An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere
Abstract
Here 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:
-
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
- 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)
- 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. https://doi.org/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. https://doi.org/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 = {Here 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 = {Fri Sep 04 00:00:00 EDT 2015},
month = {Fri Sep 04 00:00:00 EDT 2015}
}
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