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

Kenamond, Mack; Kuzmin, Dmitri; Shashkov, Mikhail

doi:10.1016/j.jcp.2021.110254

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

Journal Article · Wed Mar 03 23:00:00 EST 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110254· OSTI ID:1771097

Kenamond, Mack ^[1]; Kuzmin, Dmitri ^[2]; ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Technische Univ. of Dortmund (Germany)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396

OSTI ID:: 1771097

Report Number(s):: LA-UR--20-29129

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 435; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (23)

Formulations of Artificial Viscosity for Multi-dimensional Shock Wave Computations Caramana, E. J.; Shashkov, M. J.; Whalen, P. P. Journal of Computational Physics, Vol. 144, Issue 1 https://doi.org/10.1006/jcph.1998.5989	journal	July 1998
Reference Jacobian Optimization-Based Rezone Strategies for Arbitrary Lagrangian Eulerian Methods Knupp, Patrick; Margolin, Len G.; Shashkov, Mikhail Journal of Computational Physics, Vol. 176, Issue 1 https://doi.org/10.1006/jcph.2001.6969	journal	February 2002
On Godunov-type methods near low densities Einfeldt, B.; Munz, C. D.; Roe, P. L. Journal of Computational Physics, Vol. 92, Issue 2 https://doi.org/10.1016/0021-9991(91)90211-3	journal	February 1991
Computational methods in Lagrangian and Eulerian hydrocodes Benson, David J. Computer Methods in Applied Mechanics and Engineering, Vol. 99, Issue 2-3 https://doi.org/10.1016/0045-7825(92)90042-I	journal	September 1992
CTH: A three-dimensional shock wave physics code McGlaun, J. M.; Thompson, S. L.; Elrick, M. G. International Journal of Impact Engineering, Vol. 10, Issue 1-4 https://doi.org/10.1016/0734-743X(90)90071-3	journal	January 1990
An efficient linearity-and-bound-preserving remapping method Kucharik, Milan; Shashkov, Mikhail; Wendroff, Burton Journal of Computational Physics, Vol. 188, Issue 2 https://doi.org/10.1016/S0021-9991(03)00187-6	journal	July 2003
Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian–Eulerian methods Bailey, David; Berndt, Markus; Kucharik, Milan Journal of Computational and Applied Mathematics, Vol. 233, Issue 12 https://doi.org/10.1016/j.cam.2009.09.008	journal	April 2010
Remapping, recovery and repair on a staggered grid Margolin, L. G.; Shashkov, Mikhail Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 39-41 https://doi.org/10.1016/j.cma.2003.07.016	journal	October 2004
The distribution-based remapping of the nodal mass and momentum between arbitrary meshes for staggered arbitrary Lagrangian-Eulerian hydrodynamics Kenamond, Mack; Shashkov, Mikhail Computers & Fluids, Vol. 201 https://doi.org/10.1016/j.compfluid.2020.104469	journal	April 2020
Using the SMG scheme to study the Rayleigh-Taylor instability growth in solids Luttwak, Gabi Computers & Fluids, Vol. 208 https://doi.org/10.1016/j.compfluid.2020.104603	journal	August 2020
A novel GEEC (Geometry, Energy, and Entropy Compatible) procedure applied to a staggered direct-ALE scheme for hydrodynamics Vazquez-Gonzalez, T.; Llor, A.; Fochesato, C. European Journal of Mechanics - B/Fluids, Vol. 65 https://doi.org/10.1016/j.euromechflu.2017.05.003	journal	September 2017
Kinetic energy fix for low internal energy flows Hu, X. Y.; Khoo, B. C. Journal of Computational Physics, Vol. 193, Issue 1 https://doi.org/10.1016/j.jcp.2003.08.007	journal	January 2004
The repair paradigm and application to conservation laws Shashkov, Mikhail; Wendroff, Burton Journal of Computational Physics, Vol. 198, Issue 1 https://doi.org/10.1016/j.jcp.2004.01.014	journal	July 2004
The repair paradigm: New algorithms and applications to compressible flow Loubère, Raphaël; Staley, Martin; Wendroff, Burton Journal of Computational Physics, Vol. 211, Issue 2 https://doi.org/10.1016/j.jcp.2005.05.010	journal	January 2006
An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model Kokh, S.; Lagoutière, F. Journal of Computational Physics, Vol. 229, Issue 8 https://doi.org/10.1016/j.jcp.2009.12.003	journal	April 2010
ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method Loubère, Raphaël; Maire, Pierre-Henri; Shashkov, Mikhail Journal of Computational Physics, Vol. 229, Issue 12 https://doi.org/10.1016/j.jcp.2010.03.011	journal	June 2010
Positivity-preserving method for high-order conservative schemes solving compressible Euler equations Hu, Xiangyu Y.; Adams, Nikolaus A.; Shu, Chi-Wang Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.01.024	journal	June 2013
Arbitrary Lagrangian–Eulerian methods for modeling high-speed compressible multimaterial flows Barlow, Andrew J.; Maire, Pierre-Henri; Rider, William J. Journal of Computational Physics, Vol. 322 https://doi.org/10.1016/j.jcp.2016.07.001	journal	October 2016
Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme Burton, D. E.; Morgan, N. R.; Charest, M. R. J. Journal of Computational Physics, Vol. 355 https://doi.org/10.1016/j.jcp.2017.11.017	journal	February 2018
Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in Lagrangian hydrodynamics Barlow, Andrew; Klima, Matej; Shashkov, Mikhail Journal of Computational Physics, Vol. 371 https://doi.org/10.1016/j.jcp.2018.03.034	journal	October 2018
Conservative and entropy controlled remap for multi-material ALE simulations with space-staggered schemes Marbœuf, Alexis; Claisse, Alexandra; Le Tallec, Patrick Journal of Computational Physics, Vol. 390 https://doi.org/10.1016/j.jcp.2019.04.017	journal	August 2019
Intersection-distribution-based remapping between arbitrary meshes for staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics Kenamond, Mack; Kuzmin, Dmitri; Shashkov, Mikhail Journal of Computational Physics, Vol. 429 https://doi.org/10.1016/j.jcp.2020.110014	journal	March 2021
Group‐invariant solutions and optimal systems for multidimensional hydrodynamics Coggeshall, S. V.; Meyer‐ter‐Vehn, J. Journal of Mathematical Physics, Vol. 33, Issue 10 https://doi.org/10.1063/1.529907	journal	October 1992

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97 MATHEMATICS AND COMPUTING
arbitrary meshes
limiting techniques
multi-material remapping
positivity preservation
staggered arbitrary-Lagrangian-Eulerian hydrodynamics

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

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