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

Abstract

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 logtransmissivity 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.

A Block Circulant Embedding Method for Simulation of Stationary Gaussian Random Fields on Block-Regular Grids

“…As with the unconditional sampling discussed above, applications of conditional sampling often deal with grids which are not regular but have a regular block structure (see, e.g. conditional MLMC simulation in [17]). Since BCEM requires smaller n 1 value as it does in the unconditional case, BCEM in the conditional random field setting can outperform CEM.…”

“…Also, this method is not exact. The fast and exact method of generating large samples from stationary Gaussian fields on regular grids is the circulant embedding method (CEM) [22,6,23] which is widely used in various uncertainty quantification (UQ) applications such as groundwater flow simulation [11,17], weather field forecasting [10], and liquid composite molding processes [21]. The two main drawbacks of CEM are (i) the requirement imposed on the grid to be regular while irregular grids of a block structure naturally appear in many applications (see three typical examples below) and (ii) the need to deal with non-positive definiteness of circular embedding matrices which often occur in practical applications.…”