Analytical solution of the one-dimensional contaminant transport equation in groundwater with time-varying boundary conditions

Abstract

In this paper, an analytical solution for the one-dimensional advection–diffusion equation for studying the contaminant transport in groundwater is presented. The solution is obtained for spatially varying diffusivity and velocity terms along with time-varying boundary conditions. The differential equation considered in the paper is in the form of Legendre Linear Differential Equation which is reduced to a linear differential equation having constant coefficients by a suitable transformation. The final solution for the differential equation in the transformed domain is obtained by the method of Eigenfunction expansions. The solution is tested by considering a test problem.