Abstract
<abstract> We present the analytical solution of the two-dimensional linear advection-dispersion equation ($ 2 $-D LAD) in the quarter plane and the semi-infinite domain for two-dimensional solute transport in a porous medium. The governing equation includes terms describing advection, longitudinal and transverse dispersions and linear equilibrium adsorption. The analytical solution in terms of integrals in the complex plane is established by utilizing the unified transform method, also known as the Fokas method. The method hinges upon analysis of the divergence form of the governing equation and the so-called global relation, which is an algebraic relation coupling all known and unknown initial and boundary values. Particularly, the integral representation of the solution yields an accurate and fast numerical evaluation of the solution for the $ 2 $-D LAD equation. We demonstrate examples as an application of the developed solution and compare the analytical solution with numerical results. </abstract>
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