Logically rectangular finite volume methods with adaptive refinement on the sphere

Marsha J. Berger, Donna A. Calhoun, Christiane Helzel, Randall J. LeVeque

Research output: Contribution to journalArticlepeer-review


The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the GeoClaw software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry. This journal is

Original languageEnglish (US)
Pages (from-to)4483-4496
Number of pages14
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1907
StatePublished - Nov 28 2009


  • Adaptive mesh refinement
  • Bathymetry
  • Finite volume
  • Shallow water equations
  • Sphere
  • Well-balanced schemes

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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