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Title: Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections

Abstract

© 2019. The American Astronomical Society. All rights reserved. Simulations in stellar astrophysics involve the coupling of hydrodynamics and nuclear reactions under a wide variety of conditions, from simmering convective flows to explosive nucleosynthesis. Numerical techniques such as operator splitting (most notably Strang splitting) are usually employed to couple the physical processes, but this can affect the accuracy of the simulation, particularly when the burning is vigorous. Furthermore, Strang splitting does not have a straightforward extension to higher-order integration in time. We present a new temporal integration strategy based on spectral deferred corrections, and describe the second- and fourth-order implementations in the open source, finite-volume, compressible hydrodynamics code Castro. One notable advantage to these schemes is that they combine standard low-order discretizations for individual physical processes in a way that achieves an arbitrarily high order of accuracy. We demonstrate the improved accuracy of the new methods on several test problems of increasing complexity.

Authors:
ORCiD logo; ORCiD logo; ORCiD logo; ORCiD logo; ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Stony Brook Univ., NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1593455
Alternate Identifier(s):
OSTI ID: 1581395
Grant/Contract Number:  
AC02-05CH11231; FG02-87ER40317
Resource Type:
Accepted Manuscript
Journal Name:
The Astrophysical Journal (Online)
Additional Journal Information:
Journal Name: The Astrophysical Journal (Online); Journal Volume: 886; Journal Issue: 2; Journal ID: ISSN 1538-4357
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; 97 MATHEMATICS AND COMPUTING; Hydrodynamics; Computational methods; Nuclear astrophysics; Nucleosynthesis; Stellar nucleosynthesis

Citation Formats

Zingale, M., Katz, M. P., Bell, J. B., Minion, M. L., Nonaka, A. J., and Zhang, W. Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections. United States: N. p., 2019. Web. doi:10.3847/1538-4357/ab4e1d.
Zingale, M., Katz, M. P., Bell, J. B., Minion, M. L., Nonaka, A. J., & Zhang, W. Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections. United States. doi:10.3847/1538-4357/ab4e1d.
Zingale, M., Katz, M. P., Bell, J. B., Minion, M. L., Nonaka, A. J., and Zhang, W. Tue . "Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections". United States. doi:10.3847/1538-4357/ab4e1d.
@article{osti_1593455,
title = {Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections},
author = {Zingale, M. and Katz, M. P. and Bell, J. B. and Minion, M. L. and Nonaka, A. J. and Zhang, W.},
abstractNote = {© 2019. The American Astronomical Society. All rights reserved. Simulations in stellar astrophysics involve the coupling of hydrodynamics and nuclear reactions under a wide variety of conditions, from simmering convective flows to explosive nucleosynthesis. Numerical techniques such as operator splitting (most notably Strang splitting) are usually employed to couple the physical processes, but this can affect the accuracy of the simulation, particularly when the burning is vigorous. Furthermore, Strang splitting does not have a straightforward extension to higher-order integration in time. We present a new temporal integration strategy based on spectral deferred corrections, and describe the second- and fourth-order implementations in the open source, finite-volume, compressible hydrodynamics code Castro. One notable advantage to these schemes is that they combine standard low-order discretizations for individual physical processes in a way that achieves an arbitrarily high order of accuracy. We demonstrate the improved accuracy of the new methods on several test problems of increasing complexity.},
doi = {10.3847/1538-4357/ab4e1d},
journal = {The Astrophysical Journal (Online)},
number = 2,
volume = 886,
place = {United States},
year = {2019},
month = {11}
}

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