Upscaling an extended heterogeneous Stefan problem from the pore-scale to the Darcy scale in permafrost. (English) Zbl 1537.35039
Summary: 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, No. 3, 987–1017 (2007; Zbl 1152.35057)] 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.
MSC:
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 35R35 | Free boundary problems for PDEs |
| 35K65 | Degenerate parabolic equations |
| 80A22 | Stefan problems, phase changes, etc. |
| 76S05 | Flows in porous media; filtration; seepage |
Keywords:
heterogeneous Stefan problem; homogenization; upscaling; permafrost models; porous media; pore-scale and Darcy scale; nonlinear degenerate parabolic partial differential equationCitations:
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