Research topic: flow in porous media

Scientific context

Model description

The flow equations are Darcy and mass conservation. The permeability field can be layered or very heterogeneous. Stochastic models define a random permeability field. The geometry is fixed.

Numerical methods include Finite Volume methods with a structured regular grid and Mixed Finite Element methods with an unstructured mesh. Studies concern 2D and 3D computational domains. Discrete flow equations are a sparse linear system. Solvers so far studied are direct methods, preconditioned Krylov methods and multigrid methods.

For transient flow, we use the method of lines, with spatial discretization followed by time discretization. Discrete flow equations are a system of ODE, with a sparse Jacobian matrix. We use a ODE/DAE solver, with varying timestep and varying order.

Parallel computations are done in all steps, from data generation to velocity computation. They are based on a subdomain decomposition, where each subdomain is surrounded by ghost cells and is assigned to a processor.

Publications and results

Beaudoin, A.; de Dreuzy, J.; Erhel, J. & Mustapha, H.
Joubert, G.; Nagel, W.; Peters, F.; Plata, O.; Tirado, P. & Zapata, E. (ed.)
Parallel Simulations of Underground Flow in Porous and Fractured Media
Parallel Computing: Current and Future Issues of High-End Computing, NIC, 2006 , 33, 391-398.
Beaudoin, A.; Erhel, J. & de Dreuzy, J.
A comparison between a direct and a multigrid sparse linear solvers for highly heterogeneous flux computations
Eccomas CFD 2006, 2006, proceedings on CD.
J-R. de Dreuzy, P. Davy, J. Erhel and J. de Bremond d'Ars.
Anomalous diffusion exponents in continuous two-dimensional multifractal media.
Physical Review E., 2004, Volume 70, 016306 (6 pages).
H. Hoteit and R. Mosé and B. Philippe and P. Ackerer and J. Erhel.
The maximum principle violations of the mixed-hybrid finite-element method applied to diffusion equations.
International Journal for Numerical Methods in Engineering , 2002, Volume 55, no 12, 1373-1390.
H. Hoteit and J. Erhel and R. Mosé and B. Philippe and P. Ackerer.
Numerical Reliability for Mixed Methods applied to Flow Problems in Porous Media.
Computational Geosciences , 2002, Volume 6, no 2, pp. 161-194.

Objectives and projects

The main objective is to simulate flow in large 3D heterogeneous porous media, using hybrid solvers and high-performance computing.

Participants

This topic started in the Sage team (participants B. Philippe and J. Erhel) with the Ph-D thesis of H. Hoteit, in collaboration with R. Mosé and P. Ackerer, from IMFS at Strasbourg. The thesis was defended in 2002.

Then the research continued in the Sage team (participant J. Erhel) with the post-doc of A. Beaudoin, in 2004-2005, in collaboration with J-R. de Dreuzy, from Geosciences at Rennes. A. Beaudoin was then hired assistant professor at University of Le Havre and is now assistant professor at University of Poitiers. Also it was undertaken in collaboration with D. Tromeur-Dervout, professor at University of Lyon, who had a secondement position at Inria in 2005-2006.

The research is now done by J. Erhel in the team Sage, in collaboration with J-R. de Dreuzy, A. Beaudoin and D. Tromeur-Dervout.

Grants

This work was supported by Inria in 2004-2006, funding the post-doc and the secondement.

Then it was funded by the ANR CIS with the project MICAS in 2008-2011.

Simulations and Algorithms on Grids for Environment