Conservative numerical schemes with optimal dispersive wave relations -- Part I. Derivations and analyses
Numerical Analysis
2019-05-30 v1 Atmospheric and Oceanic Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1905.12102,
title = {Conservative numerical schemes with optimal dispersive wave relations -- Part I. Derivations and analyses},
author = {Qingshan Chen and Lili Ju and Roger Temam},
journal= {arXiv preprint arXiv:1905.12102},
year = {2019}
}