A 2D self-organized percolation model for capillary impregnation

TL;DR

This paper extends the Self-organized Gradient Percolation (SGP) model to two dimensions for simulating capillary impregnation, using diffusion solutions for initialization and comparing results with finite element methods.

Contribution

It introduces a 2D version of the SGP model for capillary impregnation, enhancing the original 1D approach with analytic initialization and validation against finite element results.

Findings

SGP model successfully extended to 2D for capillary impregnation.

Validation shows good agreement with finite element simulations.

The model captures the evolution of saturation fronts in two dimensions.

Abstract

A two-dimension extension of the Self-organized Gradient Percolation (SGP) method initially developed for the one-dimensional simulation is proposed. The initialization in the two directions is considered as the analytic solution of the 2D (homogeneous) diffusion equation. The evolution of the saturation front is assumed to be the evolution of both standard deviations in each direction. The validation of the implementation is done by comparisons between SGP and finite element results.