Vol. 10, No. 2, 2015

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

Peter McCorquodale, Paul A. Ullrich, Hans Johansen and Phillip Colella

Vol. 10 (2015), No. 2, 121–162
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.

Keywords
high order, finite-volume method, cubed sphere, shallow-water equations, adaptive mesh refinement
Mathematical Subject Classification 2010
Primary: 35L40, 65M50, 65M08
Secondary: 35L65, 86-08
Milestones
Received: 24 June 2014
Revised: 26 May 2015
Accepted: 5 June 2015
Published: 4 September 2015
Authors
Peter McCorquodale
Computational Research Division
Lawrence Berkeley National Laboratory
1 Cyclotron Road
MS 50A1148
Berkeley, CA 94720
United States
Paul A. Ullrich
Department of Land, Air and Water Resources
University of California, Davis
1 Shields Avenue
Davis, CA 95616
United States
Hans Johansen
Computational Research Division
Lawrence Berkeley National Laboratory
1 Cyclotron Road
MS 50A1148
Berkeley, CA 94720
United States
Phillip Colella
Computational Research Division
Lawrence Berkeley National Laboratory
1 Cyclotron Road
MS 50A1148
Berkeley, CA 94720
United States