Articles | Volume 15, issue 6
https://doi.org/10.5194/tc-15-2541-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/tc-15-2541-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
04 Jun 2021
Research article |
| 04 Jun 2021
| 04 Jun 2021
A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation
Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy
Stephan Gruber
Department of Geography and Environmental Studies, Carleton University, Ottawa, ON, K1S 5B6, Canada
Riccardo Rigon
Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy
Center Agriculture Food Environment, University of Trento, Trento, Italy
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- Modeling Heat Transfer through Permafrost Soil Subjected to Seasonal Freeze-Thaw A. Lubini Tshumuka et al. https://doi.org/10.3390/land11101770
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- Investigating the seepage-thermal interaction process on the thermal stability of highway embankments in permafrost regions adjacent to thermokarst lakes B. Hu et al. https://doi.org/10.1016/j.trgeo.2025.101608
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- Exploration of Thermal Bridging Through Shrub Branches in Alpine Snow F. Domine et al. https://doi.org/10.1029/2023GL105100
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27 citations as recorded by crossref.
- Numerical strategies for representing Richards' equation and its couplings in snowpack models K. Fourteau et al. https://doi.org/10.5194/gmd-19-3193-2026
- Implementing the Water, HEat and Transport model in GEOframe (WHETGEO-1D v.1.0): algorithms, informatics, design patterns, open science features, and 1D deployment N. Tubini & R. Rigon https://doi.org/10.5194/gmd-15-75-2022
- Multi-scale pattern analysis of permafrost dynamics on the Qinghai–Tibet Plateau based on machine-learning reconstruction P. Jiang et al. https://doi.org/10.1016/j.gloplacha.2026.105341
- Modelling the distribution and transport of heavy metals on water and soil: a systematic review S. Baseka et al. https://doi.org/10.1007/s13762-025-06868-6
- Mechanism analysis of simulation differences with two frozen soil permeability schemes in Noah-MP over the Tibetan Plateau W. Hu et al. https://doi.org/10.1016/j.jhydrol.2025.133437
- Microwave drying of minerals with moisture-dependent properties: Experimental and numerical analysis M. Asgarpour Khansary et al. https://doi.org/10.1080/07373937.2026.2647064
- A finite-element framework to explore the numerical solution of the coupled problem of heat conduction, water vapor diffusion, and settlement in dry snow (IvoriFEM v0.1.0) J. Brondex et al. https://doi.org/10.5194/gmd-16-7075-2023
- Evaluating the Impact of Soil Enthalpy upon the Thawing Process of the Active Layer in Permafrost Regions of the Qinghai–Tibet Plateau Using CLM5.0 S. Wang et al. https://doi.org/10.3390/rs15010249
- Multicontinuum homogenization of the fluid infiltration process in the permafrost S. Stepanov et al. https://doi.org/10.1016/j.cam.2026.117723
- Beyond MAGT: learning more from permafrost thermal monitoring data with additional metrics N. Brown & S. Gruber https://doi.org/10.5194/tc-20-1771-2026
- Investigating the thermal state of permafrost with Bayesian inverse modeling of heat transfer B. Groenke et al. https://doi.org/10.5194/tc-17-3505-2023
- Inconsistency and correction of manually observed ground surface temperatures over snow-covered regions B. Cao et al. https://doi.org/10.1016/j.agrformet.2023.109518
- Multiscale Multiphysics Modeling of the Infiltration Process in the Permafrost S. Stepanov et al. https://doi.org/10.3390/math9202545
- A non-equilibrium thermodynamics framework for daily simulation of coupled water and heat transport in variably saturated and frozen soils I. Borzì https://doi.org/10.1016/j.advwatres.2026.105257
- Modeling Heat Transfer through Permafrost Soil Subjected to Seasonal Freeze-Thaw A. Lubini Tshumuka et al. https://doi.org/10.3390/land11101770
- A novel numerical implementation for the surface energy budget of melting snowpacks and glaciers K. Fourteau et al. https://doi.org/10.5194/gmd-17-1903-2024
- Ensemble numerical simulation of permafrost thermal regimes over the Tibetan Plateau using the Flexible Permafrost Model: 1950–2023 W. Sun & B. Cao https://doi.org/10.5194/tc-20-2681-2026
- The impacts of soil enthalpy change on land–atmosphere interactions of permafrost on the Qinghai-Tibet Plateau R. Li et al. https://doi.org/10.1016/j.geoderma.2025.117183
- Comparison of Two CFD Approaches Using Constant and Temperature Dependent Heat Capacities during the Phase Transition in PCMs with Experimental and Analytical Results C. Reichl et al. https://doi.org/10.3390/pr10020302
- Investigating the seepage-thermal interaction process on the thermal stability of highway embankments in permafrost regions adjacent to thermokarst lakes B. Hu et al. https://doi.org/10.1016/j.trgeo.2025.101608
- The evolution of Arctic permafrost over the last 3 centuries from ensemble simulations with the CryoGridLite permafrost model M. Langer et al. https://doi.org/10.5194/tc-18-363-2024
- A component-based modular treatment of the soil–plant–atmosphere continuum: the GEOSPACE framework (v.1.2.9) C. D'Amato et al. https://doi.org/10.5194/gmd-18-7321-2025
- Exploration of Thermal Bridging Through Shrub Branches in Alpine Snow F. Domine et al. https://doi.org/10.1029/2023GL105100
- Numerical Study of Coupled Water and Vapor Flow, Heat Transfer, and Solute Transport in Variably‐Saturated Deformable Soil During Freeze‐Thaw Cycles X. Huang & D. Rudolph https://doi.org/10.1029/2022WR032146
- Modelling the effect of free convection on permafrost melting rates in frozen rock clefts A. Sedaghatkish et al. https://doi.org/10.5194/tc-18-4531-2024
- Efficient Discretization of the Laplacian: Application to Moving Boundary Problems S. Castillo & F. Izsák https://doi.org/10.3390/a17120541
- Estimation of Soil Water Retention Curve Based on Pore Freezing Kinetics A. Macias et al. https://doi.org/10.1088/1755-1315/1480/1/012128
Saved (final revised paper)
Latest update: 09 Jun 2026
Short summary
We present a new method to compute temperature changes with melting and freezing – a fundamental challenge in cryosphere research – extremely efficiently and with guaranteed correctness of the energy balance for any time step size. This is a key feature since the integration time step can then be chosen according to the timescale of the processes to be studied, from seconds to days.
We present a new method to compute temperature changes with melting and freezing – a fundamental...
