FINITE ELEMENT ANALYSIS OF TRANSIENT CONTAMINANT TRANSPORT: A STOCHASTIC APPROACH
A stochastic perturbation–based finite–element formulation for transient contaminant transport in the vadose 
zone was developed and implemented. The stochastic differential equation describing the large–scale transient contaminant 
transport model was implemented using a finite–element approach. The system of finite–element equations was obtained by 
applying the Galerkin method. Six–noded triangular elements were used in the mesh discretization. Gauss–Legendre 
quadrature was applied to perform the numerical integrations using nine integration points. The global system of equations 
was evaluated using a finite–difference approximation in the time domain. A two–dimensional transient contaminant 
transport in the vadose zone was simulated using a stochastic and a deterministic approach. The chemical concentration at 
each node was evaluated as a function of time and depth. The stochastic approach predicted a faster movement of the chemical 
in both horizontal and vertical directions when compared to deterministic results. For the case simulated in this study, the 
size of the contaminant plume predicted with the stochastic approach was around 20% greater than the one predicted using 
a deterministic approach. The discrepancy in the results between the two approaches can be explained by the inclusion of 
the variability of hydraulic properties of the soil into the macrodispersion coefficient (Aij) in the stochastic formulation. A 
computer code was developed to obtain the stochastic and deterministic finite–element solutions. By providing more realistic 
results, the stochastic perturbation–based finite–element formulation is a very attractive alternative to deterministic 
approaches.