finiteanalyticmethods for simulation ofadvection-dominated and pure advection solutetransportwith reaction in porousmedia

the transport of dissolved contaminants in groundwater is usually described by the advectiondispersion equation with reaction. several numerical methods for solving the one-dimensional are availableincluding 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 ofthe numerical solutions. the practical finite analytic (pfa) method was applied to the solution of two solutetransport problems: 1- one-dimensional advection–dispersion equation with reaction under advectiondominatedconditions, and 2- one-dimensional pure advection equation with reaction. a triangular explicitpfa (epfa) spatial-temporal computational molecule was developed. the epfa solutions were comparedwith solutions from the quadratic upwind differencing (quick) scheme. for both cases, the epfa solutiongives accurate results as long as the courant (cr) was close to one. stability analysis shows that the epfamolecule is always stable for high pe number.