Coupled water and energy transfers in porous media with freeze/thaw: permaFoam, a massively parallel OpenFOAM® solver
Résumé
This work presents a numerical solver for the multiphysics problem of hydric and thermal transfers in variably water saturated porous media with freeze/thaw of the poral water. The application that we aim to deal with is the study of the dynamics of permafrosts, which are constituted of soils and geological bodies frozen in depth all year round, with a thawed superficial active layer in summer. Permafrosts are present on about 20 % of continental surfaces, i.e. ~25 millions of km². The mid term objective of this numerical development effort is to contribute to the quantification of the impacts of climate change on the weathering fluxes from the boreal areas to the oceans (e.g. : [1]), although other potential fields of application exist (e.g. : engineering in cold regions).
This kind of cryohydrogeological problems involves strong couplings and strong non-linearities, and the development of related numerical solving tools has been the subject of a renewed interest during these last years (e.g. : [2]). Here we present the cryohydrogeological solver permaFoam [3] which has been develloped in the framework of the open source tool box for computational fluid dynamics OpenFOAM®. PermaFoam allows the coupled resolution of a modified Richards equation that takes into account the decrease of hydraulic conductivity related with the freezing of the poral water and of an advection-conduction equation which includes a latent heat exchange term. The use of OpenFOAM® allows to benefit from its excellent parallel performances (e.g. : [4]). This latter point is crucial given that the strong non linearities and the steep fronts encountered in cryohydrogeological modelling may induce very important computation times.
After a short introduction of the considered equations and of the used numerical methods, some analytical validations and code-to-code comparisons performed in the framework of the international benchmark Interfrost [2] will be presented. The parallel performances of permaFoam will then be discussed on the basis of strong scaling curves obtained with the supercomputer EOS (CALMIP High Performance Computing center). Finally, the capabilities of permaFoam will be illustrated with an example of application in a monitored catchment of Central Siberia, the Kulingdakan watershed (e.g. : [5], [6]).
[1] Pokrovsky et aL., 2015, Biogeosciences Discuss., 12, 10621–10677.
[2] Grenier et al., 2015, Geophysical Research Abstracts, 17, EGU2015-9723, EGU General Assembly 2015.
[3] Orgogozo et al., 2016, International Conference On Permafrost, 20-24 June 2016, Potsdam, Germany.
[4] Orgogozo et al., 2014, Computer Physics Communications, 185, 3358-3371.
[5] Prokushkin et al., 2007. Global Biogeochemical Cycles, 21, GB4003.
[6] Viers et al., 2015. Geochemical Transactions 16:3.
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