Improved Finite-Element Method for Solute Transport

Abstract

Five major modifications to the Galerkin finite-element formulation for solute transport were made in this study: (1) A mixed formulation for the time-derivative term of the governing equation was developed by combining the Galerkin method and the collocation method; (2) a general and useful formulation for the advection and dispersion terms was derived by applying Green's theorem so that any given advection-dominated boundary conditions can be correctly handled; (3) simpler expressions for leaky boundary conditions and surface flux conditions were developed using the unit step function; (4) nonambiguous expressions of the source and sink terms were derived using the Dirac delta function; and (5) a finite-integration solution scheme was developed to solve the system of ordinary differential equations, and a discussion critical to the use of the finite-difference solution scheme was presented. The effects of these five modifications on numerical solution were investigated.