrete GE, we also study what we call the Modified Apparent Topography (MAT) that satisfies these important properties. We also study time discretizations that preserve these properties. Numerical experiments illustrate the performance of the new schemes.Subjects / Keywords
Low Froude number; Hodge decomposition; Staggered schemes; Spurious mode damping; geostrophic equilibrium; Shallow water equation with Coriolis source termRelated items
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