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Analysis of heat transfer and water flow with phase change in saturated porous media by bond-based peridynamics

T0 review · 0 major / 3 minor · reviewed 2026-05-24 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Bond-based peridynamics formulation predicts the location of phase interfaces and the temperature and pressure fields in saturated porous media during pressure-driven flow with phase change.

desk verdict Bond-based peridynamics formulation for phase-change porous flow verifies cleanly on 1D and 2D cases but leaves discretization choices opaque. read the letter →

arxiv 2105.00734 v2 pith:JQNP27KX submitted 2021-05-03 physics.app-ph physics.flu-dyn

Petr Nikolaev , Majid Sedighi , Andrey P Jivkov , Lee Margetts This is my paper
classification physics.app-phphysics.flu-dyn
keywords peridynamicsporousmediaphasechangeheattransferwaterflowsaturatedfrostheavethermo-hydro-mechanical
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper develops a non-local bond-based peridynamics method to model coupled heat and mass transport with phase change in porous media. It handles the mathematical challenge of an evolving interface where material properties change abruptly while also capturing multiple interacting physical processes. The approach is shown to locate the phase boundary and compute temperature and pressure distributions under pressure-driven water flow. Verification against analytical solutions for one-dimensional cases and finite-element results for two-dimensional cases confirms the method reproduces known results.

What carries the argument

Bond-based peridynamics discretization that represents the evolving phase interface through non-local bond interactions and step changes in material properties.

What would settle it

A mismatch between the peridynamics-computed interface location or temperature-pressure fields and the existing analytical solutions for the one-dimensional Stefan-type problems, or the finite-element solutions for the two-dimensional transient cases, would falsify the accuracy claim.

Watch

Extended reading notes

Core claim

A bond-based peridynamics discretization of the governing equations for heat transfer and fluid flow in saturated porous media can locate the moving phase-change interface and compute the accompanying temperature and pressure fields without requiring problem-specific horizon adjustments or extra constitutive assumptions.

Load-bearing premise

The peridynamics discretization can capture the sharp property jumps at the moving phase interface using the same horizon and constitutive rules for all problems.

Editorial extensions

If this is right

  • The method supplies temperature and pressure distributions needed for any subsequent mechanical analysis of frost heave or permafrost deformation.
  • The same discretization framework can be extended to include mechanical deformation without changing the treatment of the phase interface.
  • Verification on both one-dimensional analytical and two-dimensional numerical benchmarks establishes that the non-local formulation reproduces classical results for pressure-driven flow with phase change.
  • The formulation removes the need for explicit interface tracking or special meshing at the phase boundary.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same peridynamics setup could be tested on three-dimensional geometries or irregular boundaries where finite-element meshing becomes cumbersome.
  • The approach may apply directly to other phase-change problems such as melting of ice lenses or solidification in casting processes.
  • Coupling the current thermal-hydraulic solver to an existing peridynamics mechanical module would produce a full thermo-hydro-mechanical model without additional interface handling.
  • The method could be checked against laboratory experiments on freezing soils to assess whether the predicted interface speed matches measured frost penetration rates.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. The manuscript develops a bond-based peridynamic formulation for coupled heat and mass transport with phase change in saturated porous media. It claims that the non-local discretization handles the evolving phase interface and associated discontinuous properties directly, enabling prediction of interface location together with temperature and pressure fields under pressure-driven flow. Verification consists of comparisons to existing 1D analytical solutions and independent 2D finite-element transient solutions; the reported agreement is presented as evidence of the methodology's accuracy. The work is framed as an intermediate step toward a full thermo-hydro-mechanical model applicable to permafrost and frost-heave problems.

