Numerical Model of Complex Porous Media

摘要

In this study, the finite element method is used in a specific approach. It facilitates the construction of a numerical model without being representative of the approximate solution of the partial differential equations. The mathematical model is only a temporary support permitting the elaboration of a weak formulation. The consistency of this approach resides in the fact that the weak formulation preserves, in a rigorous way, the physical principle that allowed the constitution of the mathematical model. In the examples concerned, we have used a vector model with a conservative flux. This approach applies particularly well to a survey of surroundings with complex physical properties that notably present strong discontinuity. The interest is reinforced in the particular case of phenomena of percolation. This method allows a new approach of the survey of the porous media's complex features. In the latter case, we used the Darcy model. Many authors agree and say that this model does not give entire satisfaction, but our new approaches confer a new interest in the Darcy model. However, it is clear that the approach used in this work does not limit itself to this type of models. Besides, for convenience reasons, some spatial correlations permit to take in account a more realistic shape of the properties of porous media. To speak only of the porous media, we can apply the same process to Richard's equation used, in particular, for unsaturated porous media. In a more general way, many physical models based on a balance of conservative or not conservative flux can be studied by our method.