Conditional Multilevel Monte Carlo Simulation of Groundwater Flow in the Culebra Dolomite at the Waste Isolation Pilot Plant (WIPP) Site

We extended the multilevel Monte of Carlo (MLMC) approach to simulation of groundwater flow in porous media by incorporating direct measurements of medium properties. Numerical simulations of Waste Isolation Pilot Plant (WIPP) repository in southeastern New Mexico are performed to test the performance of the conditional MLMC technique. The log-transmissivity of WIPP site is modeled as the conditional random fields which honor exact field values at a few locations. The conditional random fields are generated through the modified circulant embedding methods in (Dietrich and Newsam, 1996). We also study effects of a combination of the conditional MLMC accompanied by antithetic variates. The main quantity of interest is the time of radionuclides travelling from the center of repository to the site boundary. Numerical examples are presented to demonstrate the cost-effectiveness of the multilevel approach in comparison to the standard Monte Carlo (MC) simulation.