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

Speaker: James Kamm, Los Alamos National Laboratory

Date/Time: Monday, January 5, 2009, 10:00 – 11:00 am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: 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 computational cell under the assumption of a single velocity model. There are several existing pressure equilibration 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 for the non-instantaneous pressure relaxation case.  We present 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 framework.  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 quantify the results of our model for idealized, two material problems using either ideal-gas or stiffened-gas equations of state.  

CSRI POC: Randall M. Summers, (505) 844-6296