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Title: Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models

Abstract

The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit–explicit (IMEX) additive Runge–Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit – vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly. In each case, the impact of solving nonlinear systems in each implicit ARK stage in a linearly implicit fashion is also explored.The accuracy and efficiency of the IMEX splittings, ARK methods, and solver options are evaluated on a gravity wave and baroclinic wave test case. HEVI splittings that treat some vertical dynamics explicitly do not show a benefit in solution quality or run time over the most implicit HEVI formulation. While splittings that implicitly evolve some horizontal dynamics increase the maximum stable step size of a method, the gains are insufficient to overcome the additional cost of solving a globally coupled system. Solving implicit stage systems in a linearly implicit manner limits the solver cost but this is offset by a reduction inmore » step size to achieve the desired accuracy for some methods. Overall, the third-order ARS343 and ARK324 methods performed the best, followed by the second-order ARS232 and ARK232 methods.« less

Authors:
; ; ; ; ;
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) (SC-21). Scientific Discovery through Advanced Computing (SciDAC)
OSTI Identifier:
1433452
Alternate Identifier(s):
OSTI ID: 1506305
Grant/Contract Number:  
SC0014449; AC02-05CH11231
Resource Type:
Published Article
Journal Name:
Geoscientific Model Development (Online)
Additional Journal Information:
Journal Name: Geoscientific Model Development (Online) Journal Volume: 11 Journal Issue: 4; Journal ID: ISSN 1991-9603
Publisher:
Copernicus GmbH
Country of Publication:
Germany
Language:
English
Subject:
58 GEOSCIENCES; 54 ENVIRONMENTAL SCIENCES

Citation Formats

Gardner, David J., Guerra, Jorge E., Hamon, François P., Reynolds, Daniel R., Ullrich, Paul A., and Woodward, Carol S. Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models. Germany: N. p., 2018. Web. doi:10.5194/gmd-11-1497-2018.
Gardner, David J., Guerra, Jorge E., Hamon, François P., Reynolds, Daniel R., Ullrich, Paul A., & Woodward, Carol S. Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models. Germany. doi:10.5194/gmd-11-1497-2018.
Gardner, David J., Guerra, Jorge E., Hamon, François P., Reynolds, Daniel R., Ullrich, Paul A., and Woodward, Carol S. Tue . "Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models". Germany. doi:10.5194/gmd-11-1497-2018.
@article{osti_1433452,
title = {Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models},
author = {Gardner, David J. and Guerra, Jorge E. and Hamon, François P. and Reynolds, Daniel R. and Ullrich, Paul A. and Woodward, Carol S.},
abstractNote = {The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit–explicit (IMEX) additive Runge–Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit – vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly. In each case, the impact of solving nonlinear systems in each implicit ARK stage in a linearly implicit fashion is also explored.The accuracy and efficiency of the IMEX splittings, ARK methods, and solver options are evaluated on a gravity wave and baroclinic wave test case. HEVI splittings that treat some vertical dynamics explicitly do not show a benefit in solution quality or run time over the most implicit HEVI formulation. While splittings that implicitly evolve some horizontal dynamics increase the maximum stable step size of a method, the gains are insufficient to overcome the additional cost of solving a globally coupled system. Solving implicit stage systems in a linearly implicit manner limits the solver cost but this is offset by a reduction in step size to achieve the desired accuracy for some methods. Overall, the third-order ARS343 and ARK324 methods performed the best, followed by the second-order ARS232 and ARK232 methods.},
doi = {10.5194/gmd-11-1497-2018},
journal = {Geoscientific Model Development (Online)},
number = 4,
volume = 11,
place = {Germany},
year = {2018},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.5194/gmd-11-1497-2018

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Cited by: 3 works
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