Conservative numerical schemes with optimal dispersive wave relations -- Part I. Derivations and analyses

2019/05/28 by Qingshan Chen, Lili Ju, Chen, Qingshan +3
Earth and Planetary Sciences · Engineering · #35Q86 #65M08 #65P10 #Atmospheric and Oceanic Physics (physics.ao-ph) #Coastal and Marine Dynamics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.1905.12102

openalex publication_date 2019/05/28 · openalex created_date 2019/06/07 · openalex updated_date 2026/07/28

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.

Citations

• Centroidal Voronoi Tessellations: Applications and Algorithms

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