Analytical solution of the one-dimensional contaminant transport equation in groundwater with time-varying boundary conditions. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Purkayastha, Subhrangshu; Kumar, Bimlesh
• Is Part Of: ISH journal of hydraulic engineering. Volume 26:Issue 1(2020)
• Page Start: 78
• Page End: 83
• Publication Date: 2020-01-02
• Subjects: Advection–diffusion equation -- Legendre linear equation -- time-varying boundary condition -- groundwater -- contaminant -- eigenfunction expansion; Hydraulic engineering -- Periodicals; Hydraulic engineering -- India -- Periodicals; Hydraulic engineering; India; Periodicals; 627
• DOI: 10.1080/09715010.2018.1453879
• Languages: English
• ISSNs: 0971-5010

Abstract

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.