Analyzing radiation diffusion using time-dependent sensitivity-based techniques

In this paper, we discuss the computation and use of solution sensitivities for analyzing radiation diffusion problems and the dependence of solutions on input parameters. The derivation of the sensitivity equations is given, along with a description of the method for solving them in tandem with the simulation. The parameter values express material opacity as a power-law of material temperature and density. The computed sensitivities reveal important qualitative details about the temperature coupling and diffusion processes. It is also shown that these sensitivities are valuable for ranking the parameters from most to least influential, designing improved experiments, and quantifying uncertainty in the simulation results. Lastly, the numerical examples show that these various types of sensitivity analysis are only moderately expensive to perform relative to solving the simulation by itself.