Significance. If the verification results hold under the stated discretization, the approach supplies a non-local route to phase-change problems in porous media that avoids explicit interface tracking. The use of independent analytical solutions and a separate finite-element code for verification is a clear strength, as it removes the risk of circularity that would arise from fitting parameters internal to the peridynamic model itself. This contributes a concrete demonstration that bond-based operators can accommodate step changes in material properties across a moving boundary, which is relevant for extending peridynamics to coupled transport problems in heterogeneous media.

minor comments (3)
  1. [Abstract] Abstract: the description of the verification exercise would be strengthened by a brief statement of the horizon size employed, the spatial discretization parameters, and the precise manner in which latent heat is introduced into the peridynamic heat equation.
  2. [Notation / Formulation] Notation section: the peridynamic heat and mass flux operators are introduced without explicit cross-reference to the standard bond-based kernels in the literature; adding one or two citations and a short comparison would improve clarity for readers unfamiliar with the specific form used here.
  3. [Results / Figures] Figure captions (e.g., Figs. 3–5): the captions do not indicate whether the same horizon was retained across all phases or whether any local adjustment was applied near the interface; this detail is relevant to the claim that no problem-specific calibration is required.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and significance assessment of our manuscript on the bond-based peridynamic formulation for coupled heat and mass transport with phase change. The recommendation for minor revision is noted; however, the report contains no specific major comments requiring point-by-point response.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity identified

full rationale

The paper develops a bond-based peridynamic discretization for coupled heat and mass transport with phase change, then verifies the formulation directly against independent 1D analytical solutions and separate 2D finite-element transients. No load-bearing step reduces to a fitted parameter, self-defined quantity, or self-citation chain; the central claims (interface location and field distributions) are shown to match external benchmarks without internal redefinition or ansatz smuggling. The derivation chain therefore remains self-contained against external references.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract-only review yields no explicit free parameters, ad-hoc axioms, or invented entities; standard peridynamics assumptions (horizon, bond failure criteria) are presupposed but not detailed.

how reviews work

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Cite this review

Pith. "Pith review of Analysis of heat transfer and water flow with phase change in saturated porous media by bond-based peridynamics." pith.science (2026). https://pith.science/paper/JQNP27KX

@misc{pith2026210500734,
  author       = {Pith},
  title        = {Pith review of: Analysis of heat transfer and water flow with phase change in saturated porous media by bond-based peridynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JQNP27KX}},
  note         = {Machine review of arXiv:2105.00734}
}
read the original abstract

A wide range of natural and industrial processes involve heat and mass transport in porous media. In some important cases the transported substance may undergo phase change, e.g. from liquid to solid and vice versa in the case of freezing and thawing of soils. The predictive modelling of such phenomena faces physical (multiple physical processes taking place) and mathematical (evolving interface with step change of properties) challenges. In this work, we develop and test a non-local approach based on bond-based peridynamics which addresses the challenges successfully. Our formulation allows for predicting the location of the interface between phases, and for calculating the temperature and pressure distributions within the saturated porous medium under the conditions of pressure driven water flow. The formulation is verified against existing analytical solutions for 1D problems, as well as finite element transient solutions for 2D problems. The agreement found by the verification exercise demonstrates the accuracy of the proposed methodology. The detailed coupled description of heat and hydraulic processes can be considered as a critical step towards a thermo-hydro-mechanical model, which will allow, for example, description of the hydrological behaviour of permafrost soils and the frost heave phenomenon.

Figures

Figures reproduced from arXiv: 2105.00734 by the authors.

Figure 1
Figure 1. Illustration of phase regions, particle horizons and transport bonds [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. The general flow-chart of the developed PD model [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. One-dimensional heat transfer with phase change according to the PD [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: One-dimensional heat transfer with water flow according to the PD [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]
Figure 5
Figure 5. Figure 5: Schematic of frozen inclusion problem: geometry, boundary and initial [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]
Figure 6
Figure 6. Figure 6: Temperature distribution, ◦C, at different moments of time calculated with the proposed PD model It should be noted that the developed PD model can provide a solution with the same high accuracy for the case when all bonds are participating in water transfer. In this c…
Figure 7
Figure 7. Figure 7: Temperature distribution along the X–X cross section at different [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]
Figure 8
Figure 8. Figure 8: Pressure distribution, Pa, at different moments of time calculated by [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: Pressure distribution along the X–X cross-section at different moments [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]
Figure 10
Figure 10. Figure 10: Schematic of an unfrozen ’crack’ in a frozen body: geometry, boundary [PITH_FULL_IMAGE:figures/full_fig_p024_10.png]
Figure 11
Figure 11. Figure 11: Temperature distribution, ◦C, at different moments of time, according to the proposed PD model [6] J M Frederick and B A Buffett. Taliks in relict submarine permafrost and methane hydrate deposits: Pathways for gas escape under present and future conditions. Journal o…

