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Title: An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

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.

Authors:
 [1];  [2];  [1];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
  2. Univ. of California, Davis, CA (United States). Dept. of Land, Air and Water Resources
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Computational Research Division; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1236078
Alternate Identifier(s):
OSTI ID: 1407277
Report Number(s):
LBNL-183366
Journal ID: ISSN 1559-3940; ir:183366
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Communications in Applied Mathematics and Computational Science
Additional Journal Information:
Journal Volume: 10; Journal Issue: 2; Journal ID: ISSN 1559-3940
Publisher:
Mathematical Sciences Publishers
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; high order; finite-volume method; cubed sphere; shallow-water equations; adaptive mesh refinement

Citation Formats

McCorquodale, Peter, Ullrich, Paul, Johansen, Hans, and Colella, Phillip. An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere. United States: N. p., 2015. Web. doi:10.2140/camcos.2015.10.121.
McCorquodale, Peter, Ullrich, Paul, Johansen, Hans, & Colella, Phillip. An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere. United States. doi:10.2140/camcos.2015.10.121.
McCorquodale, Peter, Ullrich, Paul, Johansen, Hans, and Colella, Phillip. Fri . "An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere". United States. doi:10.2140/camcos.2015.10.121. https://www.osti.gov/servlets/purl/1236078.
@article{osti_1236078,
title = {An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere},
author = {McCorquodale, Peter and Ullrich, Paul and Johansen, Hans and Colella, Phillip},
abstractNote = {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.},
doi = {10.2140/camcos.2015.10.121},
journal = {Communications in Applied Mathematics and Computational Science},
number = 2,
volume = 10,
place = {United States},
year = {2015},
month = {9}
}

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Cited by: 7 works
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