A new mathematical modelling for describing the unsaturated flow of an incompressible liquid through a rigid porous medium

In this work, a new constitutive equation is proposed for the partial pressure of a liquid in an unsaturated flow through a rigid porous medium. This new equation gives rise to a mathematical description in which the geometrical bound, representing the rigid porous medium assumption, is naturally taken into account, avoiding the occurrence of solutions without physical meaning during simulations. Two examples are presented, in order to lend support to the new description, where a classical modelling is directly compared with the one proposed here.