Dual‐continuum models are useful for describing flow in porous systems with significant local pressure disequilibrium between slow moving water, contained in the porous matrix, and fast moving water in preferential pathways. The formation and intensity of preferential flow depends on the contrast between the hydraulic properties of the two flow domains as well as on the properties of their interface. In this study, we focused on both physical coupling of the flow domains through the mass transfer term and numerical coupling of the respective governing equations. The set of governing equations was alternatively solved using a sequentially coupled (SC) approach and a fully coupled (FC) approach. The SC approach was shown to be computationally more efficient for strongly developed preferential flow in systems with high interfacial resistance; however, it becomes numerically unstable for weak preferential flow associated with low interfacial resistance. The FC approach is a computationally more expensive yet numerically more robust alternative, capable of simulating a complete class of intermediate flow regimes ranging from strongly preferential flow in a dual‐continuum system to nonpreferential flow in a single‐continuum system. To illustrate the performance of the numerical coupling approaches in conjunction with the effect of different interfacial resistances, we present a simple example problem involving one‐dimensional near‐saturated flow in a vertical soil column.
Recurrent ponded infi ltra on experiments on undisturbed samples of coarse sandy loam have revealed a signifi cant fl ow instability characterized by a decrease in the steady-state fl ow rate of the second infi ltra on run, conducted into wet soil, compared with the fi rst infi ltra on run, conducted into drier soil. It has been hypothesized that this decrease was caused by air entrapment during the second run, with subsequent blocking of the preferen al pathways. In this study, entrapped air distribu on and its impact on water fl ow was studied through a novel combina on of magne c resonance (MR) imaging and numerical modeling. An undisturbed sample of coarse sandy loam was subject to recurrent ponded infi ltra on while being monitored by MR. Internal structure of the soil sample was visualized by x-ray computed tomography (CT). A parallel version of the three-dimensional water fl ow model based on Richards' equa on was used to simulate water fl ow through the heterogeneous soil sample. Informa on from the CT was used to describe internal heterogeneity of the soil sample via scaling factors. Magne c resonance relaxometry imaging data were u lized to derive three-dimensional maps of entrapped air. These were implemented into a simula on of the second infi ltra on run as regions of no fl ow. The MR images were used to assess the water content distribu on within the sample. The threedimensional model was able to describe measured ou low rates and pressure heads and also to reproduce the heterogeneous distribu on of water content within the sample. The results obtained support the assump on that the observed decrease in the ou low rate could be caused by entrapped air in large pores of the soil sample. Current theory for mathema cal predic ons of water fl ow and solute transport in porous media assumes that the air phase plays a relatively minor role during unsaturated fl ow and transport (e.g., van Genuchten et al., 1999). Th ere is a long-term evidence, however, of air-phase discontinuities occurring in porous media and leading either to water entrapment (Papafotiou et al., 2008) or to air entrapment eff ects on water fl ow (Christiansen, 1944;Faybishenko, 1995) and solute transport in soils (Geistlinger et al., 2005). For instance, entrapped air was found to be responsible for an increase in infi ltration variability (Wang et al., 1998), temporal changes in hydraulic conductivity (Sakaguchi et al., 2005), and fl ow instabilities (Schultze et al., 1999;Wildenschild et al., 2001).To study infi ltration processes exhibiting air entrapment eff ects, Snehota et al. (2010) performed a recurrent ponded infi ltration experiment on an undisturbed heterogeneous soil column. With the use of MR imaging, they detected signifi cant air entrapment in large pores and associated this with the decrease in the quasi-steady-state outfl ow rate during infi ltration into a wet sample. Th ey presented only qualitative results because the MR pulse sequence used did not provide spatially resolved information about changes in water cont...
SUMMARYWe extend the Balancing Domain Decomposition by Constraints (BDDC) method to flows in porous media discretised by mixed-hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are modelled by 1D or 2D elements inside three-dimensional domains. In this set-up, the global problem as well as the substructure problems have a symmetric saddle-point structure, containing a 'penalty' block due to the combination of meshes. We show that the problem can be reduced by means of iterative substructuring to an interface problem, which is symmetric and positive definite. The interface problem can thus be solved by conjugate gradients with the BDDC method as a preconditioner. A parallel implementation of this algorithm is incorporated into an existing software package for subsurface flow simulations. We study the performance of the iterative solver on several academic and real-world problems. Numerical experiments illustrate its efficiency and scalability. Preprint version.
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