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Works this paper leans on

49 extracted references · 49 canonical work pages

  1. [1]

    John Wiley & Sons, Inc., 3rd edition, 2012

    David W Hahn and M Necati Özisik.Heat conduction. John Wiley & Sons, Inc., 3rd edition, 2012

    work page 2012

  2. [2]

    J.C. C. Rowland, B.J. J. Travis, and C.J. J. Wilson. The role of advective heattransportintalikdevelopmentbeneathlakesandpondsindiscontinuous permafrost. Geophysical Research Letters, 38(17):n/a–n/a, 9 2011

    work page 2011

  3. [3]

    Prokushkin, Oleg S

    Laurent Orgogozo, Anatoly S. Prokushkin, Oleg S. Pokrovsky, Christophe Grenier, Michel Quintard, Jérôme Viers, and Stéphane Audry. Water and energy transfer modeling in a permafrost-dominated, forested catchment of central siberia: The key role of rooting depth.Permafrost and Periglacial Processes, 30(2):75–89, 2019

    work page 2019

  4. [4]

    Hanli Wan, Jianmin Bian, Han Zhang, and Yihan Li. Assessment of future climate change impacts on water-heat-salt migration in unsaturated frozen soil using CoupModel.Frontiersof Environmental Science & Engineering, 15(1):10, feb 2021

    work page 2021

  5. [5]

    Coupling analysis of the heat-water dynamics and frozen depth in a seasonally frozen zone

    Xudong Zhang, Yajun Wu, Encheng Zhai, and Peng Ye. Coupling analysis of the heat-water dynamics and frozen depth in a seasonally frozen zone. Journal of Hydrology, 593:125603, 2021. 24 Figure 11: Temperature distribution,◦C, at different moments of time, according to the proposed PD model

    work page 2021

  6. [6]

    Taliks in relict submarine permafrost and methane hydrate deposits: Pathways for gas escape under present and future conditions

    J M Frederick and B A Buffett. Taliks in relict submarine permafrost and methane hydrate deposits: Pathways for gas escape under present and future conditions. Journal of Geophysical Research: Earth Surface, 119(2):106–122, 2 2014

    work page 2014

  7. [7]

    Modeling of groundwater flow at depth in crystalline rock beneath a moving ice-sheet margin, exemplified by the Fennoscandian Shield, Sweden

    Patrik Vidstrand, Sven Follin, Jan-Olof Selroos, Jens-Ove Näslund, and Ingvar Rhén. Modeling of groundwater flow at depth in crystalline rock beneath a moving ice-sheet margin, exemplified by the Fennoscandian Shield, Sweden. Hydrogeology Journal, 21(1):239–255, 2 2013

    work page 2013

  8. [8]

    Christophe Grenier, Damien Régnier, Emmanuel Mouche, Hakim Benab- derrahmane, François Costard, and Philippe Davy. Impact of permafrost development on groundwater flow patterns: a numerical study considering 25 freezing cycles on a two-dimensional vertical cut through a generic river-plain system. Hydrogeology Journal, 21(1):257–270, 2 2013

    work page 2013

Show all 49 references
  1. [9]

    Vitel, A

    M. Vitel, A. Rouabhi, M. Tijani, and F. Guérin. Modeling heat and mass transfer during ground freezing subjected to high seepage velocities. Computers and Geotechnics, 73:1–15, 2016

    2016

  2. [10]

    M. M. Zhou and G. Meschke. A three-phase thermo-hydro-mechanical finite element model for freezing soils.International Journal for Numerical and Analytical Methods in Geomechanics, 37(18):3173–3193, 2013

    2013

  3. [11]

    Tounsi, A

    H. Tounsi, A. Rouabhi, and E. Jahangir. Thermo-hydro-mechanical mod- eling of artificial ground freezing taking into account the salinity of the saturating fluid. Computers and Geotechnics, 119(September 2019):103382, 3 2020

