Homogenization of Richardsʼ equation of van Genuchten-Mualem model

This paper is devoted to the homogenization of Richardsʼ equation of van Genuchten-Mualem model, which is a nonlinear degenerate parabolic differential equation. It is usually used to model the motion of saturated-unsaturated water flow in porous media. We firstly apply the Kirchhoff transformation to the equation and obtain a simpler equivalent equation with a linear oscillated diffusion term. Then under the real assumption for van Genuchten-Mualem model, we obtain the homogenized equation based on the two-scale convergence theory. Some results on the first order corrector are also presented.