Analytical Solution of ADE with Spatiotemporal Dependence of Dispersion Coefficient and Velocity using Green's Function Method

One dimensional advection diffusion equation (ADE) with variable coefficients is solved analytically using Green’s Function Method (GFM). ADE describes the pollutant mass transport in a heterogeneous medium originating from an instantaneous source. The heterogeneity of the medium is delineated through considering dispersion coefficient and velocity as functions of both the independent variables. The source term is defined by the non-homogeneous term in the ADE. A moving coordinate transformation is developed through which variable coefficients of the ADE are reduced into constant coefficients.