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Title: A pressure relaxation closure model for one-dimensional, two-material Lagrangian hydrodynamics based on the Riemann problem

Abstract

Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on the problem of closing a system of equations for a two-material cell under the assumption of a single velocity model. There are several existing models and approaches, each possessing different levels of fidelity to the underlying physics and each exhibiting unique features in the computed solutions. We consider the case in which the change in heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast as four equations in four unknowns, comprised of the updated values of the specific internal energy and the specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which the updated values of the sub-cell, relaxing-toward-equilibrium constituent pressures are related to a local Riemann problem through an optimization principle. This approach couples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the framework of a standard predictor-corrector time integration scheme. We evaluate our model usingmore » idealized, two material problems using either ideal-gas or stiffened-gas equations of state and compare these results to those computed with the method of Tipton and with corresponding pure-material calculations.« less

Authors:
 [1];  [1]
  1. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
956372
Report Number(s):
LA-UR-09-00659; LA-UR-09-659
TRN: US1004041
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Name: Communications in Computational Physics
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; EQUATIONS OF STATE; HYDRODYNAMICS; LAGRANGIAN FUNCTION; STRESS RELAXATION; COMPUTERIZED SIMULATION; RIEMANN FUNCTION

Citation Formats

Kamm, James R, and Shashkov, Mikhail J. A pressure relaxation closure model for one-dimensional, two-material Lagrangian hydrodynamics based on the Riemann problem. United States: N. p., 2009. Web.
Kamm, James R, & Shashkov, Mikhail J. A pressure relaxation closure model for one-dimensional, two-material Lagrangian hydrodynamics based on the Riemann problem. United States.
Kamm, James R, and Shashkov, Mikhail J. 2009. "A pressure relaxation closure model for one-dimensional, two-material Lagrangian hydrodynamics based on the Riemann problem". United States. https://www.osti.gov/servlets/purl/956372.
@article{osti_956372,
title = {A pressure relaxation closure model for one-dimensional, two-material Lagrangian hydrodynamics based on the Riemann problem},
author = {Kamm, James R and Shashkov, Mikhail J},
abstractNote = {Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on the problem of closing a system of equations for a two-material cell under the assumption of a single velocity model. There are several existing models and approaches, each possessing different levels of fidelity to the underlying physics and each exhibiting unique features in the computed solutions. We consider the case in which the change in heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast as four equations in four unknowns, comprised of the updated values of the specific internal energy and the specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which the updated values of the sub-cell, relaxing-toward-equilibrium constituent pressures are related to a local Riemann problem through an optimization principle. This approach couples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the framework of a standard predictor-corrector time integration scheme. We evaluate our model using idealized, two material problems using either ideal-gas or stiffened-gas equations of state and compare these results to those computed with the method of Tipton and with corresponding pure-material calculations.},
doi = {},
url = {https://www.osti.gov/biblio/956372}, journal = {Communications in Computational Physics},
number = ,
volume = ,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 2009},
month = {Thu Jan 01 00:00:00 EST 2009}
}