## Section: New Results

### Numerical models and simulations in geophysics

#### Mass transport in geological self-organizing systems

Participants : Jenny Al Khoury, Jocelyne Erhel.

This work was done in collaboration with M. Al Ghoul, from the American University of Beirut, Lebanon, in the context of the Sarima project ( 8.3.3 ).

The project consists of setting forth a theoretical and numerical model describing the transport and chemical reaction processes taking place in a geological self-organizing system, as an attempt to simulate the observed banding. We would like then to compare the simulation results with novel experiments designed and performed in the laboratory of Professor Rabih Sultan, American University of Beirut. These novel experiments are to explore the possible similarities between the well-known Liesegang banding phenomenon in precipitate systems and the stripe formation observed in a large number of rocks. Banded rock formations are supposed to arise from the cyclic precipitation as mineral-rich water infiltrates a porous rock and reacts to form an insoluble product. Very few attempts have been cited in the literature to simulate the Liesegang banding phenomena in rocks, experimentally and in situ. In this study, we propose to carry out theoretical simulation of reaction-diffusion in a rock-bearing medium. The coupling of transport (diffusion and flow velocity) to chemical reactions (here precipitation) causes the deposition of the mineral in the form of bands resembling those of a Liesegang pattern. In 2D, concentric rings of the precipitate originating from a central diffusion source are expected to form. The dynamics of this system can be described by coupled reaction-diffusion equations where the weakly soluble salts are represented by a continuous spatio-temporal size distribution functions. The reaction-diffusion equations for the aqueous species are given by conservation equations for the concentrations of these various species using Fick's second law. The global system of Partial Differential Equations is discretised by a Finite Difference Method and an implicit time scheme adapted to stiff systems. Sparse linear systems arising in each time step are solved by a direct method. Simulation results are validated through comparison with experimental results. We plan now to use a Finite Element Method and to reduce computational time by mesh adapting methods.

#### Flow and transport in highly heterogeneous porous medium

Participants : Étienne Bresciani, Jocelyne Erhel.

This work is done in collaboration with A. Beaudoin, from the University of le Havre and J.-R. de Dreuzy, from the department of Geosciences at the University of Rennes 1, in the context of the HYDROLAB project (see 8.1.5 , 5.6 ). We have developed a parallel software for simulating flow and solute transport in a 2D rectangle, where the permeability field is highly heterogeneous. The flow module includes problem generation, spatial discretization by a finite volume method using a structured mesh, linear solving, flux computation and visualization. The transport module includes a parallel particle tracker for advection-dispersion. All algorithms are parallelized using a message-passing approach and a subdomain decomposition. We have used this software to run many random simulations and to derive a stochastic analysis of the results. To obtain a well-defined asymptotic regime, we have used very large computational domains and run our simulations on a cluster ( 6.1.3 ). We could compute with no ambiguity the longitudinal and transverse dispersion coefficient for large heterogeneities (paper submitted to Water Resources Research).

#### Flow in 3D networks of fractures

Participants : Étienne Bresciani, Jocelyne Erhel.

This work was done in collaboration with J.-R. de Dreuzy, from the department of Geosciences at the University of Rennes 1, and with J. Demmel, from the University of Berkeley.

We have developed a parallel software for simulating flow in a 3D network of interconnected plane fractures; we assume that the matrix (the rock) surrounding the fractures is impervious and that the fractures have a constant thickness. Flow computation includes problem generation, mesh generation, spatial discretization by a mixed finite element method, linear solving, flux computation and visualization. Numerical results show that we are able to deal with complex large 3D networks of fractures (paper in preparation).

During his internship at the University of Berkeley and Irisa, B. Poirriez has analyzed the matrix structures and studied a computational model, in order to increase performances.

#### Heat transfer in soil and prehistoric fires

Participants : Édouard Canot, Jocelyne Erhel, Mohamad Muhieddine.

Mohamad Muhhiedine begins his PhD thesis in october 2006 on the subject: "Numerical simulations of prehistoric fires", co-advised by Ramiro March (ArcheoSciences, Rennes). This project takes place in the archeological/human sciences program: "Man and fire: towards a comprehension of the evolution of thermal energy control and its technical, cultural and paleo-environmental consequences". Both physical and numerical approach is used to understand the functioning mode and the thermal history of the studied structures. We plan to improve an existent numerical code to include heat transfer phenomena taking into account the propagation of a dry/humid front. Modelling structures in three dimensions needs to give up the current method used (finite differences) and to switch to a finite element method.