A PHYSICALLY-BASED APPROACH TO THE SOLUTION OF THE FOKKER-PLANCK EQUATION

Two motor forces, namely capillarity and gravity, play a major role as water moves down a soil profile. Initially capillary forces are dominant but assume a lesser role as infiltration becomes slowed down progressively by viscous forces. On the other hand, the gravity force is negligible at the beginning, but becomes quite active and noticeable rapidly. These changes suggest modification of solution methods for flow through porous media. In this study the non-linear Fokker-Planck equation is firstly non-dimensionalised to reflect the time-dependent motion of flow through a soil profile and the resulting equation is linearised with the Newton-Richtmeyer scheme. Some representative cases are studied with the numerical model and the results obtained are found to be physically realistic.