Uncertainty Quantification Of Analytic Radiation Driven Nonlinear Heat Waves

Uncertainty quantification methods are applied to a known equilibrium diffusion thermal radiation wave solution, the Marshak wave, to estimate statistical properties of some diagnostics, the wave breakout time and material temperature profile, in the presence of uncertain material properties and experimental parameters. It is shown that polynomial chaos expansions are well suited for representing the analytic breakout time function and moments of the temperature profile, but are a poor choice for calculating percentile values of the temperature profile, which posses sharp wavefronts. The results presented are intended to benchmark uncertainty quantifying radiative transfer codes and provide qualitative insight into the interpretation of experimental results with measurement errors as well as to present an illustrative example of the limitations of polynomial chaos expansions on functions with steep gradients.