Differential Sensitivity Theory applied to the MESA2D code for multi-material problems

The technique called Differential Sensitivity Theory (DST) is extended to the multi-component system of equations solved by the MESA2D hydrocode. DST uses adjoint techniques to determine exact sensitivity derivatives, i.e., if R is a calculation result of interest (response R) and αi is a calculation input (parameter αi), then ∂R/∂αi is defined as the sensitivity. The advantage of using DST is that for an n-parameter problem all n sensitivities can be obtained by integrating the solutions from only two calculations, a MESA calculation and its corresponding adjoint calculation using an Adjoint Continuum Mechanics (ACM) code. Previous papers have described application of the technique to one-dimensional, single-material problems. This work presents the derivation and solution of the additional adjoint equations for the purpose of computing sensitivities for two-dimensional, multi-component problems. As an example, results for a multi-material flyer plate impact problem featuring an oblique impact are given.