Novel Solution of the Diffusion Equation Utilizing Optimization through Genetic Algorithm

The horizontal movement of water in a porous unsaturated medium is considered. An analytical expression is given for the diffusion coefficient that appears in the governing nonlinear partial differential equation. This expression contains adjustment parameters, allowing fitting to diffusion measurements. Four sets of such measurements of the pertinent literature were used for this fitting and for examining the validity of the model. The same procedure was employed to another expression of the literature for the diffusion coefficient and comparisons were made. The results showed that the diffusion expression presented in this paper exhibited a better fit (with respect to the relative mean square error) to the experimental data, compared to the expression of the literature. The calibration problem was treated by a combination of a genetic algorithm and the NelderMead method. The expression of this paper for the analytical diffusion coefficient is based on a transformation of a corresponding expression for the moisture profile and, after the parameters’ determination, moisture profiles and sorptivity become readily available.