skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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 [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [3]; ORCiD logo [3]; ORCiD logo [3]
  1. Stony Brook Univ., NY (United States)
  2. NVIDIA Corp., Santa Clara, CA (United States)
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Stony Brook Univ., NY (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1593455
Alternate Identifier(s):
OSTI ID: 1581395; OSTI ID: 1656793
Grant/Contract Number:  
FG02-87ER40317; AC02-05CH11231
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:https://doi.org/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:https://doi.org/10.3847/1538-4357/ab4e1d. https://www.osti.gov/servlets/purl/1593455.
@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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry
journal, March 2016


Accelerating the convergence of spectral deferred correction methods
journal, May 2006

  • Huang, Jingfang; Jia, Jun; Minion, Michael
  • Journal of Computational Physics, Vol. 214, Issue 2
  • DOI: 10.1016/j.jcp.2005.10.004

A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics
journal, January 2008

  • Kadioglu, Samet Y.; Klein, Rupert; Minion, Michael L.
  • Journal of Computational Physics, Vol. 227, Issue 3
  • DOI: 10.1016/j.jcp.2007.10.008

A fourth-order adaptive mesh refinement algorithm for the multicomponent, reacting compressible Navier–Stokes equations
journal, January 2019


FLASH: An Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes
journal, November 2000

  • Fryxell, B.; Olson, K.; Ricker, P.
  • The Astrophysical Journal Supplement Series, Vol. 131, Issue 1
  • DOI: 10.1086/317361

pyro: a framework for hydrodynamics explorations and prototyping
journal, February 2019

  • Harpole, Alice; Zingale, Michael; Hawke, Ian
  • Journal of Open Source Software, Vol. 4, Issue 34
  • DOI: 10.21105/joss.01265

pyro: A teaching code for computational astrophysical hydrodynamics
journal, October 2014


VODE: A Variable-Coefficient ODE Solver
journal, September 1989

  • Brown, Peter N.; Byrne, George D.; Hindmarsh, Alan C.
  • SIAM Journal on Scientific and Statistical Computing, Vol. 10, Issue 5
  • DOI: 10.1137/0910062

Semi-implicit spectral deferred correction methods for ordinary differential equations
journal, January 2003


APSARA: A multi-dimensional unsplit fourth-order explicit Eulerian hydrodynamics code for arbitrary curvilinear grids
journal, October 2016


Toward Resolved Simulations of Burning Fronts in Thermonuclear X-ray Bursts
journal, May 2019


Low Mach Number Modeling of Type Ia Supernovae. III. Reactions
journal, September 2008

  • Almgren, A. S.; Bell, J. B.; Nonaka, A.
  • The Astrophysical Journal, Vol. 684, Issue 1
  • DOI: 10.1086/590321

Numerical Stability of Detonations in White Dwarf Simulations
journal, April 2019


Beyond second-order convergence in simulations of magnetized binary neutron stars with realistic microphysics
journal, October 2019

  • Most, E. R.; Papenfort, L. Jens; Rezzolla, L.
  • Monthly Notices of the Royal Astronomical Society, Vol. 490, Issue 3
  • DOI: 10.1093/mnras/stz2809

A piecewise parabolic method for cosmological hydrodynamics
journal, August 1995


A Direct Eulerian MUSCL Scheme for Gas Dynamics
journal, January 1985

  • Colella, Phillip
  • SIAM Journal on Scientific and Statistical Computing, Vol. 6, Issue 1
  • DOI: 10.1137/0906009

The Accuracy, Consistency, and Speed of an Electron‐Positron Equation of State Based on Table Interpolation of the Helmholtz Free Energy
journal, February 2000

  • Timmes, F. X.; Swesty, F. Douglas
  • The Astrophysical Journal Supplement Series, Vol. 126, Issue 2
  • DOI: 10.1086/313304

AMReX: a framework for block-structured adaptive mesh refinement
journal, May 2019

  • Zhang, Weiqun; Almgren, Ann; Beckner, Vince
  • Journal of Open Source Software, Vol. 4, Issue 37
  • DOI: 10.21105/joss.01370

Screening Factors for Nuclear Reactions. 11. Intermediate Screen-Ing and Astrophysical Applications
journal, April 1973

  • Graboske, H. C.; Dewitt, H. E.; Grossman, A. S.
  • The Astrophysical Journal, Vol. 181
  • DOI: 10.1086/152062

