Non intrusive iterative stochastic spectral representation with application to compressible gas dynamics

In this paper, we propose a new iterative formulation improving the convergence of standard non intrusive stochastic spectral method for uncertainty quantification. We demonstrate that the method is more accurate than the classical approach with the same level of approximation and at no significant additional computational or memory cost, since it is deployed in a post-processing stage. Moreover, the accuracy of the representation improves no matter the regularity of the random quantity of interest. Therefore, the method is particularly well suited when nonlinear transformations of random variables are in play and can be viewed as a new way of tackling the Gibbs phenomenon. We apply the method to several test cases with different levels of regularity, dimensionality and complexity, including the case of compressible gas dynamics and long time-integration problems. The new and the classical approaches are compared for the resolution of a stochastic Riemann problem governed by an Euler system.