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Smoothed particle hydrodynamics (SPH) models were used to simulate unsaturated flow in fractures with complex geometries. The SPH is a fully Lagrangian particle‐based method that allows the dynamics of interfaces separating fluids to be modeled without employing complex front tracking schemes. In SPH simulations, the fluid density field is represented by a superposition of weighting functions centered on particles which represent the fluids. The pressure is related to the fluid density through an equation of state, and the particles move in response to the pressure gradient. The SPH does not require the construction of grids that would otherwise introduce numerical dispersion. The model can be used to simulate complex free‐surface flow phenomenon such as invasion of wetting and nonwetting fluids into three‐dimensional fractures. These processes are a severe challenge for grid‐based methods. Surface tension was simulated by using a van der Waals equation of state and a combination of short‐range repulsive and longer‐range attractive interactions between fluid particles. The wetting behavior was simulated using similar interactions between mobile fluid particles and stationary boundary particles. The fracture geometry was generated from self‐affine fractal surfaces. The fractal model was based on a large body of experimental work, which indicates that fracture surfaces have a self‐affine fractal geometry characterized by a material independent (quasi universal) Hurst exponent of about 0.75.
Tartakovsky et al. (Mon,) studied this question.