Conservative finite‐volume schemes for the quasi‐geostrophic equation on coastal‐conforming unstructured primal–dual meshes

Abstract

In this article 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 parts 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 behaviours of these schemes. Finally some potential applications of these schemes in different situations are discussed.