Conditional Simulation of Flow in Heterogeneous Porous Media with the Probabilistic Collocation Method (Communications in Computational Physics, 2014)
A stochastic approach to conditional simulation of flow in randomly heterogeneous media is proposed with the combination of the Karhunen-Loeve expansionand the probabilistic collocation method (PCM). The conditional log hydraulic conductivity field is represented with the Karhunen-Loeve expansion, in terms of somedeterministic functions and a set of independent Gaussian random variables. Thepropagation of uncertainty in the flow simulations is carried out through the PCM,which relies on the efficient polynomial chaos expansion used to represent the flowresponses such as the hydraulic head. With the PCM, existing flow simulators can beemployed for uncertainty quantification of flow in heterogeneous porous media whendirect measurements of hydraulic conductivity are taken into consideration. With illustration of several numerical examples of groundwater flow, this study reveals thatthe proposed approach is able to accurately quantify uncertainty of the flow responsesconditioning on hydraulic conductivity data, while the computational efforts are significantly reduced in comparison to the Monte Carlo simulations.