Conservative finite volume schemes for the quasi-geostrophic equation on coastal-conforming unstructured primal-dual meshes
This work provides a numerical method for geophysical fluid dynamics, but the results are incremental as they extend existing finite volume approaches to a specific mesh type.
The paper develops finite volume schemes for the quasi-geostrophic equation on coastal-conforming unstructured meshes, demonstrating conservation of potential vorticity and enstrophy, with numerical tests confirming these properties.
In this paper we propose finite volume schemes for solving the inviscid and viscous quasi-geostrophic equations on coastal-conforming unstructured primal-dual meshes. Several approaches for enforcing the boundary conditions are also explored along with these schemes. The pure transport part in these schemes are shown to conserve the potential vorticity along fluid paths in an averaged sense, and conserve the potential enstrophy up to the time truncation errors. Numerical tests based on the centroidal Voronoi-Delaunay meshes are performed to confirm these properties, and to distinguish the dynamical behaviors of these schemes. Finally some potential applications of these schemes in different situations are discussed.