A perturbation stochastic finite-element method for groundwater flow models based on an undetermined-coefficients approach

Abstract

A new perturbation technique and finite-element method, which incorporates an undetermined-coefficients approach, is proposed to conduct stochastic simulation for problems of groundwater flow. Formulas of the mean value and variance of groundwater head are derived to exclude the process of computing the first and second-order derivatives of groundwater head with respect to stochastic variables (coefficient of transmissibility, storage coefficient, etc.) in the calculation process of common finite element methods. For ordinary stochastic groundwater problems, the statistical properties of groundwater head can be easily obtained by using the proposed method, which is especially efficient for the stochastic problems that have fewer input stochastic variables. A stochastic numerical simulation of a two-dimensional confined-groundwater flow problem has been conducted to validate effectiveness and determine the limitations of the proposed method. The results illustrate that the accuracy and efficiency of the method proposed are satisfactory, and that the computing time is shorter when there is a small number of input stochastic variables.