Directional integration on unstructured meshes via supermesh construction

J. R. Maddison*, P. E. Farrell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Unstructured meshes are in widespread use throughout computational physics, but calculating diagnostics of simulations on such meshes can be challenging. For example, in geophysical fluid dynamics, it is frequently desirable to compute directional integrals such as vertical integrals and zonal averages; however, it is difficult to compute these on meshes with no inherent spatial structure. This is widely regarded as an obstacle to the adoption of unstructured mesh numerical modelling in this field. In this paper, we describe an algorithm by which one can exactly compute such directional integrals on arbitrarily unstructured meshes. This is achieved via the solution of a problem of computational geometry, constructing the supermesh of two meshes. We demonstrate the utility of this approach by applying it to a classical geophysical fluid dynamics system: the thermally driven rotating annulus. This addresses an important objection to the more widespread use of unstructured mesh modelling. (C) 2012 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)4422-4432
Number of pages11
JournalJournal of Computational Physics
Volume231
Issue number12
DOIs
Publication statusPublished - 20 Jun 2012

Keywords

  • Galerkin projection
  • FINITE-VOLUME
  • BASIN
  • Supermesh
  • ADAPTIVITY
  • Unstructured mesh
  • FLOWS
  • EQUATIONS
  • COASTAL OCEAN
  • CYLINDRICAL ANNULUS
  • MODEL
  • Azimuthal integration
  • SIMULATIONS
  • Vertical integration
  • Zonal integration
  • Finite element

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