Unsteady Finite-Analytic Method for Solute Transport in Ground-Water Flow

Abstract

This work illustrates the development and application of the unsteady finite-analytic (FA) numerical solution for the migration of ground-water contamination. A functional/optimal time-weighting factor, established based on the analytic solutions of the one-dimensional, linear advection-diffusion equation, is proposed for the expression of the unsteady term in the solute-transport equation. The upstream shift nature of FA coefficients and the all-positive algebraic equation automatically originate from the FA solution, providing a physically meaningful and stable numerical scheme. Another feature of the method presented is that a very large time interval can be used in the numerical simulation. Therefore, only few time steps are needed to complete the whole computation. In the examples, the performance of unsteady FA numerical solutions is demonstrated by simulating the solute transport emitting from a Gaussian-line source. It is shown that the use of the functional time-weighting factor associated with the finite-analytic method appears to be a better choice for avoiding numerical diffusions and oscillations than, through comparison with, the fully implicit (time-weighting factor = 0) and the Crank-Nicholson (time-weighting factor = 0.5) FA schemes.