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

Document Type : Original Research Paper


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


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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