Application of the discontinuous spectral Galerkin method to groundwater flow

Fagherazzi, Sergio; Furbish, David Jon; Rasetarinera, Patrick; Hussaini, M. Y.

doi:10.1016/j.advwatres.2003.11.001

Cited by 26 publications

(11 citation statements)

References 27 publications

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“…Over the last 15 years, DG finite element methods have received increasing attention in many fields for hyperbolic PDEs [26,[31][32][33] as well as elliptic and parabolic problems [10,11,29,34,46,70,74,75]. The term discontinuous Galerkin covers a wide range of finite element methods based on discontinuous approximations.…”

Section: Discontinuous Galerkin Methodsmentioning

confidence: 99%

Local discontinuous Galerkin approximations to Richards’ equation

Farthing

Dawson

et al. 2007

Advances in Water Resources

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Section: Discontinuous Galerkin Methodsmentioning

confidence: 99%

Local discontinuous Galerkin approximations to Richards’ equation

Farthing

Dawson

et al. 2007

Advances in Water Resources

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“…As in a usual FV method, the Riemann solver [46] stabilizes the solution. However in this case higher accuracy may be achieved by increasing the order of the approximation, N, as well as by reducing the size of the elements, h. The DGSEM is used in a wide range of applications such as compressible flows [5,35], electromagnetics and optics [1,13,14,29], heat transfer [32], aeroacoustics [9,36,42,43], meteorology [22,23,38], and geophysics [16,17].…”

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confidence: 99%

Quasi-A Priori Truncation Error Estimation in the DGSEM

et al. 2014

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In this paper we show how to accurately perform a quasi-a priori estimation of the truncation error of steady-state solutions computed by a discontinuous Galerkin spectral element method. We estimate the spatial truncation error using the r-estimation procedure. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimation, we use non time-converged solutions on one grid with different polynomial orders. The quasi-a priori approach estimates the error while the residual of the time-iterative method is not negligible. Furthermore, the method permits one to decouple the surface and the volume contributions of the truncation error, and provides information about the anisotropy of the solution as well as its rate of convergence in polynomial order. First, we focus on the analysis of one dimensional scalar conservation laws to examine the accuracy of the estimate. Then, we extend the analysis to two dimensional problems. We demonstrate that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error.

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“…Despite these limitations, the Richards equation is now a well-established approach to simulate water table dynamics; see, for instance, Celia et al (1990) for a thorough discussion of numerical aspects including choice of the main unknown, of the nonlinear iterative solver and of the space and time discretization schemes. Using the Richards equation presents two advantages, namely the use of a single (nonlinear) partial differential equation that can be discretized by fairly standard or more advanced finite element or finite volume techniques (Woodward and Dawson, 2000;Knabner and Schneid, 2002;Bastian, 2003;Bause and Knabner, 2004;Fagherazzi et al, 2004;Manzini and Ferraris, 2004) and the fact that the saturated and unsaturated portions of the soil can be treated simultaneously as a single computational domain. Models based on the Richards equation can be used to simulate the response of the water table to infiltration caused by rainfall.…”

Section: Introductionmentioning

confidence: 99%

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

Beaugendre

Ern

Esclaffer

et al. 2006

Journal of Hydrology

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International audienceThis paper presents a model to simulate overland flow genesis induced by shallow water table movements in hillslopes. Variably saturated subsurface flows are governed by the Richards equation discretized by continuous finite elements on unstructured meshes. An obstacle-type formulation is used to determine where saturation conditions, and thus seepage face conditions, are met at the ground surface. The impact of hillslope geometry, boundary conditions, and soil hydraulic parameters on model predictions is investigated on two-dimensional test cases at the metric and hectometric scales. The obstacle-type formulation is also compared with a more detailed model coupling subsurface and overland flow, the latter being described by the shallow water equations in the diffusive wave regime

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Application of the discontinuous spectral Galerkin method to groundwater flow

Cited by 26 publications

References 27 publications

Local discontinuous Galerkin approximations to Richards’ equation

Local discontinuous Galerkin approximations to Richards’ equation

Quasi-A Priori Truncation Error Estimation in the DGSEM

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

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