FINITE ELEMENT ANALYSIS OF TRANSIENT CONTAMINANT TRANSPORT: A STOCHASTIC APPROACH

Abstract

A stochastic perturbationbased finiteelement formulation for transient contaminant transport in the vadosezone was developed and implemented. The stochastic differential equation describing the largescale transient contaminanttransport model was implemented using a finiteelement approach. The system of finiteelement equations was obtained byapplying the Galerkin method. Sixnoded triangular elements were used in the mesh discretization. GaussLegendrequadrature was applied to perform the numerical integrations using nine integration points. The global system of equationswas evaluated using a finitedifference approximation in the time domain. A twodimensional transient contaminanttransport in the vadose zone was simulated using a stochastic and a deterministic approach. The chemical concentration ateach node was evaluated as a function of time and depth. The stochastic approach predicted a faster movement of the chemicalin both horizontal and vertical directions when compared to deterministic results. For the case simulated in this study, thesize of the contaminant plume predicted with the stochastic approach was around 20% greater than the one predicted usinga deterministic approach. The discrepancy in the results between the two approaches can be explained by the inclusion ofthe variability of hydraulic properties of the soil into the macrodispersion coefficient (Aij) in the stochastic formulation. Acomputer code was developed to obtain the stochastic and deterministic finiteelement solutions. By providing more realisticresults, the stochastic perturbationbased finiteelement formulation is a very attractive alternative to deterministicapproaches.