Local discontinuous Galerkin approximations to Richards’ equation

Li, H.; Farthing, Matthew W.; Dawson, Clint; Miller, Cass T.

doi:10.1016/j.advwatres.2006.04.011

Cited by 38 publications

(44 citation statements)

References 89 publications

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“…As with CG methods, overshoot and undershoot can also occur for sharp front problems without upwinding and reduced order quadrature approximations [4]. Similarly, LDG approximations can exhibit overshoot and undershoot when direct evaluation of relative hydraulic conductivities is used without upwinding [3]. It should be noted that this behavior is a function of grid resolution.…”

Section: Finite Element Approximations For Richards' Equationmentioning

confidence: 99%

“…The medium corresponds to the "Sand" test problem used in [71, see Table 1] as well as [3,7]. To be concrete, VGM p-s-k relations are used with n vg = 4.26, and α vg = 5.47, while θ s = 0.301, θ r = 0.093, and the saturated conductivity is isotropic with T everywhere.…”

Section: Problem IIImentioning

confidence: 99%

“…In order to be robust, spatial and temporal approximations must be capable of resolving sharp fronts infiltrating dry media and handling transitions to elliptic or nearly elliptic conditions in saturated regions [3]. Regardless of the discretization used, the result is almost always a large nonlinear system that is hard to solve efficiently [4,5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Locally conservative, stabilized finite element methods for variably saturated flow

Kees

Farthing

Dawson

2008

Computer Methods in Applied Mechanics and Engineering

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Section: Finite Element Approximations For Richards' Equationmentioning

confidence: 99%

Section: Problem IIImentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Locally conservative, stabilized finite element methods for variably saturated flow

Kees

Farthing

Dawson

2008

Computer Methods in Applied Mechanics and Engineering

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“…Using the Gardner exponential model, the linearized governing equation can be expressed as Equation (12). The initial condition was the soil in dry condition maintained as h d = −100 (m).…”

Section: Transient Modeling Of One-dimensional Flow In Unsaturated Soilmentioning

confidence: 99%

“…Nonlinear physical relationships can be described using soil-water characteristic curves [6][7][8]. Since the Richards equation is highly nonlinear and cannot directly provide an analytical solution, modeling flow process in unsaturated soils is usually based on the numerical solutions of the Richards equation [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Transient Modeling of Flow in Unsaturated Soils Using a Novel Collocation Meshless Method

Liu

Xiao

et al. 2017

Water

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Abstract:In this paper, a novel meshless method for the transient modeling of subsurface flow in unsaturated soils was developed. A linearization process for the nonlinear Richards equation using the Gardner exponential model to analyze the transient flow in the unsaturated zone was adopted. For the transient modeling, we proposed a pioneering work using the collocation Trefftz method and utilized the coordinate system in Minkowski spacetime instead of that in the original Euclidean space. The initial value problem for transient modeling of subsurface flow in unsaturated soils can then be transformed into the inverse boundary value problem. A numerical solution obtained in the spacetime coordinate system was approximated by superpositioning Trefftz basis functions satisfying the governing equation for boundary collocation points on partial problem domain boundary in the spacetime coordinate system. As a result, the transient problems can be solved without using the traditional time-marching scheme. The validity of the proposed method is established for several test problems. Numerical results demonstrate that the proposed method is highly accurate and computationally efficient. The results also reveal that it has great numerical stability for the transient modeling of subsurface flow in unsaturated soils.

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Analytical solution to transient Richards' equation with realistic water profiles for vertical infiltration and parameter estimation

Hayek

2016

Water Resources Research

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A general analytical model for one‐dimensional transient vertical infiltration is presented. The model is based on a combination of the Brooks and Corey soil water retention function and a generalized hydraulic conductivity function. This leads to power law diffusivity and convective term for which the exponents are functions of the inverse of the pore size distribution index. Accordingly, the proposed analytical solution covers many existing realistic models in the literature. The general form of the analytical solution is simple and it expresses implicitly the depth as function of water content and time. It can be used to model infiltration through semi‐infinite dry soils with prescribed water content or flux boundary conditions. Some mathematical expressions of practical importance are also derived. The general form solution is useful for comparison between models, validation of numerical solutions and for better understanding the effect of some hydraulic parameters. Based on the analytical expression, a complete inverse procedure which allows the estimation of the hydraulic parameters from water content measurements is presented.

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Local discontinuous Galerkin approximations to Richards’ equation

Cited by 38 publications

References 89 publications

Locally conservative, stabilized finite element methods for variably saturated flow

Locally conservative, stabilized finite element methods for variably saturated flow

Transient Modeling of Flow in Unsaturated Soils Using a Novel Collocation Meshless Method

Analytical solution to transient Richards' equation with realistic water profiles for vertical infiltration and parameter estimation

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