Numerical simulation code for 1D water flow in porous media with competition between transport and diffusion

This software package contains the Matlab scripts used to generate the numerical simulations and figures presented in the publication: "Some remarks on a mathematical model for water flow in porous media with competition between transport and diffusion" (DOI: 10.14311/AP.2025.65.0341). The scripts implement a 1-D numerical solver using the pdepe function to model moisture front propagation in porous media. The code specifically describes the competition between diffusion and gravitational transport, as theoretically derived in the associated paper. The three uploaded files correspond to the three specific numerical examples studied in the article: example1.m: Implementation and results for Example 1. example2.m: Implementation and results for Example 2. example3.m: Implementation and results for Example 3. Technical Details: Language: Matlab Method: Finite Element Method (via pdepe solver) Requirements: Standard Matlab installation (no additional toolboxes required)