Problems encountered during impact calculations using analytic equations of state

Abstract

During modeling of the impact of a projectile on a target or other calculations that bring materials together at high velocities, computer simulations of materials being shocked to high pressure and then releasing to low pressure are performed. Depending on the circumstances, the release to low pressure is often accompanied by release to a very low density. Numerical problems leading to very large sound speeds (and thus small time steps) or to negative Lagrangian volumes have been encountered during MESA-2D calculations of this nature. These problems can be traced to the behavior of the equation of state (EOS) in the limit as the density becomes much less than the normal or reference density. Although analytic solutions for expansion isentropes may show acceptable behavior in the low-density limit, numerical solutions can show undesirable behavior. Examples of this undesirable behavior in the low-density regime are given for some simple, analytic equations of state that have closed-form solutions for isentropes. The behavior of three analytic EOSs that are frequently used in MESA-2D calculations are then discussed. These EOSs are the Los Alamos EOS, the MESA polynomial EOS, and a Mie-Gruneisen EOS based on a linear relation between shock and particle velocity. The problems in the low-density region can be corrected for the Los Alamos EOS and the MESA polynomial EOS by the proper choice of EOS coefficients in the expansion region (density less than the reference density). Problems with the Mie-Gruneisen EOS can be corrected if the functional relationship between the Gruneisen parameter ({Tau}) and density differs above and below the reference density.