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\begin{document}

\title{Three-dimensional smoothed particle hydrodynamics modeling of
preferential flow dynamics at fracture intersections on a
high-performance computing platform}



\author[1]{Lysander Bresinsky}%
\author[1]{Jannes Kordilla}%
\affil[1]{University of Göttingen, Geoscientific Centre, Göttingen, Germany}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\begin{abstract}
The physical mechanisms that govern preferential flow dynamics in
unsaturated fractured rock formations are complex and not well
understood. Fracture intersections are critical relay points along
preferential flow paths and control the partitioning behavior, leading
to temporal delay and intermittent flow. In this work, a
three-dimensional Pairwise-Force Smoothed Particle Hydrodynamics
(PF-SPH) model is being applied in order to simulate gravity- driven
droplet flow at synthetic fracture intersections. SPH, as a mesh-less
Lagrangian method, is particularly suitable for modeling deformable
interfaces, such as three-phase contact dynamics of droplets. The static
and dynamic contact angle can be recognized as the most important
parameter of gravity-driven free-surface flow. In SPH, surface tension
and adhesion naturally emerges from the implemented pairwise fluid-fluid
(s\_f f ) and solid- fluid (s\_sf ) interaction force. The model was
calibrated to a contact angle of 65 * , which corresponds to the wetting
properties of water on Poly(methyl methacrylate). The accuracy of the
SPH simulations were validated against an analytical solution of
Poiseuille flow between two parallel plates and against laboratory
experiments. Using the SPH model, the complex flow mode transitions from
droplet to rivulet flow of an experimental study were repro- duced.
Additionally, laboratory dimensionless scaling experiments of water
droplets were successfully replicated in SPH. Finally, SPH simulations
were used to investigate the partitioning dynamics of single droplets
into syn- thetic horizontal fractures with various apertures ([?]d\_f = 0,
0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 mm) and offsets ([?]d\_of f = 1.5,
1.0, 0.5, 0, 1.0, 2.0, 3.0 mm). The perfect conditions of ideally smooth
surfaces and the SPH inherent advantage of particle tracking allow the
recognition of small scale partitioning mechanisms and its importance
for bulk flow behavior. The aim of this study is to derive an analytical
correlation and interpretation of partitioning dynamics, droplet height
and aperture%
\end{abstract}%



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