A percolation model for numerical simulations of 2D non-gravity impregnation in porous media

The aim of this work is to propose a new percolation model for numerical simulation of impregnation in porous media. Indeed, the impregnation phenomena concern many engineering fields, and could affect mechanical behavior of the medium, specifically when it is coupled with other physics such as heat or chemistry. The understanding of this phenomenon requires sophisticated numerical models that take into account the coupling between different physics. Classical numerical methods present known problems such as high computational costs, spurious oscillations and are not well adapted to such a complex coupling problem. To avoid these computational difficulties, Self-organized Gradient Percolation (SGP) model could be a good compromise. SGP is a numerical model based on a probabilistic approach, namely gradient percolation, already introduced in the 1D case, [1]. In this work we explore the non-reactive case. Instead of using finite element methods to solve Richards' equation, we model the propagation of the saturation in the medium by the evolution of gradient percolation clusters. We hence delimitate the "wet" zone of the porous media to which we associate macroscopic saturation using interpolation techniques. The obtained results are free from spurious oscillation, and computational cost is drastically reduced compared with the classical approaches based on the finite element method. We believe that the 2D-SGP method can be enhanced by a futur 3D extension, but also to include the chemical and thermo-mechanical aspects.