Premium
Analytical Solutions for Water Flow and Solute Transport in the Unsaturated Zone
Author(s) -
Nachabe Mahmood H.,
Islas Alvaro L.,
Illangasekare Tissa H.
Publication year - 1995
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.1995.tb00285.x
Subject(s) - discretization , richards equation , mechanics , advection , parametric statistics , infiltration (hvac) , flow (mathematics) , nonlinear system , mathematics , dispersion (optics) , convection–diffusion equation , vadose zone , capillary action , porous medium , water flow , mathematical analysis , thermodynamics , physics , water content , geotechnical engineering , geology , porosity , groundwater , statistics , quantum mechanics , optics
Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge and White nonlinear model to solve the Richards’ equation for vertical flow under a constant infiltration rate. Then we extend the water flow solution and develop an exact parametric solution for the advection‐dispersion equation. The method of characteristics is adopted to determine the location of a solute front in the unsaturated zone. The dispersion component is incorporated into the final solution using a singular perturbation method. The formulation of the analytical solutions is simple, and a complete solution is generated without resorting to computationally demanding numerical schemes. Indeed, the simple analytical solutions can be used as tools to verify the accuracy of numerical models of water flow and solute transport. Comparison with a finite‐element numerical solution indicates that a good match for the predicted water content is achieved when the mesh grid is one‐fourth the capillary length scale of the porous medium. However, when numerically solving the solute transport equation at this level of discretization, numerical dispersion and spatial oscillations were significant.