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-The hydrological team at LSCE has been active in the field of hydrological & hydrogeological modeling with applications in heterogeneous porous media, fractured media, coupled transfers. See some references below. +{{ :participant_pages:logo_lsce.jpg?200|}} The hydrological team at LSCE (http://www.lsce.ipsl.fr/) has been active in the field of hydrological & hydrogeological modeling with applications in heterogeneous porous media, fractured media, coupled transfers. See some references below. 
  
 **The Cast3M code (http://www-cast3m.cea.fr/)**  **The Cast3M code (http://www-cast3m.cea.fr/)** 
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 The procedure developed for the complete set of equations relies upon the elementary time step resolution of the diffusive & advective equation provided in TRANGEOL. It offers MHFE and VF schemes, a theta method (from implicit to explicit) for diffusion and advection. These numerical schemes were originally designed for the resolution of the conductive heat transfer (equivalently diffusive transport). The extensions to advection were made expressing the advection as a source term for MHFE (Dabbene et al 1998) and using a modified version of the method by () for the FV (Le Potier 2004). The stability and accuracy of the resolution has to be controlled with the evaluation of Fourier and CFL numbers respectively. For high Peclet numbers (strong advection), some options are provided in TRANGEOL to obtain an automatic unconditional stability of the resolution. The procedure behind it is an upwind scheme, formally equivalent to the introduction of a dispersion coefficient equal to mesh size. This leads to the CFL value of 1 in the corresponding meshes.  The procedure developed for the complete set of equations relies upon the elementary time step resolution of the diffusive & advective equation provided in TRANGEOL. It offers MHFE and VF schemes, a theta method (from implicit to explicit) for diffusion and advection. These numerical schemes were originally designed for the resolution of the conductive heat transfer (equivalently diffusive transport). The extensions to advection were made expressing the advection as a source term for MHFE (Dabbene et al 1998) and using a modified version of the method by () for the FV (Le Potier 2004). The stability and accuracy of the resolution has to be controlled with the evaluation of Fourier and CFL numbers respectively. For high Peclet numbers (strong advection), some options are provided in TRANGEOL to obtain an automatic unconditional stability of the resolution. The procedure behind it is an upwind scheme, formally equivalent to the introduction of a dispersion coefficient equal to mesh size. This leads to the CFL value of 1 in the corresponding meshes. 
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 +//Resolution of the coupled set of equations//
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 +The resolution of the coupled set of equations is achieved iteratively, with a Picard scheme: the properties for both equations are computed from the values of the unknown at former iteration until convergence of both unknowns. The convergence criterion is expressed as the maximum value of the relative discrepancy between the two last computed pressure and temperature fields. For each time step, the convergence of the iteration scheme was considered achieved when the value of former criterion fell below a threshold. A threshold of 10-4 is commonly considered. 
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 **Some references** **Some references**
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 +Bernard-Michel, G., Le Potier, C., Beccantini, A., Gounand, S., Chraibi M. : The Andra Couplex 1 test case: comparisons between finite-element, mixed hybrid finite element and finite volume element discretizations. Comput Geosci 8:187–201, 2004
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 +Dabbene, F., Paillere, H., Magnaud, J.P.: Mixed hybrid finite elements for transport of pollutants by undergound water. Proc. 10th Conference on Finite Elements in Fluids, Tucson, AZ, January 1998
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 +Durbin, T., Delemos, D.: Adaptative underrrelaxation of Picard iterations in ground water models. Ground Water, 45(5):648-651, 2007
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 +Grenier, C., Bernard-Michel, G., Benabderrahmane, H.: Evaluation of retention properties of a semi-synthetic fractured block from modelling at performance assessment time scales (Äspö Hard Rock Laboratory, Sweden). Hydrogeology Journal 17: 1051–1066, 2009
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 +Grenier, C., Régnier, D., Mouche, E., Benabderrahmane, H., Costard, F., Davy, P.: Impact of permafrost development on underground flow patterns: a numerical study considering freezing cycles on a two dimensional vertical cut through a generic river-plain system. Hydrogeology Journal, 2013, Volume 21, Issue 1, pp 257-270
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 +Le Potier, C.: A nonlinear correction and maximum principle for diffusion operators discretized using cell-centered finite volume schemes. C. R. Acad. Sci. Paris, Ser. I, 348 (2010) 691-695, 2010.
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 +Le Potier, C. : Schémas volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages de triangles non structurés [Finite volume schemes for highly anisotropic diffusion operators on non-structured triangular meshes]. C R Acad Sci 341(12):787–792, 2005.
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 +Le Potier, C.: Finite volume scheme in two or three dimensions for a diffusion-convection equation applied to porous media with CASTEM2000. Dev. Water Sci. 55(2), 1015-102,6 2004.
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 +Mosé, R., Siegel, P., Ackerer, P., Chavent, G.: Application of the mixed hybrid finite element approximation in a groundwater flow model: luxury or necessity? Water Resour Res 30(11):3001–3012, 1994
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 +Régnier D.: Modélisation physique et numérique de la dynamique d’un pergélisol au cours d’un cycle climatique. Implications pour le site Meuse / Haute-Marne. Mémoire de thèse, Université Rennes I, 2012.
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 +Weill, S., Mouche, E., Patin, J.: A generalized Richards equation for surface/subsurface flow modeling. Journal of Hydrology 366, pp. 9-20, 2009
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