Multilevel spectral deferred corrections scheme for the shallow water equations on the rotating sphere
Abstract
Efficient time integration schemes are necessary to capture the complex processes involved in atmospheric flows over long periods of time. We propose a highorder, implicit–explicit numerical scheme that combines MultiLevel Spectral Deferred Corrections (MLSDC) and the Spherical Harmonics (SH) transform to solve the wavepropagation problems arising from the shallowwater equations on the rotating sphere. The iterative temporal integration is based on a sequence of corrections distributed on coupled space–time levels to perform a significant portion of the calculations on a coarse representation of the problem and hence to reduce the timetosolution while preserving accuracy. In our scheme, referred to as MLSDCSH, the spatial discretization plays a key role in the efficiency of MLSDC, since the SH basis allows for consistent transfer functions between space–time levels that preserve important physical properties of the solution. We study the performance of the MLSDCSH scheme with shallowwater test cases commonly used in numerical atmospheric modeling. We use this suite of test cases, which gradually adds more complexity to the nonlinear system of governing partial differential equations, to perform a detailed analysis of the accuracy of MLSDCSH upon refinement in time. We illustrate the stability properties of MLSDCSH and show that the proposed scheme achievesmore »
 Authors:

 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Center for Computational Sciences and Engineering
 Univ. of Exeter (United Kingdom). Dept. of Mathematics/Computer Science; Technical Univ. of Munich (Germany). Chair of Computer Architecture and Parallel Systems
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Dept. of Applied Mathematics
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
 OSTI Identifier:
 1490706
 Alternate Identifier(s):
 OSTI ID: 1635906
 Grant/Contract Number:
 AC0205CH11231; AC02005CH11231
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 376; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; highorder time integration; multilevel spectral deferred corrections; implicit–explicit splitting; atmospheric flows; shallowwater equations on the rotating sphere; spherical harmonics
Citation Formats
Hamon, François P., Schreiber, Martin, and Minion, Michael L. Multilevel spectral deferred corrections scheme for the shallow water equations on the rotating sphere. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.09.042.
Hamon, François P., Schreiber, Martin, & Minion, Michael L. Multilevel spectral deferred corrections scheme for the shallow water equations on the rotating sphere. United States. https://doi.org/10.1016/j.jcp.2018.09.042
Hamon, François P., Schreiber, Martin, and Minion, Michael L. Wed .
"Multilevel spectral deferred corrections scheme for the shallow water equations on the rotating sphere". United States. https://doi.org/10.1016/j.jcp.2018.09.042. https://www.osti.gov/servlets/purl/1490706.
@article{osti_1490706,
title = {Multilevel spectral deferred corrections scheme for the shallow water equations on the rotating sphere},
author = {Hamon, François P. and Schreiber, Martin and Minion, Michael L.},
abstractNote = {Efficient time integration schemes are necessary to capture the complex processes involved in atmospheric flows over long periods of time. We propose a highorder, implicit–explicit numerical scheme that combines MultiLevel Spectral Deferred Corrections (MLSDC) and the Spherical Harmonics (SH) transform to solve the wavepropagation problems arising from the shallowwater equations on the rotating sphere. The iterative temporal integration is based on a sequence of corrections distributed on coupled space–time levels to perform a significant portion of the calculations on a coarse representation of the problem and hence to reduce the timetosolution while preserving accuracy. In our scheme, referred to as MLSDCSH, the spatial discretization plays a key role in the efficiency of MLSDC, since the SH basis allows for consistent transfer functions between space–time levels that preserve important physical properties of the solution. We study the performance of the MLSDCSH scheme with shallowwater test cases commonly used in numerical atmospheric modeling. We use this suite of test cases, which gradually adds more complexity to the nonlinear system of governing partial differential equations, to perform a detailed analysis of the accuracy of MLSDCSH upon refinement in time. We illustrate the stability properties of MLSDCSH and show that the proposed scheme achieves up to eighthorder convergence in time. Finally, we study the conditions in which MLSDCSH achieves its theoretical speedup, and we show that it can significantly reduce the computational cost compared to singlelevel Spectral Deferred Corrections (SDC).},
doi = {10.1016/j.jcp.2018.09.042},
url = {https://www.osti.gov/biblio/1490706},
journal = {Journal of Computational Physics},
issn = {00219991},
number = ,
volume = 376,
place = {United States},
year = {2018},
month = {10}
}
Web of Science
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