Non-equilibrium model for gravity-driven fingering in water repellent soils: Formulation and 2D simulations

Numerical simulations of gravity‐driven fingering in unsaturated porous media using a nonequilibrium model

“…Based on physical arguments, Hassanizadeh and Gray [1993] advocated that a nonequilibrium version of the capillary pressure relationship should be employed in situations where the relaxation time is comparable to other time scales in the flow. This work inspired Nieber et al [2003] to propose their RNERE model in which the RE was supplemented by a relaxation equation of the form where p *(θ*) represents the equilibrium water pressure head [m], ρ is the density of water [kg/m 3 ], g is the gravitational acceleration [m/s 2 ], and τ * = τ *( ψ *, θ*) > 0 is a suitably chosen capillary relaxation function [kg/m s]. They presented numerical simulations of finger‐like instabilities and concluded that a nonequilibrium effect is sufficient to initiate the instabilities and that hysteresis is necessary to sustain the fingers once formed.…”

“…We begin by presenting the governing equations for the RNERE model as presented by Nieber et al [2003], while at the same time reviewing earlier work on fingered flow in porous media. The RE is written in mixed form as where t * represents time [s], θ* is the volumetric water content or saturation [m 3 /m 3 ], and ψ * is the water pressure head [m].…”

“… Egorov et al [2003] provide an overview of the mathematical formulation showing that Richards equation is unconditionally stable even for heterogeneous media. Furthermore, Nieber et al [2003] claim that dynamic (or nonequilibrium) effects are sufficient to cause formation of fingered flow, while persistence of fingers is dominated by hysteresis. In parallel with these developments, several novel mathematical models have been developed which incorporate these and other effects.…”

Coupled inverse modeling of vadose zone water, heat, and solute transport: calibration constraints, parameter nonuniqueness, and predictive uncertainty

“…In this variably saturated domain, the transport of mass and energy can be either uniform or nonuniform (Hendrickx and Flury, 2000). Uniform transport that is considered in this report leads to stable mass and energy fronts, whereas non-uniform transport results in irregular and unstable mass and energy fronts commonly associated with fingering (Glass et al, 1989;Nieber et al, 2002). When a numerical model is used to simulate uniform subsurface transport of mass and(or) energy in the vadose zone, transport parameter values must be supplied to the model.…”

“…Despite the stability and extraction of maximum information content during a regularized inversion, parameter nonuniqueness is often encountered during the model calibration process (Pang et al, 2000;Friedel, 2002;McKenna et al, 2003). Parameter nonuniqueness reflects the fact that it is possible to calibrate a model against a set of measurements with optimal yet alternate sets of parameter values.…”