Numerical methods for reinterpreted discrete fracture models with random inputs

Abstract

This paper investigates the impact of uncertainty on the reinterpreted discrete fracture model (RDFM) for flow in porous media featuring fractures and barriers. The stochastic RDMF is formulated by parameterizing the uncertainty in the permeability, as well as the width of the fracture and barrier networks as random variables. To discretize these random variable, we adopt a stochastic collocation method based on a special choice of nodes. This collocation scheme offers optimal accuracy and easy implementation. The resulting collocation scheme is then combined with the local discontinuous Galerkin (LDG) method to accommodate the hybrid-dimensional Darcy’s law and the nature of the pressure/flux discontinuity. Additionally, a slope limiter is utilized to enhance stability. Numerical experiments are carried out to illustrate the accuracy and stability of the proposed scheme.