TY - JOUR
T1 - A Pressure Relaxation Closure Model for One-Dimensional, Two-Material Lagrangian Hydrodynamics Based on the Riemann Problem
AU - James R. Kamm & Mikhail J. Shashkov
JO - Communications in Computational Physics
VL - 5
SP - 927
EP - 976
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/10.4208/cicp.2009.09.032
UR - https://global-sci.org/intro/article_detail/cicp/7660.html
KW - 
AB - <p style="text-align: justify;">Despite decades of development, Lagrangian hydrodynamics of strength-free
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.</p>