Solving a multiscale problem of drying of porous media

Drying of a porous medium is an inherently multiscale problem. While the local phase equilibrium is established very quickly, phase change is associated with heat and mass transport that occur on much slower time scales. The corresponding mathematical model, which describes the transport of liquid, vapor, and heat through the porous medium, is therefore extremely stiff and expensive to solve numerically. We show that it is possible to construct a reduced model for this process that is not stiff using adiabatic elimination of the fast variable(s). We validate the reduced model by comparing its numerical solution to that of the original, stiff problem.