Conservative numerical schemes with optimal dispersive wave relations -- Part I. Derivations and analyses
Provides conservative numerical methods for geophysical fluid dynamics, improving long-term stability and accuracy in simulations.
The paper derives energy-conserving and energy-and-enstrophy conserving numerical schemes for inviscid shallow water flows on unstructured orthogonal dual meshes, achieving optimal dispersive wave relations like the Z-grid scheme.
An energy-conserving and an energy-and-enstrophy conserving numerical schemes are derived, by approximating the Hamiltonian formulation, based on the Poisson brackets and the vorticity-divergence variables, of the inviscid shallow water flows. The conservation of the energy and/or enstrophy stems from skew-symmetry of the Poisson brackets, which is retained in the discrete approximations. These schemes operate on unstructured orthogonal dual meshes, over bounded or unbounded domains, and they are also shown to possess the same optimal dispersive wave relations as those of the Z-grid scheme.