    2019

  4. [12]

    Alzoubi, and Agus P

    Ahmad Zueter, Aurelien Nie-Rouquette, Mahmoud A. Alzoubi, and Agus P. Sasmito. Thermal and hydraulic analysis of selective artificial ground freezing using air insulation: Experiment and modeling.Computers and Geotechnics, 120(July 2019):103416, 4 2020

    2019

  5. [13]

    Peridynamic Theory and Its Applications, volume 9781461484

    Erdogan Madenci and Erkan Oterkus. Peridynamic Theory and Its Applications, volume 9781461484. Springer New York, New York, NY, 2014

    2014

  6. [14]

    S.A. Silling. Reformulation of elasticity theory for discontinuities and long- range forces.Journal of the Mechanicsand Physicsof Solids, 48(1):175–209, 1 2000

    2000

  7. [15]

    Peridynamic states and constitutive modeling.Journal of Elasticity, 88(2):151–184, 2007

    Stewart A Silling, M Epton, O Weckner, Ji Xu, and E23481501120 Askari. Peridynamic states and constitutive modeling.Journal of Elasticity, 88(2):151–184, 2007

    2007

  8. [16]

    A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities.Journal of Computational Physics, 231(7):2764–2785, 2012

    Florin Bobaru and Monchai Duangpanya. A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities.Journal of Computational Physics, 231(7):2764–2785, 2012

    2012

  9. [17]

    Peridynamics review

    Ali Javili, Rico Morasata, Erkan Oterkus, and Selda Oterkus. Peridynamics review. Mathematics and Mechanics of Solids, 24(11):3714–3739, 2019

    2019

  10. [18]

    Predicting crack propagation with peridynamics: a comparative study.InternationalJournal of Fracture, 171(1):65–78, sep 2011

    Abigail Agwai, Ibrahim Guven, and Erdogan Madenci. Predicting crack propagation with peridynamics: a comparative study.InternationalJournal of Fracture, 171(1):65–78, sep 2011

    2011

  11. [19]

    A new type of peridynamics: Element-based peridynamics.Computer Methods in Applied Mechanics and Engineering, 366:113098, 7 2020

    Shuo Liu, Guodong Fang, Jun Liang, Maoqing Fu, and Bing Wang. A new type of peridynamics: Element-based peridynamics.Computer Methods in Applied Mechanics and Engineering, 366:113098, 7 2020

    2020

  12. [20]

    Peridynamic differential operator and its applications

    Erdogan Madenci, Atila Barut, and Michael Futch. Peridynamic differential operator and its applications. Computer Methods in Applied Mechanics and Engineering, 304:408–451, jun 2016. 26

    2016

  13. [21]

    Peridynamic Differential Operator for Numerical Analysis

    Erdogan Madenci, Atila Barut, and Mehmet Dorduncu. Peridynamic Differential Operator for Numerical Analysis. Springer International Publishing, Cham, 2019

    2019

  14. [22]

    Peridynamic simulation of electromigration

    Walter Gerstle, Stewart Silling, David Read, Vinod Tewary, and Richard Lehoucq. Peridynamic simulation of electromigration. Comput Mater Continua, 8(2):75–92, 2008

    2008

  15. [23]

    The peridynamic formulation for transient heat conduction.InternationalJournal of Heat and Mass Transfer, 53(19-20):4047–4059, 2010

    Florin Bobaru and Monchai Duangpanya. The peridynamic formulation for transient heat conduction.InternationalJournal of Heat and Mass Transfer, 53(19-20):4047–4059, 2010

    2010

  16. [24]

    Selecting the kernel in a peridynamic formulation: A study for transient heat diffusion

    Ziguang Chen and Florin Bobaru. Selecting the kernel in a peridynamic formulation: A study for transient heat diffusion. Computer Physics Communications, 197:51–60, 2015

    2015

  17. [25]

    Refined bond-based peridy- namics for thermal diffusion.Engineering Computations, 36(8):2557–2587, oct 2019

