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.
We use the method of lines, with spatial discretization followed by time discretization. Numerical methods include Finite Volume methods with a structured regular grid and Mixed Finite Element methods with an unstructured mesh. Currently, studies concern 2D computational domains. 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.
The main objective is to simulate transient flow in 3D heterogeneous porous media. This task is described in the project Micas.
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.
The research is now done by J. Erhel in the team Sage, in collaboration with J-R. de Dreuzy.
Current work is funded by the ANR CIS with the project MICAS in 2008-2011.