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

TL;DR

This paper develops a conditional multilevel Monte Carlo method for groundwater flow simulation at the WIPP site, incorporating direct measurements to improve efficiency and accuracy in modeling radionuclide transport.

Contribution

It introduces a conditional MLMC technique that integrates exact field measurements and studies its performance in groundwater flow modeling.

Findings

Conditional MLMC reduces computational cost compared to standard MC.

Incorporating measurements improves model accuracy.

Combining with antithetic variates enhances efficiency.

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 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.