On the Use of Higher-Order Projection Methods for Incompressible Turbulent Flow
journal, January 2013

  • Almgren, A. S.; Aspden, A. J.; Bell, J. B.
  • SIAM Journal on Scientific Computing, Vol. 35, Issue 1
  • DOI: 10.1137/110829386

Thermonuclear reaction rates V
journal, November 1988


A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport
journal, December 2018


Turbulent Convection in Stellar Interiors. I. Hydrodynamic Simulation
journal, September 2007

  • Meakin, Casey A.; Arnett, David
  • The Astrophysical Journal, Vol. 667, Issue 1
  • DOI: 10.1086/520318

Nuclear reaction rate enhancement in dense stellar matter
journal, December 1978

  • Alastuey, A.; Jancovici, B.
  • The Astrophysical Journal, Vol. 226
  • DOI: 10.1086/156681

Stiff ODE solvers: A review of current and coming attractions
journal, May 1987


Maestro: an Adaptive low mach Number Hydrodynamics Algorithm for Stellar Flows
journal, May 2010

  • Nonaka, A.; Almgren, A. S.; Bell, J. B.
  • The Astrophysical Journal Supplement Series, Vol. 188, Issue 2
  • DOI: 10.1088/0067-0049/188/2/358

Mapping Initial Hydrostatic Models in Godunov Codes
journal, December 2002

  • Zingale, M.; Dursi, L. J.; ZuHone, J.
  • The Astrophysical Journal Supplement Series, Vol. 143, Issue 2
  • DOI: 10.1086/342754

A high-order finite-volume method for conservation laws on locally refined grids
journal, January 2011

  • McCorquodale, Peter; Colella, Phillip
  • Communications in Applied Mathematics and Computational Science, Vol. 6, Issue 1
  • DOI: 10.2140/camcos.2011.6.1

High-order multi-implicit spectral deferred correction methods for problems of reactive flow
journal, August 2003


On the Construction and Comparison of Difference Schemes
journal, September 1968

  • Strang, Gilbert
  • SIAM Journal on Numerical Analysis, Vol. 5, Issue 3
  • DOI: 10.1137/0705041

Matplotlib: A 2D Graphics Environment
journal, January 2007


A higher-order Godunov method for radiation hydrodynamics: Radiation subsystem
journal, January 2009

  • Sekora, Michael; Stone, James
  • Communications in Applied Mathematics and Computational Science, Vol. 4, Issue 1
  • DOI: 10.2140/camcos.2009.4.135

Python for Scientific Computing
journal, January 2007


Multidimensional upwind methods for hyperbolic conservation laws
journal, March 1990


SymPy: symbolic computing in Python
journal, January 2017

  • Meurer, Aaron; Smith, Christopher P.; Paprocki, Mateusz
  • PeerJ Computer Science, Vol. 3
  • DOI: 10.7717/peerj-cs.103

The NumPy Array: A Structure for Efficient Numerical Computation
journal, March 2011

  • van der Walt, Stéfan; Colbert, S. Chris; Varoquaux, Gaël
  • Computing in Science & Engineering, Vol. 13, Issue 2
  • DOI: 10.1109/MCSE.2011.37

Enhancement of thermonuclear reaction rate due to strong screening. II - Ionic mixtures
journal, December 1979

  • Itoh, N.; Totsuji, H.; Ichimaru, S.
  • The Astrophysical Journal, Vol. 234
  • DOI: 10.1086/157590

yt: A MULTI-CODE ANALYSIS TOOLKIT FOR ASTROPHYSICAL SIMULATION DATA
journal, December 2010

  • Turk, Matthew J.; Smith, Britton D.; Oishi, Jeffrey S.
  • The Astrophysical Journal Supplement Series, Vol. 192, Issue 1
  • DOI: 10.1088/0067-0049/192/1/9

A Conservative Three-Dimensional Eulerian Method for Coupled Solid–Fluid Shock Capturing
journal, November 2002


High-order algorithms for compressible reacting flow with complex chemistry
journal, May 2014


White Dwarf Mergers on Adaptive Meshes. i. Methodology and code Verification
journal, March 2016


Castro: a new Compressible Astrophysical Solver. i. Hydrodynamics and Self-Gravity
journal, May 2010


On the Piecewise Parabolic Method for Compressible flow with Stellar Equations of State
journal, February 2015