Mathematics

Permafrost is a dynamic environment ubiquitous in the polar regions, and we are interested in modeling its response to the climate controls, starting from the pore-scale of [mm] scale up to field scale of [m]. We start with a model for heat conduction and ice/water phase transitions in a domain composed of rock grains and water in liquid or solid phase, and consider next its numerical upscaling. Specifically, we consider phase field relaxation of the Stefan problem, a non-linear free boundary value problem. We discuss challenges of numerical approximation but focus on the upscaling of coefficients of the model as well as of the temperature-enthalpy relationship.