Evaluating the uncertainty of Darcy velocity with sparse grid collocation method

Spatial variability of Darcy velocity is presented due to the heterogeneity of aquifer parameters. The uncertainty qualification of velocity suffers great challenge in the complex porous media. This work focuses on the use of sparse grid collocation method in velocity simulation. Since the sparse grid collocation method provides a non-intrusive way to incorporate any existing deterministic solver, the mixed finite element method is combined as the deterministic solver to retain the local continuity of Darcy velocity. We decompose the error of the velocity into three components, and illustrate that the Karhunen-Loeve truncation brings more error into velocity approximation than into head. The convergence properties of velocity moments restrict the application of sparse grid collocation method in the problems with small correlation lengths. This work provides insights towards the application of sparse grid collocation method to velocity modeling. It is demonstrated that for which problems the sparse grid collocation method is expected to be competitive with the Monte Carlo simulation. Further work about the anisotropic sparse grid collocation method should be extended to circumvent the obstacle of dimensionality.