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2015 An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere
Peter McCorquodale, Paul Ullrich, Hans Johansen, Phillip Colella
Commun. Appl. Math. Comput. Sci. 10(2): 121-162 (2015). DOI: 10.2140/camcos.2015.10.121

Abstract

We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed sphere. This approach combines a Runge–Kutta time discretization with a fourth-order-accurate spatial discretization and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy but with many fewer operations.

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Peter McCorquodale. Paul Ullrich. Hans Johansen. Phillip Colella. "An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere." Commun. Appl. Math. Comput. Sci. 10 (2) 121 - 162, 2015. https://doi.org/10.2140/camcos.2015.10.121

Information

Received: 24 June 2014; Revised: 26 May 2015; Accepted: 5 June 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1326.65114
MathSciNet: MR3402348
Digital Object Identifier: 10.2140/camcos.2015.10.121

Subjects:
Primary: 35L40, 65M08, 65M50
Secondary: 35L65, 86-08

Rights: Copyright © 2015 Mathematical Sciences Publishers

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