On coupled heat transport and water flow in partially frozen variably saturated porous media

We propose and analyze a model of coupled heat transport and water flow in variably saturated porous media under conditions of freezing and thawing. Solution of the model provides temperature, liquid water content and ice content in porous media as a function of space and time. We employ the Rothe method to construct systems of approximate solutions for which the existence and regularity are proved. Numerical scheme is based on specific semi-implicit discretization in time, which preserve the pseudo-monotone structure of the discrete problem. Numerical results are compared with experimental data reported in the literature. The model satisfactorily predicts characteristic phenomena in porous media under frost actions such as water movement toward freezing fronts and the presence of liquid water in frozen regions.