An Error Estimate of a Modified Method of Characteristics Modeling Advective-Diffusive Transport in Randomly Heterogeneous Porous Media

Abstract

We analyze a stochastic modified method of characteristics (MMOC) modeling advective-diffusive transport in randomly heterogeneous porous media. Under the log-normal assumption of the porous media and the finite-dimensional noise assumption that leads to unbounded diffusivity, we prove an optimal-order error estimate for the stochastic MMOC scheme. Numerical experiments are presented to substantiate the numerical analysis.