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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Alain Lubini Tshumuka & Abdelkader Krimi & Musandji Fuamba, 2022. "Modeling Heat Transfer through Permafrost Soil Subjected to Seasonal Freeze-Thaw," Land, MDPI, vol. 11(10), pages 1-19, October.
    • Handle: RePEc:gam:jlands:v:11:y:2022:i:10:p:1770-:d:940076
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    References listed on IDEAS

    as
    1. Olga Semenova & Yury Vinogradov & Tatyana Vinogradova & Luidmila Lebedeva, 2014. "Simulation of Soil Profile Heat Dynamics and their Integration into Hydrologic Modelling in a Permafrost Zone," Permafrost and Periglacial Processes, John Wiley & Sons, vol. 25(4), pages 257-269, October.
    2. Liudmila Lebedeva & Olga Semenova & Tatyana Vinogradova, 2014. "Simulation of Active Layer Dynamics, Upper Kolyma, Russia, using the Hydrograph Hydrological Model," Permafrost and Periglacial Processes, John Wiley & Sons, vol. 25(4), pages 270-280, October.
    3. Xie Changwei & William A. Gough, 2013. "A Simple Thaw‐Freeze Algorithm for a Multi‐Layered Soil using the Stefan Equation," Permafrost and Periglacial Processes, John Wiley & Sons, vol. 24(3), pages 252-260, July.
    4. Daniel Riseborough & Nikolay Shiklomanov & Bernd Etzelmüller & Stephan Gruber & Sergei Marchenko, 2008. "Recent advances in permafrost modelling," Permafrost and Periglacial Processes, John Wiley & Sons, vol. 19(2), pages 137-156, April.
    5. S.L. Smith & V.E. Romanovsky & A.G. Lewkowicz & C.R. Burn & M. Allard & G.D. Clow & K. Yoshikawa & J. Throop, 2010. "Thermal state of permafrost in North America: a contribution to the international polar year," Permafrost and Periglacial Processes, John Wiley & Sons, vol. 21(2), pages 117-135, April.
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