Generalized Analytical Solutions of The Advection-Dispersion Equation with Variable Flow and Transport Coefficients

Demand has increased for analytical solutions to determine the velocities and dispersion coefficients that describe solute transport with spatial, temporal, or spatiotemporal variations encountered in field. However, few have considered spatially, temporally, spatiotemporally dependent velocities. The proposed consider eight cases of velocities: both spatially dependent, temporally coefficient velocity, constant constant, velocity. spatial dependence is linear, while temporal may be exponential, asymptotical, sinusoidal. An advection–dispersion equation these variable was reduced a non-homogeneous diffusion using pertinent coordinate transform method. Then, were obtained an infinite medium Green’s function. validated against existing numerical when unavailable. In this study, we showed could applied various patterns velocity coefficient, shedding light on feasibility solution under highly transient flow heterogeneous porous medium.