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

摘要

In this paper we present numerical results on the pseudoparabolic equationθs/θt-div(k(S)(-p'_c(S) S+τ θs/θt))=b (1) describing unsaturated flows in porous media with dynamic capillary pressure - saturation relationship, introduced in [2]-[6]. In the equation (1)τ is a positive constant, S is the wetting phase saturation, k is the hydraulic conductivity and P_c is the static capillary pressure, μ the viscosity of the fluid and b 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.