A seepage face model for the interaction of shallow water tables with the ground surface: Application of the obstacle-type method

Beaugendre, Héloïse; Ern, Alexandre; Esclaffer, Thomas; Gaumé, Éric; Ginzburg, Irina; Kao, C.

doi:10.1016/j.jhydrol.2006.02.019

Cited by 12 publications

(7 citation statements)

References 39 publications

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“…The actual problem is to find the extent of the seepage face on γ S (t), since its boundary is a free boundary and part of the solution that has to be determined, often within an iterative process (cf. [8]), e.g., by switching between Neumann and Dirichlet boundary conditions [17]. With regard to this problem, our approach turns out to be quite elegant and appropriate, because the boundary conditions (2.13) constitute just another obstacle in the convex minimization problem that we obtain in Section 3.…”

Section: Kirchhoff Transformationmentioning

confidence: 99%

Fast and Robust Numerical Solution of the Richards Equation in Homogeneous Soil

Berninger¹,

Kornhuber²,

Sander³

2011

SIAM J. Numer. Anal.

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Abstract. We derive and analyse a solver-friendly finite element discretization of a time discrete Richards equation based on Kirchhoff transformation. It can be interpreted as a classical finite element discretization in physical variables with non-standard quadrature points. Our approach allows for nonlinear outflow or seepage boundary conditions of Signorini type. We show convergence of the saturation and, in the non-degenerate case, of the discrete physical pressure. The associated discrete algebraic problems can be formulated as discrete convex minimization problems and, therefore, can be solved efficiently by monotone multigrid methods. In numerical examples for two and three space dimensions we observe L 2 -convergence rates of order O(h 2 ) and H 1 -convergence rates of order O(h) as well as robust convergence behaviour of the multigrid method with respect to extreme choices of soil parameters.

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Section: Kirchhoff Transformationmentioning

confidence: 99%

Fast and Robust Numerical Solution of the Richards Equation in Homogeneous Soil

Berninger¹,

Kornhuber²,

Sander³

2011

SIAM J. Numer. Anal.

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“…Moreover, we observe that in contrast to front tracking schemes, Algorithm 2 does not use any information from the previous time step to determine the wet portion of the interface. This offers the advantage of robustness and ease of extension to 3D/2D settings, but can entail higher computational costs than those incurred by front tracking schemes in the absence of exfiltration (see for instance [7]). …”

Section: Admissibility Of (ψ H)mentioning

confidence: 99%

“…This means that the hydraulic head of the subsurface flow matches the depth of the overland flow at the interface, while the normal ground flow velocity is used as a source term in the governing equation of the overland flow. Examples of studies based on this approach include coupling one-dimensional surface flow with vertical soil columns [30], coupling the two-dimensional Richards' equation with a one-dimensional kinematic or diffusive wave approximation for the overland flow [22,7], and coupling the two-dimensional Darcy's equation with one-dimensional shallow-water equations [11] .…”

Section: Introductionmentioning

confidence: 99%

Mass conservative BDF-discontinuous Galerkin/explicit finite volume schemes for coupling subsurface and overland flows

Sochala

Ern

Piperno

2009

Computer Methods in Applied Mechanics and Engineering

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Robust and accurate schemes are designed to simulate the coupling between subsurface and overland flows. The coupling conditions at the interface enforce the continuity of both the normal flux and the pressure. Richards' equation governing the subsurface flow is discretized using a Backward Differentiation Formula and a symmetric interior penalty Discontinuous Galerkin method. The kinematic wave equation governing the overland flow is discretized using a Godunov scheme. Both schemes individually are mass conservative and can be used within single-step or multi-step coupling algorithms that ensure overall mass conservation owing to a specific design of the interface fluxes in the multi-step case. Numerical results are presented to illustrate the performances of the proposed algorithms.

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“…More recently, Beaugendre et al . [] simulated water exfiltration at the ground surface with a coupled surface/subsurface model and compared the results with those obtained by using a simpler subsurface seepage face model. They show how, for simple scenarios involving constant slope and rainfall, the two approaches yield similar results.…”

Section: Introductionmentioning

confidence: 99%

Examination of the seepage face boundary condition in subsurface and coupled surface/subsurface hydrological models

Scudeler

Paniconi

Pasetto

et al. 2017

Water Resources Research

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A seepage face is a nonlinear dynamic boundary that strongly affects pressure head distributions, water table fluctuations, and flow patterns. Its handling in hydrological models, especially under complex conditions such as heterogeneity and coupled surface/subsurface flow, has not been extensively studied. In this paper, we compare the treatment of the seepage face as a static (Dirichlet) versus dynamic boundary condition, we assess its resolution under conditions of layered heterogeneity, we examine its interaction with a catchment outlet boundary, and we investigate the effects of surface/subsurface exchanges on seepage faces forming at the land surface. The analyses are carried out with an integrated catchment hydrological model. Numerical simulations are performed for a synthetic rectangular sloping aquifer and for an experimental hillslope from the Landscape Evolution Observatory. The results show that the static boundary condition is not always an adequate stand‐in for a dynamic seepage face boundary condition, especially under conditions of high rainfall, steep slope, or heterogeneity; that hillslopes with layered heterogeneity give rise to multiple seepage faces that can be highly dynamic; that seepage face and outlet boundaries can coexist in an integrated hydrological model and both play an important role; and that seepage faces at the land surface are not always controlled by subsurface flow. The paper also presents a generalized algorithm for resolving seepage face outflow that handles heterogeneity in a simple way, is applicable to unstructured grids, and is shown experimentally to be equivalent to the treatment of atmospheric boundary conditions in subsurface flow models.

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A seepage face model for the interaction of shallow water tables with the ground surface: Application of the obstacle-type method

Cited by 12 publications

References 39 publications

Fast and Robust Numerical Solution of the Richards Equation in Homogeneous Soil

Fast and Robust Numerical Solution of the Richards Equation in Homogeneous Soil

Mass conservative BDF-discontinuous Galerkin/explicit finite volume schemes for coupling subsurface and overland flows

Examination of the seepage face boundary condition in subsurface and coupled surface/subsurface hydrological models

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