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:
-
- 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:
- Research Org.:
- Lawrence Livermore National Laboratory (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. https://doi.org/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. https://doi.org/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 = {Wed Apr 27 00:00:00 EDT 2016},
month = {Wed Apr 27 00:00:00 EDT 2016}
}
Web of Science
Works referenced in this record:
A Pressure Relaxation Closure Model for One-dimensional, Two-material Lagrangian Hydrodynamics Based on the Riemann Problem
journal, June 2010
- Shashkov, James R. Kamm and Mikhail J.
- Communications in Computational Physics, Vol. 7, Issue 5
Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian–Eulerian methods
journal, February 2014
- Kucharik, Milan; Shashkov, Mikhail
- Journal of Computational Physics, Vol. 258
A comparative study of interface reconstruction methods for multi-material ALE simulations
journal, April 2010
- Kucharik, Milan; Garimella, Rao V.; Schofield, Samuel P.
- Journal of Computational Physics, Vol. 229, Issue 7
A Free-Lagrange Augmented Godunov Method for the Simulation of Elastic–Plastic Solids
journal, January 2002
- Howell, B. P.; Ball, G. J.
- Journal of Computational Physics, Vol. 175, Issue 1
A thermodynamic and dynamic subgrid closure model for two-material cells: THERMODYNAMIC AND DYNAMIC CLOSURE MODEL
journal, March 2013
- Sun, Mingyu
- International Journal for Numerical Methods in Fluids, Vol. 73, Issue 2
An arbitrary Lagrangian-Eulerian computing method for all flow speeds
journal, March 1974
- Hirt, C. W.; Amsden, A. A.; Cook, J. L.
- Journal of Computational Physics, Vol. 14, Issue 3
An algorithm for time evolving volume fractions in mixed zones in Lagrangian hydrodynamics calculations
journal, February 2009
- Miller, D. S.; Zimmerman, G. B.
- Russian Journal of Physical Chemistry B, Vol. 3, Issue 1
Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian–Eulerian hydrodynamics
journal, November 2014
- Barlow, Andrew; Hill, Ryan; Shashkov, Mikhail
- Journal of Computational Physics, Vol. 276
Entropy–viscosity method for the single material Euler equations in Lagrangian frame
journal, March 2016
- Guermond, Jean-Luc; Popov, Bojan; Tomov, Vladimir
- Computer Methods in Applied Mechanics and Engineering, Vol. 300
High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics
journal, January 2012
- Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
- SIAM Journal on Scientific Computing, Vol. 34, Issue 5
Numerical resolution of a two-component compressible fluid model with interfaces
journal, January 2007
- Despres, Bruno; Lagoutiere, Frederic
- Progress in Computational Fluid Dynamics, An International Journal, Vol. 7, Issue 6
Closure models for multimaterial cells in arbitrary Lagrangian–Eulerian hydrocodes
journal, January 2008
- Shashkov, M.
- International Journal for Numerical Methods in Fluids, Vol. 56, Issue 8
A comparative study of various pressure relaxation closure models for one-dimensional two-material Lagrangian hydrodynamics
journal, May 2010
- Kamm, J. R.; Shashkov, M. J.; Fung, J.
- International Journal for Numerical Methods in Fluids, Vol. 65, Issue 11-12
Interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian gas dynamics
report, February 2012
- Hill, Ryan; Shashkov, Mikhail; Barlow, Andrew
High order curvilinear finite elements for elastic–plastic Lagrangian dynamics
journal, January 2014
- Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
- Journal of Computational Physics, Vol. 257
Multi-material pressure relaxation methods for Lagrangian hydrodynamics
journal, August 2013
- Yanilkin, Yury V.; Goncharov, Evgeny A.; Kolobyanin, Vadim Yu.
- Computers & Fluids, Vol. 83
Works referencing / citing this record:
A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces
journal, January 2020
- Pandare, Aditya K.; Waltz, Jacob; Bakosi, Jozsef
- International Journal for Numerical Methods in Fluids, Vol. 92, Issue 8