January 15, 2013
Journal Article

CDF Solutions of Buckley-Leverett Equation with Uncertain Parameters

Abstract

The Buckley-Leverett (nonlinear advection) equation is often used to describe two-phase flow in porous media. We develop a new probabilistic method to quantify parametric uncertainty in the Buckley-Leverett model. Our approach is based on the concept of fine-grained cumulative density function (CDF) and provides a full statistical description of the system states. Hence, it enables one to obtain not only average system response but also the probability of rare events, which is critical for risk assessment. We obtain a closed-form, semi-analytical solution and test it against the results from Monte Carlo simulations.

Revised: February 18, 2013 | Published: January 15, 2013

Citation

Wang P., D.M. Tartakovsky, K.D. Jarman, and A.M. Tartakovsky. 2013. CDF Solutions of Buckley-Leverett Equation with Uncertain Parameters. Multiscale Modeling & Simulation 11, no. 1:118-133. PNNL-SA-85908. doi:10.1137/120865574