Modeling Heat Transfer through Permafrost Soil Subjected to Seasonal Freeze-Thaw

Alain Lubini Tshumuka (), Abdelkader Krimi and Musandji Fuamba
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Alain Lubini Tshumuka: Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, Montréal, QC H3T 1J4, Canada
Abdelkader Krimi: Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, Montréal, QC H3T 1J4, Canada
Musandji Fuamba: Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, Montréal, QC H3T 1J4, Canada

Land, 2022, vol. 11, issue 10, 1-19

Abstract: The present paper proposes an iterative implicit numerical method for simulating the thaw depth of permafrost soil. For this purpose, the enthalpy-porosity model was used for the phase change process, and the finite difference scheme FTCS (Forward Time Centered Space) was used for discretization. An artificial mushy zone was maintained with the same thickness by keeping the regularization parameter proportional to the temperature gradient. In doing so, we made the scheme more stable and convergence occurred faster. The model accuracy was validated by comparing the numerical results with the analytical Stefan solution and with the results of a derived numerical model, based on an explicit scheme. The model performance was also tested against observation data collected on four different landscapes with different soil profiles and located on a basin underlain by continuous permafrost. It was found that the proposed model matched noticeably well the analytical solution for a volumetric liquid fraction (phi) equal to 0.5 regardless of the grid resolution. Furthermore, compared with the observation data, the model reproduced the annual maximum thaw depth with an absolute error lying between 0.7 and 7.7%. In addition, the designed algorithm allowed the model to converge after a maximum of eight iterations, reducing the computational time by around 75% compared to the explicit model. The results were so encouraging that the model can be included in a hydrological modeling of permafrost watersheds or cold regions in general.

Keywords: Stefan problem; permafrost; active layer; finite difference; iterative method; thaw depth (search for similar items in EconPapers)
JEL-codes: Q15 Q2 Q24 Q28 Q5 R14 R52 (search for similar items in EconPapers)
Date: 2022
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