Multi-scale Smoothed Particle Hydrodynamics model for flow and transport in unsaturated fractured porous media

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The main goal of this proposal is the development of a particle-based multi-scale modelling tool to simulate flow and transport dynamics in unsaturated fractures embedded in a porous matrix. The characterization of flow and transport in unsaturated fractured porous media remains one of the most challenging problems in hydrogeology and is of importance for a wide range of applications, such as the quantification of infiltration through thick unsaturated zones of fractured media (nuclear waste repositories), prediction of groundwater recharge and aquifer vulnerability. Flow and transport dynamics in unsaturated fractured porous aquifers are often dominated by a strong heterogeneous geometry and large contrasts in hydraulic properties. Flow dynamics in fractures are difficult to describe quantitatively because of the complex interplay between gravitational, inertial and capillary forces, surface tension, wetting dynamics and the fracture geometry. Small-scale laboratory experiments and numerical models are commonly the only feasible way to capture the highly non-linear flow dynamics and complex interface movements. In particular, strong deforming interfaces pose a challenge to most grid-based modelling approaches, problems that can easily be solved by particle-based models, as particles simply move with the interfaces and/or free surfaces and do not require complex front-tracking schemes. In many cases fractures are embedded in a porous matrix, which does not behave as an impervious medium. The matrix-fracture interface therefore forms an essential connection between the porous matrix, which provides the main storage and the fractures, that acts as the dominating hydraulic pathway through the vadose zone. To model the coupling between these two elements and to simulate the potential feedback mechanisms at the process scale, appropriate modelling approaches are required to reproduce the scale-dependent flow and transport processes. In terms of model discretization it is not feasible to resolve the pore-space and fracture geometry in detail using a single modelling approach as pore throat and fracture apertures are several orders of magnitude apart. Therefore we propose the development of an adapted multi-scale Smoothed Particle Hydrodynamics code. Flow and transport within the porous matrix will be simulated via classical approaches for unsaturated flow such as the Richards equation, which shall be coupled to the discrete free-surface flow dynamics (e.g. adsorbed films, droplets, rivulets) in the fracture. The fully-coupled model will be embedded in a single numerical framework and thus does not require the management of a complex combination of solver routines and coupling methods. The model will be validated by laboratory and numerical experiments and employed to study the effects of the complex free-surface flows and the wetting and transport dynamics at the matrix-fracture interface.