    Xin Gu, Qing Zhang, and Erdogan Madenci. Refined bond-based peridy- namics for thermal diffusion.Engineering Computations, 36(8):2557–2587, oct 2019

    2019

  18. [26]

    L. J. Wang, J. F. Xu, and J. X. Wang. The green’s functions for peridynamic non-local diffusion. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2193):20160185, 2016

    2016

  19. [27]

    Numerical analysis of peridynamic and classical models in transient heat transfer, employing galerkin approach.Heat Transfer—Asian Research, 47(3):531–555, 2018

    Akbar Jafari, Reza Bahaaddini, and Hasan Jahanbakhsh. Numerical analysis of peridynamic and classical models in transient heat transfer, employing galerkin approach.Heat Transfer—Asian Research, 47(3):531–555, 2018

    2018

  20. [28]

    A peridynamic framework and simulation of non-Fourier and nonlocal heat conduction.International Journal of Heat and Mass Transfer, 118:1284–1292, mar 2018

    Linjuan Wang, Jifeng Xu, and Jianxiang Wang. A peridynamic framework and simulation of non-Fourier and nonlocal heat conduction.International Journal of Heat and Mass Transfer, 118:1284–1292, mar 2018

    2018

  21. [29]

    Erdogan Madenci, Mehmet Dorduncu, Atila Barut, and Michael Futch. Numerical solution of linear and nonlinear partial differential equations using the peridynamic differential operator.Numerical Methods for Partial Differential Equations, 33(5):1726–1753, sep 2017

    2017

  22. [30]

    Foster, Hisanao Ouchi, and Mukul M

    Amit Katiyar, John T. Foster, Hisanao Ouchi, and Mukul M. Sharma. A peridynamic formulation of pressure driven convective fluid transport in porous media. Journal of Computational Physics, 261:209–229, 2014

    2014

  23. [31]

    Rami Jabakhanji and Rabi H. Mohtar. A peridynamic model of flow in porous media. Advances in WaterResources, 78(January):22–35, 4 2015

    2015

  24. [32]

    Construction of a peridynamic model for transient advection-diffusion prob- lems

    Jiangming Zhao, Ziguang Chen, Javad Mehrmashhadi, and Florin Bobaru. Construction of a peridynamic model for transient advection-diffusion prob- lems. International Journal of Heat and Mass Transfer, 126:1253–1266, 11 2018. 27

    2018

  25. [33]

    Peridynamicsmodelling of clay erosion.Géotechnique, 0(0):1–12, 12 2020

    MajidSedighi, HuaxiangYan, andAndreyPJivkov. Peridynamicsmodelling of clay erosion.Géotechnique, 0(0):1–12, 12 2020

    2020

  26. [34]

    Huaxiang Yan, Majid Sedighi, and Andrey P. Jivkov. Peridynamics mod- elling of coupled water flow and chemical transport in unsaturated porous media. Journal of Hydrology, 591(October):125648, 2020

    2020

  27. [35]

    A refined thermo- mechanical fully coupled peridynamics with application to concrete cracking

    Wanhan Chen, Xin Gu, Qing Zhang, and Xiaozhou Xia. A refined thermo- mechanical fully coupled peridynamics with application to concrete cracking. Engineering Fracture Mechanics, 242:107463, 2021

    2021

  28. [36]

    A review for numerical simulation methods of ship–ice interaction.Ocean Engineering, 215:107853, 2020

    Yanzhuo Xue, Renwei Liu, Zheng Li, and Duanfeng Han. A review for numerical simulation methods of ship–ice interaction.Ocean Engineering, 215:107853, 2020

    2020

  29. [37]

    Peridynamic Modelling of Fracture in Polycrystalline Ice.Journal of Mechanics, 36(2):223–234, 2020

    Wei Lu, Mingyang Li, Bozo Vazic, Selda Oterkus, Erkan Oterkus, and Qing Wang. Peridynamic Modelling of Fracture in Polycrystalline Ice.Journal of Mechanics, 36(2):223–234, 2020

    2020

  30. [38]

