Coupling Stokes and Darcy equations

Urquiza, José; N'dri, Donatien; Garon, André; Delfour, Michel C.

doi:10.1016/j.apnum.2006.12.006

Cited by 71 publications

(37 citation statements)

References 15 publications

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“…This boundary condition requires an iterative or a sequential computation, although the iterative one is more precise (Sulis et al, 2010). Sometimes the iterative process also leads to a discontinuity of the tangential component of the water velocity at the interface with the streambed (Discacciati et al, 2002;Miglio et al, 2003;Urquiza et al, 2008). This is not a problem, as this discontinuity can be interpreted as representative of the streambed load.…”

Section: Models For Simulating Stream-aquifer Interfacementioning

confidence: 99%

“…Along with the sediment heterogeneities, the geomorphological structures of the alluvial plain can also create preferential pathways, which can have a significant impact on stream-aquifer exchanges (Conant, 2004;Fleckenstein et al, 2006;Poole et al, 2002Poole et al, , 2008Storey et al, 2003;van Balen et al, 2008;Weng et al, 2003;Woessner, 2000). Overall, the preferential flow paths lead to a spatially and temporally complex piezometric head distribution in the alluvial plain, especially during transitional event as floods (Bendjoudi et al, 2002;Heeren et al, 2014;Koch et al, 2011;Wondzell and Swanson, 1999;Wroblicky et al, 1998), when bank storage occurs (Whiting and Pomeranets, 1997).…”

Section: Hydrofacies Related To the Alluvial Plain Architecturementioning

confidence: 99%

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Continental hydrosystem modelling: the concept of nested stream–aquifer interfaces

Flipo

Mouhri

Labarthe

et al. 2014

Hydrol. Earth Syst. Sci.

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Abstract. Coupled hydrological-hydrogeological models, emphasising the importance of the stream-aquifer interface, are more and more used in hydrological sciences for pluridisciplinary studies aiming at investigating environmental issues. Based on an extensive literature review, stream-aquifer interfaces are described at five different scales: local [10 cm- . This led us to develop the concept of nested stream-aquifer interfaces, which extends the well-known vision of nested groundwater pathways towards the surface, where the mixing of low frequency processes and high frequency processes coupled with the complexity of geomorphological features and heterogeneities creates hydrological spiralling. This conceptual framework allows the identification of a hierarchical order of the multi-scale control factors of stream-aquifer hydrological exchanges, from the larger scale to the finer scale. The hyporheic corridor, which couples the river to its 3-D hyporheic zone, is then identified as the key component for scaling hydrological processes occurring at the interface. The identification of the hyporheic corridor as the support of the hydrological processes scaling is an important step for the development of regional studies, which is one of the main concerns for water practitioners and resources managers.In a second part, the modelling of the stream-aquifer interface at various scales is investigated with the help of the conductance model. Although the usage of the temperature as a tracer of the flow is a robust method for the assessment of stream-aquifer exchanges at the local scale, there is a crucial need to develop innovative methodologies for assessing stream-aquifer exchanges at the regional scale. After formulating the conductance model at the regional and intermediate scales, we address this challenging issue with the development of an iterative modelling methodology, which ensures the consistency of stream-aquifer exchanges between the intermediate and regional scales.Finally, practical recommendations are provided for the study of the interface using the innovative methodology MIM (Measurements-Interpolation-Modelling), which is graphically developed, scaling in space the three pools of methods needed to fully understand stream-aquifer interfaces at various scales. In the MIM space, stream-aquifer interfaces that can be studied by a given approach are localised. The efficiency of the method is demonstrated with two examples. The first one proposes an upscaling framework, structured around river reaches of ∼ 10-100 m, from the local to the watershed scale. The second example highlights the usefulness of space borne data to improve the assessment of streamaquifer exchanges at the regional and continental scales. We conclude that further developments in modelling and field measurements have to be undertaken at the regional scale to enable a proper modelling of stream-aquifer exchanges from the local to the continental scale.

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Section: Models For Simulating Stream-aquifer Interfacementioning

confidence: 99%

Section: Hydrofacies Related To the Alluvial Plain Architecturementioning

confidence: 99%

Continental hydrosystem modelling: the concept of nested stream–aquifer interfaces

Flipo

Mouhri

Labarthe

et al. 2014

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

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“…[2], [9], [10], [11], [13], [14], [18], [20], [21], [27], [28], [29], [33], [34], [35], [37], and the references therein). This fact has been motivated by the diverse applications of this coupled model (in petroleum engineering, hydrology, and environmental sciences, to name a few), and also by the increasing need of simpler, more accurate, and more efficient procedures to solve it.…”

Section: Introductionmentioning

confidence: 99%

Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem

Gatica¹,

Oyarzúa²,

Sayas

2011

Math. Comp.

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Abstract.In this paper we analyze fully-mixed finite element methods for the coupling of fluid flow with porous media flow in 2D. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. The fully-mixed concept employed here refers to the fact that we consider dual-mixed formulations in both media, which means that the main unknowns are given by the pseudostress and the velocity in the fluid, together with the velocity and the pressure in the porous medium. In addition, the transmission conditions become essential, which leads to the introduction of the traces of the porous media pressure and the fluid velocity as the associated Lagrange multipliers. We apply the Fredholm and Babuška-Brezzi theories to derive sufficient conditions for the unique solvability of the resulting continuous and discrete formulations. In particular, we show that the existence of uniformly bounded discrete liftings of the normal traces simplifies the derivation of the corresponding stability estimates. A feasible choice of subspaces is given by Raviart-Thomas elements of lowest order and piecewise constants for the velocities and pressures, respectively, in both domains, together with continuous piecewise linear elements for the Lagrange multipliers. Finally, several numerical results illustrating the good performance of the method with these discrete spaces, and confirming the theoretical rate of convergence, are provided.

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“…The three coupling conditions described in this section have been extensively studied and analyzed also in [20,21,40,45,48,51].…”

Section: Coupling Conditions Across the Interfacementioning

confidence: 99%

Navier–Stokes/Forchheimer models for filtration through porous media

Cimolin

Discacciati

2013

Applied Numerical Mathematics

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a b s t r a c tModeling the filtration of incompressible fluids through porous media requires dealing with different types of partial differential equations in the fluid and porous subregions of the computational domain. Such equations must be coupled through physically significant continuity conditions at the interface separating the two subdomains. To avoid the difficulties of this heterogeneous approach, a widely used strategy is to consider the Navier-Stokes equations in the whole domain and to correct them introducing suitable terms that mimic the presence of the porous medium. In this paper we discuss these two different methodologies and we compare them numerically on a sample test case after proposing an iterative algorithm to solve a Navier-Stokes/Forchheimer problem. Finally, we apply these strategies to a problem of internal ventilation of motorbike helmets.

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Coupling Stokes and Darcy equations

Cited by 71 publications

References 15 publications

Continental hydrosystem modelling: the concept of nested stream–aquifer interfaces

Continental hydrosystem modelling: the concept of nested stream–aquifer interfaces

Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem

Navier–Stokes/Forchheimer models for filtration through porous media

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