In this talk, we present our work on the mathematical and computational modeling of phenomena of energy and mass transport, as well as of mechanical deformation in the Arctic soils; these are coupled to the processes in the atmosphere controlled by the Earth’s climate and weather.

We begin by exploring heat conduction and water flow involving the ice/water phase transitions in permafrost soils coupled to the processes in the snow cover.  While many aspects have been well studied by geophysicists using Darcy scale models based on empirical data, our approach works in silicio, aiming to find explanations and interpretations for these models starting at the pore-scale and scaling up.

We also outline the principles of robust and efficient computational algorithms for simulations from the pore- to the Darcy scales. Finally, we illustrate how these efforts can be used to build more and better models, which  is also important for applications beyond the Arctic, such as in biological tissue and extraterrestrial materials.