UNCERTAINTY QUANTIFICATION OF DETONATION THROUGH ADAPTED POLYNOMIAL CHAOS

摘要

Mathematical models used to describe detonation consist usually of coupled nonlinear partial differential equations, with phenomena occurring at a multitude of scales. While numerical solutions of these problems require significant computational resources, the evolution of the physics along multiple spatial and temporal scales makes the associated predictions sensitive to fluctuations that are beyond normal experimental control. Modeling, characterizing, and propagating uncertainties in predictions of detonation dynamics exacerbates both the mathematical, algorithmic, and computational challenges. These challenges are addressed in the present paper by using basis adaptation in the context of polynomial chaos expansions. The multivariate Rosenblatt transformation is used to first map all the random variables to independent Gaussian variables, following which a rotation is affected on these Gaussians that is adapted to any specified quantity of interest. Thus, accurate estimates of statistical moments and even probability density functions are obtained at specified Lagrangian reference points.