FiniteAnalyticMethods for Simulation ofAdvection-Dominated and Pure Advection SoluteTransportWith Reaction in PorousMedia

Document Type : Original Research Paper


1 Graduate Faculty ofEnvironment,University of Tehran, P.O.Box 14155-6135, Tehran, Iran

2 Department ofMechanical Engineering, University of Toronto, Toronto,Ontario, Canada,M5S 3G8


The transport of dissolved contaminants in groundwater is usually described by the advection
dispersion equation with reaction. Several numerical methods for solving the one-dimensional are available
including finite difference methods, finite volume methods, and finite element methods. Stringent conditions,
such as small Peclet (Pe) and Courant (Cr) numbers, must be satisfied to ensure the accuracy and stability of
the numerical solutions. The practical finite analytic (PFA) method was applied to the solution of two solute
transport problems: 1- One-dimensional advection–dispersion equation with reaction under advectiondominated
conditions, and 2- One-dimensional pure advection equation with reaction. A triangular explicit
PFA (EPFA) spatial-temporal computational molecule was developed. The EPFA solutions were compared
with solutions from the quadratic upwind differencing (QUICK) scheme. For both cases, the EPFA solution
gives accurate results as long as the Courant (Cr) was close to one. Stability analysis shows that the EPFA
molecule is always stable for high Pe number.