Stochastic finite element analysis of transient unsaturated flow in porous media

A stochastic perturbation-based finite element formulation for prediction of transient unsaturated flow in porous media was developed and implemented. The stochastic differential equation describing the large-scale transient flow model was implemented using a finite element approach. The system of finite element equations was obtained using Galerkins method. Six-noded triangular elements were used in the mesh discretization, and Gauss-Legendre quadrature was employed to perform the numerical integrations. The global system of differential equations was evaluated using a finite difference approximation in the time domain. A two-dimensional transient unsaturated flow was simulated using both a stochastic and a deterministic approach. The mean moisture content and capillary pressure head distributions were evaluated as a function of time and depth. Results showed a significant difference between the two approaches. A Fortran 90 computer code was also developed to obtain the stochastic and deterministic finite element solutions. The stochastic perturbation-based finite element formulation is a very attractive alternative to deterministic approaches in terms of cost, efficiency, and accuracy of the results.