A finite-element algorithm for modeling variably saturated flows

Wu, Mengxi

doi:10.1016/j.jhydrol.2010.09.004

Cited by 22 publications

(18 citation statements)

References 19 publications

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“…An adjustment procedure needs to be used during the iterative solution so that zero pressure is kept inside the seepage face and negative pressures are maintained outside the seepage face, the flux flowing out of the face [12]. During the iteration, the nodes at the boundary (suspended to be a seepage face) with a positive pressure should be altered as Dirichlet nodes with a zero pressure value, the prescribed seepage face nodes with a negative flux need to be identified and treated as nodes outside the seepage face in the next iterative solution of the finite element equations [15,27]. The flux of a node can be evaluated by…”

Section: Procedures For Seepage Face Iterationmentioning

confidence: 99%

“…where Q I is the flux at node I, z is the elevation above a reference datum, K IJ is the seepage coefficient tensor assemblage of all the elements [15] shown in eq. (6).…”

Section: Procedures For Seepage Face Iterationmentioning

confidence: 99%

“…These approaches which focus the calculation on the saturated zone require the locating of the free surface by an iterative process. Another group of approaches uses unsaturated theory and the calculation domain involves both the saturated and unsaturated zones [11][12][13][14][15]. The conductivity of the material in an unsaturated zone varies with the degree of the saturation or the minus pore pressure.…”

Section: Introductionmentioning

confidence: 99%

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Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field

LianZhi

2013

Sci. China Phys. Mech. Astron.

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An inner seepage face phenomenon is given and a numerical simulation procedure has been developed. It may appear at the interface of two materials when an unconfined seepage flows from a porous media to a coarser porous media with a higher permeability. Inaccuracy and divergent problems may arise both in a saturated-only and in a variably saturated analysis while an inner seepage face is not simulated with a special procedure. The position of the seepage face is determined during the nonlinear iteration process and the flux of the inner seepage face nodes is transferred to the downstream side nodes. Validity and efficiency of the procedure are illustrated by the simulation of two dimensional steady state seepage examples of heterogeneous zoned dams which is usually used to validate algorithms. An analysis of a three-dimensional earth core rockfill dam is also presented here. The procedure can also be applied to general transient seepage problems. Citation:Wu M X, Yang L Z, Yu T. Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field.

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Section: Procedures For Seepage Face Iterationmentioning

confidence: 99%

“…where Q I is the flux at node I, z is the elevation above a reference datum, K IJ is the seepage coefficient tensor assemblage of all the elements [15] shown in eq. (6).…”

Section: Procedures For Seepage Face Iterationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field

LianZhi

2013

Sci. China Phys. Mech. Astron.

Self Cite

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“…Although it has long been studied, seeking numerical solutions to unsaturated flow problems remains a challenging issue, due mainly to the strong nonlinearity of the constitutive relationships (i.e., the water retention curve and the conductivity function) and the boundary conditions. Great efforts have been made to overcome the numerical difficulties induced by the nonlinearity of the water retention properties of soils, with a focus on the improvement of the numerical accuracy and stability (e.g., [3,8,17,18,20,23,26,28,31,33,35,36]). The boundary conditions on the outflow seepage surfaces and soil-atmosphere interfaces are another source of nonlinearity involved in the numerical modeling of groundwater flow, and these conditions are commonly present on the surfaces of wells, drains, lakes, rivers, wetland or ground surface where rainfall/evaporation occurs.…”

Section: Introductionmentioning

confidence: 99%

A numerical formulation with unified unilateral boundary condition for unsaturated flow problems in porous media

Chen

Zhou

et al. 2016

Acta Geotech.

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This paper proposed a numerical formulation for unsaturated flow problems with nonlinear boundaries of seepage face and soil-atmosphere interface via the concept of parabolic variational inequality (PVI) method. A unified unilateral boundary condition was first proposed to represent the conditions on the seepage face and soil-atmosphere interface boundaries within the partial differential equation (PDE) formulation. A PVI formulation mathematically equivalent to the PDE formulation was then proposed, which automatically transforms the flux part of the unified unilateral boundary condition into the natural boundary condition and eliminates the singularity at seepage points. By discretizing the PVI formulation, a finite element procedure together with an iterative algorithm was suggested. An existing experiment of unsaturated flow in a layered hillside and a laboratory test of unsaturated flow through sand flume performed in this study were used to validate the proposed method, with a good agreement between the measured and computed results and a satisfactory balance of mass being maintained during the simulations. The numerical results also indicated that the problem of mesh dependence associated with unsaturated flow simulations is well addressed with the proposed numerical method. Finally, the process of unsaturated flow in a soil slope with layers of horizontal drains subjected to rainfall/evaporation was further examined. The numerical results reveal that the deployment of drains in a soil slope can significantly lower the pore water pressure around the drains, with the bottom layer drains being most effective in controlling the seepage flow.

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“…For the case of saturated-unsaturated flow, we mention the contributions of Forsyth et al (1995), Pan and Wierenga (1995), Diersch and Perrochet (1999), Berganaschi and Putti (1999), Wiliams et al (2000), Lima-Vivancos and Voller (2004), Bause and Knabner (2004), Hao et al (2005), Marinoschi (2005), Basombrio et al (2006), McBride et al (2006), Pei et al (2006), Kees et al (2008), Bevilacqua et al (2009), Casulli and Zanolli (2010), Radu et al (2010), and Wu (2010). For 2D and 3D problems, the standard numerical approach consists of: -space discretization by finite volume, finite element (Galerkin), mixed finite element, finite differences; -method of lines for time discretization; -solution of the discrete nonlinear problems using Newton/Picard method; -solution of the linear problems by iterative linear solvers (preconditioned conjugated gradient, preconditioned Krylov subspace methods, algebraic multigrid, and so on).…”

mentioning

confidence: 99%

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

2011

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The need of accurate and efficient numerical schemes to solve Richards' equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards' equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated-unsaturated soils with hydraulic properties described by van Genuchten-Mualem models. The numerical results obtained are compared with those provided by the modified Picard-preconditioned conjugated gradient (Krylov subspace) approach.

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A finite-element algorithm for modeling variably saturated flows

Cited by 22 publications

References 19 publications

Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field

Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field

A numerical formulation with unified unilateral boundary condition for unsaturated flow problems in porous media

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

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