  The aim of this work is to develop a new numerical method to overcome the
computational difficulties of numerical simulation of unsaturated impregnation
in porous media. The numerical analysis by classical methods (F.E.M,
theta-method, ...) for this phenomenon require small time-step and space
discretization to ensure both convergence and accuracy. Yet this leads to a
high computational cost. Moreover, a very small time-step can lead to spurious
oscillations that impact the precision of the results. Thus, we propose to use
a Self-organized Gradient Percolation (SGP) algorithm to reduce the
computational cost and overcome these numerical drawbacks. The (SGP) method is
based on gradient percolation theory, relevant to calculation of local
saturation. The initialization of this algorithm is driven by an analytic
solution of the homogenous diffusion equation, which is a convolution between a
Probability Density Function (PDF) and a smoothing function. Thus, we propose
to reproduce the evolution of the capillary pressure profiles by the evolution
of the standard deviation of the PDF. This algorithm is validated by comparing
the results with the capillary pressure profiles and the mass gain curve
obtained by finite element simulations and experimental measurements,
respectively. The computational time of the proposed algorithm is lower than
that of finite element models for one-dimension case. In conclusion, the SGP
method permits to reduce the computational cost and does not produce spurious
oscillations. The work is still going on for extension in 3D and the first
results are promising.
