Fully Discrete Scheme for the Equations Describing Unsaturated Flow in Porous Media with Dynamic Capillary Pressure

In this paper we present numerical results on the pseudoparabolic equation partial derivative S/partial derivative t - div (k(S) (-P'(c)(S)del S + tau del partial derivative S/partial derivative t)) = b describing unsaturated flows in porous media with dynamic capillary pressure - saturation relationship, introduced in [2]-[6]. In the equation (1) tau is a positive constant, S is the wetting phase saturation, k is the hydraulic conductivity and P-c is the static capillary pressure, mu the viscosity of the fluid and mu a source term. In general, such models arise in a number of cases when non-equilibrium thermodynamics or extended non-equilibrium thermodynamics are used to compute the flux.