A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere

D. Lee, A. Palha

Research output: Contribution to journalArticleAcademicpeer-review

17 Citations (Scopus)

Abstract

In a previous article [J. Comp. Phys. 357 (2018) 282–304] [4], the mixed mimetic spectral element method was used to solve the rotating shallow water equations in an idealized geometry. Here the method is extended to a smoothly varying, non-affine, cubed sphere geometry. The differential operators are encoded topologically via incidence matrices due to the use of spectral element edge functions to construct tensor product solution spaces in H(rot), H(div) and L2. These incidence matrices commute with respect to the metric terms in order to ensure that the mimetic properties are preserved independent of the geometry. This ensures conservation of mass, vorticity and energy for the rotating shallow water equations using inexact quadrature on the cubed sphere. The spectral convergence of errors are similarly preserved on the cubed sphere, with the generalized Piola transformation used to construct the metric terms for the physical field quantities.

Original languageEnglish
Pages (from-to)240-262
Number of pages23
JournalJournal of Computational Physics
Volume375
DOIs
Publication statusPublished - 15 Dec 2018

Funding

David Lee would like to thank Dr. Mark Taylor for several helpful discussions on the formulation of the Jacobian mapping, and Prof. Hugh Blackburn for the generous use of machine time for the production of the results. This research was supported as part of the Launching an Exascale ACME Prototype (LEAP) project, funded by the US Department of Energy, Office of Science, Office of Biological and Environmental Research . This research used resources provided by the Los Alamos National Laboratory Institutional Computing Program, which is supported by the U.S. Department of Energy National Nuclear Security Administration under Contract No. DE-AC52-06NA25396 .

Keywords

  • Cubed sphere
  • Mimetic
  • Shallow water
  • Spectral convergence

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