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Title: A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes

Abstract

In this study, we introduce new intersection-distribution-based remapping tools for indirect staggered arbitrary Lagrangian-Eulerian (ALE) simulations of multi-material shock hydrodynamics on arbitrary meshes. In addition to conserving momentum and total energy, the three-stage remapper proposed in this work preserves non-negativity of the internal energy. At the first stage, we construct slope-limited piecewise-linear reconstructions of all conserved quantities on zones of the source mesh and perform intersection-based remap to obtain bound-preserving zonal quantities on the target mesh. At the second stage, we define bound-preserving nodal quantities of the staggered ALE discretization as convex combinations of corner quantities. The nodal internal energy is corrected in a way which keeps it non-negative, while providing exact conservation of total energy. At the final stage, we distribute the non-negative nodal internal energy to corners, zones and materials using non-negative weights. Proofs of positivity preservation are provided for each stage. This work is a natural extension of our paper [14] in which a similar intersection-distribution-based remapping procedure was employed. The original version used a nodal kinetic energy fix which did not provably ensure positivity preservation for the zonal internal energy after the final distribution stage. The new algorithm cures this potential drawback by using ‘coordinated’ limitersmore » for piecewise-linear reconstructions, remapping the internal energy to nodes and correcting it before redistribution. The effectiveness of the new nodal fix is illustrated by numerical examples.« less

Authors:
 [1];  [2]; ORCiD logo [1]
+ Show Author Affiliations
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Technische Univ. of Dortmund (Germany)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
OSTI Identifier:
1771097
Alternate Identifier(s):
OSTI ID: 1815190
Report Number(s):
LA-UR-20-29129
Journal ID: ISSN 0021-9991; TRN: US2208225
Grant/Contract Number:  
89233218CNA000001; AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 435; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; staggered arbitrary-Lagrangian-Eulerian hydrodynamics; multi-material remapping; arbitrary meshes; limiting techniques; positivity preservation

Citation Formats

Kenamond, Mack, Kuzmin, Dmitri, and Shashkov, Mikhail. A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes. United States: N. p., 2021. Web. doi:10.1016/j.jcp.2021.110254.
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Kenamond, Mack, Kuzmin, Dmitri, & Shashkov, Mikhail. A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes. United States. https://doi.org/10.1016/j.jcp.2021.110254
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Kenamond, Mack, Kuzmin, Dmitri, and Shashkov, Mikhail. Thu . "A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes". United States. https://doi.org/10.1016/j.jcp.2021.110254. https://www.osti.gov/servlets/purl/1771097.
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@article{osti_1771097,
title = {A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes},
author = {Kenamond, Mack and Kuzmin, Dmitri and Shashkov, Mikhail},
abstractNote = {In this study, we introduce new intersection-distribution-based remapping tools for indirect staggered arbitrary Lagrangian-Eulerian (ALE) simulations of multi-material shock hydrodynamics on arbitrary meshes. In addition to conserving momentum and total energy, the three-stage remapper proposed in this work preserves non-negativity of the internal energy. At the first stage, we construct slope-limited piecewise-linear reconstructions of all conserved quantities on zones of the source mesh and perform intersection-based remap to obtain bound-preserving zonal quantities on the target mesh. At the second stage, we define bound-preserving nodal quantities of the staggered ALE discretization as convex combinations of corner quantities. The nodal internal energy is corrected in a way which keeps it non-negative, while providing exact conservation of total energy. At the final stage, we distribute the non-negative nodal internal energy to corners, zones and materials using non-negative weights. Proofs of positivity preservation are provided for each stage. This work is a natural extension of our paper [14] in which a similar intersection-distribution-based remapping procedure was employed. The original version used a nodal kinetic energy fix which did not provably ensure positivity preservation for the zonal internal energy after the final distribution stage. The new algorithm cures this potential drawback by using ‘coordinated’ limiters for piecewise-linear reconstructions, remapping the internal energy to nodes and correcting it before redistribution. The effectiveness of the new nodal fix is illustrated by numerical examples.},
doi = {10.1016/j.jcp.2021.110254},
journal = {Journal of Computational Physics},
number = ,
volume = 435,
place = {United States},
year = {Thu Mar 04 00:00:00 EST 2021},
month = {Thu Mar 04 00:00:00 EST 2021}
}
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https://doi.org/10.1016/j.jcp.2021.110254
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