Chatterjee, A., Singh, M. (2018). 'Two-dimensional advection-dispersion equation with depth- dependent variable source concentration', Pollution, 4(1), pp. 1-8. doi: 10.22059/poll.2017.230145.265

Chatterjee, A., Singh, M. Two-dimensional advection-dispersion equation with depth- dependent variable source concentration. Pollution, 2018; 4(1): 1-8. doi: 10.22059/poll.2017.230145.265

Two-dimensional advection-dispersion equation with depth- dependent variable source concentration

^{}Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, India

Abstract

The present work solves two-dimensional Advection-Dispersion Equation (ADE) in a semi-infinite domain. A variable source concentration is regarded as the monotonic decreasing function at the source boundary (x=0). Depth-dependent variables are considered to incorporate real life situations in this modeling study, with zero flux condition assumed to occur at the exit boundary of the domain, i.e. its semi-infinite part. Without losing any generality, one can consider that the aquifer is initially contamination-free. Thus, the current study explores variations of two-dimensional contaminant concentration with depth throughout the domain, showing them graphically. Non-point source problem, i.e. the line source problem, can be discussed by solving two-dimensional depth-dependent variable source problem, as x=0 is a 2D line. A new transformation has been used to transform the time-dependent ADE to one with constant coefficients, with Matlab (pdetool) being employed in order to solve the problem, numerically, using finite element method.

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