Testing a Gaussian assumption on the stochastic Buckley---Leverett equation

We analyze a multivariate Gaussian assumption for transformations of saturation and flux using Monte Carlo simulations of the stochastic Buckley---Leverett equation. The Gaussian assumption is of interest both for closure of moment equations and for estimating the size of third- and higher-order moments, and is commonly invoked in stochastic subsurface models. Random permeability fields are generated from a multivariate log-Gaussian distribution using a Fast Fourier Transform method. Flux and saturation fields are numerically solved on a simplified 2-D domain. Using chi-square tests we find that a Gaussian approximation is inappropriate for transformations of saturation. We suggest a mixture model for distribution of saturation near a saturation front.