The Arctic is a complex environment. In this talk we continue discussing thermal processes (i.e., the nonlinear heat equation with a free boundary) at the pore- and Darcy scale, which we connect by upscaling. The main mathematical challenge is to handle the upscaling of multivalued graphs which are needed to account for the physically realistic freezing point depression in small pores. We also outline the computational aspects for the coupled systems involving heat, flow and deformation.

This talk is partially based on joint work with Lisa Bigler (Math PHD 2022, currently in Sandia National Lab), and Naren Vohra (Math PHD 2023, currently at Los Alamos National Lab), as well as with current students and collaborators to be named in the talk.