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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.

The Cast3M code (http://www-cast3m.cea.fr/)

Cast3M is a multi-physics code dealing with various applications, initially developed with a finite element scheme for nuclear reactor applications, including solid and structure mechanics, fluid and heat transfers. It consists of various elemental bricks called procedures that can be organized together for the resolution of more complex problems or equations. The resolution of equations dealing with transfers in porous media has been developed from the 90s on. Cast3M now provides tools to resolve a large range of problems including saturated flows, unsaturated flows (Richard’s equation and multi-phase flow), Eulerian and Lagrangian transport by means of Finite Volume and Mixed Hybrid Finite Element schemes. The latter proved accurate and efficient for nuclear waste storage applications (flow and transport) within an inter-comparison exercise (Bernard-Michel, 2004) making Cast3M a reference code for applications in the transfer in porous media. Several extensions including these procedures were developed in the past taking advantage of the modular properties of the code, for instance to simulate couplings of hydrological processes with mechanics and/or heat transfers, or to solve a set of equations coupling surface and sub-surface transfers (Weil et al, 2009), or specialize the simulation tools for applications dealing with fractured media (e.g. Grenier et al, 2009).

Numerical approach for the coupled set of Thermo-Hydrological equations within the benchmark

The procedure solving coupled TH transfers with phase change was developed based on the core procedure TRANGEOL solving time step Eulerian transport (diffusive-dispersive & advective transport). TRANGEOL provides a variety of options: a VF (Le Potier 2004, 2005, 2010) or a MHFE (Mosé et al. 1994; Dabbene et al. 1998) numerical scheme, theta-methods (from implicit to explicit) for diffusion and advection, as well as various options for system matrix inversion and conditioning (www-cast3m.cea.fr). It was largely tested for nuclear waste storage applications showing the practical pros and cons of most of these options and approaches.

To resolve the TH benchmark cases the TRANGEOL procedure was used with the implementation of new development, 1°) adding the phase change term and 2°) solving the set of non-linear coupled equations by means of a Picard iteration scheme. Some points are detailed below.

Phase change resolution

The phase change term is treated as a storage term controlling the velocity of the propagation. Phase change has indeed a strong local influence on the propagation of a cooling front for instance by slowing it down as compared with the same temperature front case without phase change. This is due to the energy required to bring the elementary volume of porous medium to the temperature of phase change and then provide the energy for phase change. This leads to steep fronts. Special effort was put to stabilize the resolution with an under-relaxation scheme. The basic idea is to compute some terms of the equation which are function of the temperature (unknown for the heat equation) by their estimation based on the linear combination of temperature at present calculated time and at the previous. This approach stabilizes the convergence of the iteration but under-relaxation is generally less required after a certain amount of iteration and should be stopped to accelerate convergence. So, to optimize this approach we used the procedure by (Durbin & Delemos 2007). The basic idea is there that the under-relaxation factor depends on the progress of the iterations: the further from convergence, the larger the weight on the former time computation of the variable.

Some references