Stochastic collocation using Kronrod-Patterson-Hermite quadrature with moderate delay for subsurface flow and transport

Abstract:

Uncertainty quantification aims at characterizing the impact of input parameters on the output responses and plays an important role in many areas including subsurface flow and transport. In this study, a sparse grid collocation approach, which uses a nested Kronrod-Patterson-Hermite quadrature rule with moderate delay for Gaussian random parameters, is proposed to quantify the uncertainty of model solutions. The conventional stochastic collocation method serves as a promising non-intrusive approach and has drawn a great deal of interests. The collocation points are usually chosen to be Gauss-Hermite quadrature nodes, which are naturally unnested. The Kronrod-Patterson-Hermite nodes are shown to be more efficient than the Gauss-Hermite nodes due to nestedness. We propose a Kronrod-Patterson-Hermite rule with moderate delay to further improve the performance. Our study demonstrates the effectiveness of the proposed method for uncertainty quantification through subsurface flow and transport examples.