Conservative High-Order Time Integration for Lagrangian Hydrodynamics
Abstract
This work develops novel time integration methods for the compressible Euler equations in the Lagrangian frame that are of arbitrary high order and exactly preserve the mass, momentum, and total energy of the system. The equations are considered in nonconservative form, that is, common for staggered grid hydrodynamics (SGH) methods; namely, the evolved quantities are mass, momentum, and internal energy. A general family of time integration schemes is formulated, and practical pairs for orders three and four are derived. Numerical results on standard hydrodynamics benchmarks confirm the high-order convergence on smooth problems and the exact numerical preservation of all physically conserved quantities.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: A221 - A241
DOI: 10.1137/20M1314495
ISSN (online): 1095-7197
Copyright
© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 22 January 2020
Accepted: 2 October 2020
Published online: 12 January 2021
Keywords
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Authors
Funding Information
Air Force Office of Scientific Research https://doi.org/10.13039/100000181 : 15RT1037
Lawrence Livermore National Laboratory https://doi.org/10.13039/100006227 : DE-AC52-07NA27344
National Science Foundation https://doi.org/10.13039/100000001 : CCF-1613905, ACI-1709727
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