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

Journal Article · · International Journal for Numerical Methods in Fluids
DOI:https://doi.org/10.1002/fld.4236· OSTI ID:1341976
 [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
+ Show Author Affiliations

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.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1341976
Report Number(s):
LLNL-JRNL-680774
Journal Information:
International Journal for Numerical Methods in Fluids, Vol. 82, Issue 10; ISSN 0271-2091
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 15 works
Citation information provided by
Web of Science

References (16)

A Pressure Relaxation Closure Model for One-dimensional, Two-material Lagrangian Hydrodynamics Based on the Riemann Problem journal June 2010
Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian–Eulerian methods journal February 2014
A comparative study of interface reconstruction methods for multi-material ALE simulations journal April 2010
A Free-Lagrange Augmented Godunov Method for the Simulation of Elastic–Plastic Solids journal January 2002
A thermodynamic and dynamic subgrid closure model for two-material cells: THERMODYNAMIC AND DYNAMIC CLOSURE MODEL journal March 2013
An arbitrary Lagrangian-Eulerian computing method for all flow speeds journal March 1974
An algorithm for time evolving volume fractions in mixed zones in Lagrangian hydrodynamics calculations journal February 2009
Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian–Eulerian hydrodynamics journal November 2014
Entropy–viscosity method for the single material Euler equations in Lagrangian frame journal March 2016
High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics journal January 2012
Numerical resolution of a two-component compressible fluid model with interfaces journal January 2007
Closure models for multimaterial cells in arbitrary Lagrangian–Eulerian hydrocodes journal January 2008
A comparative study of various pressure relaxation closure models for one-dimensional two-material Lagrangian hydrodynamics journal May 2010
Interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian gas dynamics report February 2012
High order curvilinear finite elements for elastic–plastic Lagrangian dynamics journal January 2014
Multi-material pressure relaxation methods for Lagrangian hydrodynamics journal August 2013

Cited By (1)

A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces journal January 2020

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97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
closure models
pressure equilibration
shock hydrodynamics
multi-material hydrody-namics
finite element methods
high-order methods