A Pressure Relaxation Closure Model for One-Dimensional, Two-Material Lagrangian Hydrodynamics Based on the Riemann Problem

Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on theproblem of closing a system of equations for a two-material cell under the assumptionof a single velocity model. There are several existing models and approaches, eachpossessing different levels of fidelity to the underlying physics and each exhibitingunique features in the computed solutions. We consider the case in which the changein 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 infour unknowns, comprised of the updated values of the specific internal energy andthe 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 theupdated values of the sub-cell, relaxing-toward-equilibrium constituent pressures arerelated to a local Riemann problem through an optimization principle. This approachcouples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the frameworkof a standard predictor-corrector time integration scheme. We evaluate our model using idealized, two material problems using either ideal-gas or stiffened-gas equationsof state and compare these results to those computed with the method of Tipton andwith corresponding pure-material calculations.