Stochastic Numerical Modeling of Groundwater in a Phreatic Aquifer with Perturbation Finite Element Method

Dynamically stochastic simulation of flow in a phreatic aquifer is a complicated and challenging issue. A perturbation finite element model for transient two-dimensional flow in a phreatic aquifer is developed and presented in this paper. In the model, stochastic variables include hydraulic conductivity and specific yield in governing equation, as well as source/sink and boundary conditions, 9 equations are derived in order to solve expectation and variance of two-dimensional unsteady flow and specific numeric treatment is adopted for different equation discreteness. In the end, simulated results are analyzed by a hypothetical example, and it shows that the influence of variation of boundary condition variance and hydraulic conductivity variance is little and that of variation of specific yield variance is significant. This model can be applied to general stochastic simulation of unsteady flow in a phreatic aquifer due to the fact that it takes into account all relevant factors. The study presents the influence on dynamic simulation of flow in phreatic water by stochastic variables of boundary condition, hydraulic conductivity and specific yield and it offers an alternative theory of stochastic simulation of ground water flow.