Logically rectangular finite volume methods with adaptive refinement on the sphere

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

doi:10.1098/rsta.2009.0168

Logically rectangular finite volume methods with adaptive refinement on the sphere

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

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	4483-4496
Number of pages	14
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	367
Issue number	1907
DOIs	https://doi.org/10.1098/rsta.2009.0168
State	Published - Nov 28 2009

Keywords

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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10.1098/rsta.2009.0168

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KW - Adaptive mesh refinement

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KW - Well-balanced schemes

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Logically rectangular finite volume methods with adaptive refinement on the sphere

Abstract

Keywords

ASJC Scopus subject areas

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