Solving the Contaminant Transport Problem Over a Random Conductivity Field

In this paper, I explore the solution of the contaminant transport problem over a random conductivity field. First, I generate a random, correlated conductivity field by convolving independent, uniformly distributed random variables with the identity function. I use finite differences to discretize the diffusion equation to solve for the steady-state pressure gradient using Backward Euler. This allows calculation of the Darcy flux and hence the pore velocity over the random conductivity field. Finally, I solve the two dimensional advection-dispersion equation using an Adams-Bashforth, Adams-Moulton predictor corrector method to step forward in time. The generation of the random conductivity field and pressure gradient seem both accurate and efficient, and the finite difference method of solving the contaminant transport problem seems to be providing qualitatively correct solutions, but it is not volume conservative.