    Studies on model- scale ice using micro-potential-based peridynamics

    Renwei Liu, Yanzhuo Xue, Duanfeng Han, and Baoyu Ni. Studies on model- scale ice using micro-potential-based peridynamics. Ocean Engineering, 221:108504, 2021

    2021

  31. [39]

    A stochastic multiscale peridynamic model for corrosion-induced fracture in reinforced concrete

    Jiangming Zhao, Ziguang Chen, Javad Mehrmashhadi, and Florin Bobaru. A stochastic multiscale peridynamic model for corrosion-induced fracture in reinforced concrete. Engineering FractureMechanics, 229:106969, 2020

    2020

  32. [40]

    A peridynamic model for brittle damage and fracture in porous materials.International Journal of Rock Mechanics and Mining Sciences, 122:104059, 2019

    Ziguang Chen, Sina Niazi, and Florin Bobaru. A peridynamic model for brittle damage and fracture in porous materials.International Journal of Rock Mechanics and Mining Sciences, 122:104059, 2019

    2019

  33. [41]

    A coupled mechano-chemical peridynamic model for pit-to-crack transition in stress-corrosion cracking

    Ziguang Chen, Siavash Jafarzadeh, Jiangming Zhao, and Florin Bobaru. A coupled mechano-chemical peridynamic model for pit-to-crack transition in stress-corrosion cracking. Journal of the Mechanics and Physics of Solids, 146:104203, 2021

    2021

  34. [42]

    Kurylyk and Kunio Watanabe

    Barret L. Kurylyk and Kunio Watanabe. The mathematical representation of freezing and thawing processes in variably-saturated, non-deformable soils. Advances in Water Resources, 60:160–177, Oct 2013

    2013

  35. [43]

    Gen- eralising the kozeny-carman equation to frozen soils.Journal of Hydrology, 594:125885, 2021

    Jidong Teng, Han Yan, Sihao Liang, Sheng Zhang, and Daichao Sheng. Gen- eralising the kozeny-carman equation to frozen soils.Journal of Hydrology, 594:125885, 2021

    2021

  36. [44]

    JeffreyM.McKenzie, CliffordI.Voss, andDonaldI.Siegel. Groundwaterflow with energy transport and water–ice phase change: Numerical simulations, benchmarks, and application to freezing in peat bogs.Advances in Water Resources, 30(4):966–983, 4 2007. 28

    2007

  37. [45]

    Comparative study of relating equations in coupled thermal-hydraulic finite element analyses.ColdRegions Science and Technology, 161:150–158, 2019

    Zheng Yu, Longcai Yang, and Shunhua Zhou. Comparative study of relating equations in coupled thermal-hydraulic finite element analyses.ColdRegions Science and Technology, 161:150–158, 2019

    2019

  38. [46]

    Evaluation of the calculated unfrozen water contents determined by different measured subzero temperature ranges

    Haiyan Wen, Jun Bi, and Ding Guo. Evaluation of the calculated unfrozen water contents determined by different measured subzero temperature ranges. Cold Regions Science and Technology, 170:102927, 2020

    2020

  39. [47]

    Fully coupled poroe- lasticperidynamicformulationforfluid-filledfractures

    Selda Oterkus, Erdogan Madenci, and Erkan Oterkus. Fully coupled poroe- lasticperidynamicformulationforfluid-filledfractures. EngineeringGeology, 225:19–28, 7 2017

    2017

  40. [48]

    Groundwater flow and heat transport for systems undergoing freeze-thaw: Intercomparison of numerical simulators for 2D test cases

    Christophe Grenier, Hauke Anbergen, Victor Bense, Quentin Chanzy, Ethan Coon, Nathaniel Collier, François Costard, Michel Ferry, Andrew Frampton, Jennifer Frederick, Julio Gonçalvès, Johann Holmén, Anne Jost, Samuel Kokh, Barret Kurylyk, Jeffrey McKenzie, John Molson, Emmanuel ...

    2018

  41. [49]

    Dall’Amico, S

    M. Dall’Amico, S. Endrizzi, S. Gruber, and R. Rigon. A robust and energy-conserving model of freezing variably-saturated soil.The Cryosphere, 5(2):469–484, Jun 2011. 29

    2011

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