Upscaling an Extended Heterogeneous Stefan Problem from the Pore-Scale to the Darcy Scale in Permafrost
Małgorzata Peszyńska, Naren Vohra, Lisa Bigler · Multiscale Modeling and Simulation · 2024
Abstract. In this paper we upscale thermal models from the pore–scale to the Darcy scale for applications in permafrost. We incorporate thawing and freezing of water at the pore-scale and adapt rigorous homogenization theory from [A. Visintin, SIAM J. Math. Anal., 39 (2007), pp. 987–1017] to the original nonlinear multivalued relationship to derive the effective properties. To obtain agreement of the effective model with the known Darcy scale empirical models, we revisit and extend the pore-scale model to include the delicate microscale physics in small pores. We also propose a practical reduced model for the nonlinear effective conductivity. We illustrate with simulations.