University of TehranPollution2383-451X4120180101Two-dimensional advection-dispersion equation with depth- dependent variable source concentration186432110.22059/poll.2017.230145.265ENAyanChatterjeeDepartment of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, IndiaMritunjaySinghDepartment of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, IndiaJournal Article20170405The 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.https://jpoll.ut.ac.ir/article_64321_25107ed9fb13e8149bc1f120f00ba09c.pdf