Finite Analytic Methods for Simulation of Advection-Dominated and Pure Advection Solute Transport With Reaction in Porous Media

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.