MultiMaterial Closure Model for HighOrder Finite Element Lagrangian Hydrodynamics
We present a new closure model for single fluid, multimaterial Lagrangian hydrodynamics and its application to highorder finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a highorder variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial noninstantaneous pressure equilibration, while the full pressure equilibration is achieved by both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard onedimensional twomaterial problems, followed by twodimensional and threedimensional multimaterial highvelocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.
 Authors:

^{[1]};
^{[1]};
^{[2]};
^{[3]}
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific ComputingA
 Publication Date:
 Report Number(s):
 LLNLJRNL680774
Journal ID: ISSN 02712091
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 International Journal for Numerical Methods in Fluids
 Additional Journal Information:
 Journal Volume: 82; Journal Issue: 10; Journal ID: ISSN 02712091
 Publisher:
 Wiley
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; closure models; pressure equilibration; shock hydrodynamics; multimaterial hydrodynamics; finite element methods; highorder methods
 OSTI Identifier:
 1341976
Dobrev, V. A., Kolev, T. V., Rieben, R. N., and Tomov, V. Z.. MultiMaterial Closure Model for HighOrder Finite Element Lagrangian Hydrodynamics. United States: N. p.,
Web. doi:10.1002/fld.4236.
Dobrev, V. A., Kolev, T. V., Rieben, R. N., & Tomov, V. Z.. MultiMaterial Closure Model for HighOrder Finite Element Lagrangian Hydrodynamics. United States. doi:10.1002/fld.4236.
Dobrev, V. A., Kolev, T. V., Rieben, R. N., and Tomov, V. Z.. 2016.
"MultiMaterial Closure Model for HighOrder Finite Element Lagrangian Hydrodynamics". United States.
doi:10.1002/fld.4236. https://www.osti.gov/servlets/purl/1341976.
@article{osti_1341976,
title = {MultiMaterial Closure Model for HighOrder Finite Element Lagrangian Hydrodynamics},
author = {Dobrev, V. A. and Kolev, T. V. and Rieben, R. N. and Tomov, V. Z.},
abstractNote = {We present a new closure model for single fluid, multimaterial Lagrangian hydrodynamics and its application to highorder finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a highorder variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial noninstantaneous pressure equilibration, while the full pressure equilibration is achieved by both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard onedimensional twomaterial problems, followed by twodimensional and threedimensional multimaterial highvelocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.},
doi = {10.1002/fld.4236},
journal = {International Journal for Numerical Methods in Fluids},
number = 10,
volume = 82,
place = {United States},
year = {2016},
month = {4}
}