New Algorithms to Accelerate Chemical Equilibrium Calculations of Shocked Materials Submission

Chemical equilibrium is approximately achieved in shocked materials when the temperature is sufficiently high that reaction times are fast compared to the experimental duration. Shocked organic solids, such as polymers, may achieve states of chemical equilibrium when the shock is sufficiently strong. The calculation of chemical equilibrium is equivalent to minimizing a free energy appropriate to thermodynamic constraints and stoichiometric constraints. The chemical equilibrium minimization problem is well-known to be ill-conditioned numerically. This makes the reliable calculation of chemical equilibrium difficult to achieve in a fixed number of iterations. I will discuss methods to adaptively determine approximate solutions to the chemical equilibrium problem based on nearby prior solutions. The methods are based on grid-free interpolation. The effectiveness of several grid-free interpolation algorithms for calculating chemical equilibrium will be discussed. The approximate solution method dramatically reduces the worst-case number of iterations required to determine chemical equilibrium. Application to the calculation of the equation of state of a shocked polymer will be presented.