Article ID Journal Published Year Pages File Type
4626525 Applied Mathematics and Computation 2015 11 Pages PDF
Abstract

Recent concerns over the safety of oil and natural gas extraction, fracking, and carbon sequestration have driven the need to develop methods for uncertainty quantification for coupled subsurface flow and deformation processes. Traditional Monte Carlo methods are versatile but exhibit prohibitively slow convergence. In this work, we develop an intrusive polynomial chaos expansion method for Biot’s poroelasticity equations based on the Galerkin projection with uniform and log-normally distributed material parameters. We analyze accuracy and efficiency of our method and compare it to the Monte Carlo method. We verify exponential convergence of the stochastic Galerkin approach.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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