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Title: Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics

Abstract

We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order 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 high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous 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 one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity 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]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific ComputingA
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1341976
Report Number(s):
LLNL-JRNL-680774
Journal ID: ISSN 0271-2091
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Fluids
Additional Journal Information:
Journal Volume: 82; Journal Issue: 10; Journal ID: ISSN 0271-2091
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; closure models; pressure equilibration; shock hydrodynamics; multi-material hydrody-namics; finite element methods; high-order methods

Citation Formats

Dobrev, V. A., Kolev, T. V., Rieben, R. N., and Tomov, V. Z. Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics. United States: N. p., 2016. Web. doi:10.1002/fld.4236.
Dobrev, V. A., Kolev, T. V., Rieben, R. N., & Tomov, V. Z. Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics. United States. doi:10.1002/fld.4236.
Dobrev, V. A., Kolev, T. V., Rieben, R. N., and Tomov, V. Z. Wed . "Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics". United States. doi:10.1002/fld.4236. https://www.osti.gov/servlets/purl/1341976.
@article{osti_1341976,
title = {Multi-Material Closure Model for High-Order 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, multi-material Lagrangian hydrodynamics and its application to high-order 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 high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous 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 one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity 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}
}

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