Numerical Simulations for Preferential Finger Flow Using a Two-Dimensional Non-Equilibrium Richards’ Equation with Preisach Hysteresis

A thorough understanding of preferential finger flow through the vadose zone is critical to deepen our knowledge on the processes of infiltration, runoff, erosion, plant growth, and contaminant transport. The paths formed during this fingered flow can be “remembered” by the soil matrix during future infiltration, even after periods of desaturation.

 

It has been shown many times that the traditional porous media equation, Richards’ equation, is incapable of capturing this phenomenon [1]. However, recent studies demonstrate the process can be described by combining a non-equilibrium, relaxation version of Richards’ equation [2] with Preisach hysteresis (applied to the pressure-saturation relationship). In this work, the authors build upon their previously published one-dimensional work [3]. The first part of this study is to present a numerical scheme for the two-dimensional non-equilibrium Richards’ equation using operator splitting methods. The second part is a comparison to previously published experimental results that demonstrates the ability of the model to capture realistic fingering behaviour.

 

[1] Nieber, J., et al. “Non-equilibrium model for gravity-driven fingering in water repellent soils: Formulation and 2D simulations.” Soil water repellency: occurrence, consequences and amelioration (2003): 245-258.

[2] G C Sander et al 2008 J. Phys.: Conf. Ser. 138 012023

[3] Roche, Warren & Murphy, K. & Flynn, Denis. (2021). Modelling preferential flow through unsaturated porous media with the Preisach model and an extended Richards Equation to capture hysteresis and relaxation behaviour. Journal of Physics: Conference Series. 1730. 012002. 10.1088/1742-6596/1730/1/012002.