Studying the model of air and water filtration in a melting or freezing snowpack

The article is devoted to a theoretical study of a non-stationary problem on thermomechanical processes in snow taking into account the effects of melting and freezing. Snow is modeled as a continuous medium consisting of water, air and porous ice skeleton. The governing equations of snow are based on the fundamental conservation laws of continuum mechanics. For the one-dimensional setting, the Rothe scheme is constructed as an approximation of the considered problem and the Rothe method is formally justified, i.e., convergence of approximate solutions to the solution of the considered problem is established under some additional regularity requirements.