Reduced-order Monte Carlo simulation framework for groundwater flow in randomly heterogeneous composite transmissivity fields

We develop a reduced-order modeling strategy aimed at providing numerical Monte Carlo simulations of groundwater flow in randomly heterogeneous transmissivity fields. We rely on moment equations for groundwater flow and conduct space reductions for both transmissivity, T, and hydraulic head, h. A truncated singular value decomposition (SVD) solver is employed to cope with the ill-conditioned stiffness matrix caused by (negative and thus) unphysical values of T that might arise due to possible low accuracy stemming from the order of model reduction. The performance of the approach is assessed through the analysis of various synthetic reference scenarios. These encompass diverse degrees of heterogeneity of the transmissivity field and various values of reduced-order dimensions, n and m, associated with h and T, respectively. Transmissivity is conceptualized as a composite (spatial) random field where there is uncertainty in the locations of regions associated with diverse geomaterials as well as in the heterogeneity of transmissivity therein. Our results are also compared against their counterparts that one could obtain upon performing a model reduction solely on the basis of hydraulic heads. Our findings show that: (i) resting on the truncated SVD solver is beneficial for coping with ill-conditioned stiffness matrices; (ii) the two model reduction strategies provide comparable solution accuracy for m ≥ 5n, while (iii) the computational cost associated with the reduced-order model based on space reduction for both T and h is always significantly smaller than that associated with space reduction based solely on h.