Discrete Fluxes and Mass Balance in Finite Elements

Berger, R. C.; Howington, Stacy E.

doi:10.1061/(asce)0733-9429(2002)128:1(87)

Cited by 42 publications

(17 citation statements)

References 7 publications

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“…This approach is similar to one proposed by Berger and Howington [3] for conservation laws in primitive form.…”

Section: A Consistent Fluxmentioning

confidence: 85%

“…(17). In a fashion similar to that detailed by Berger et al [3], we consider a nodej and its adjacent neighbors which form the patch Qj. We present in Fig.…”

Section: A Consistent Fluxmentioning

confidence: 99%

“…The mass error used to evaluate local conservation in these applications to date has typically been computed element-wise using a volumetric approach by which the discrete form of the primitive conservation law is formulated using physical arguments, see [8] for example. While conceptually satisfying, this approach is inconsistent with the finite element basis and equations used to solve the GWCE itself as brought to light by Berger and Howington [3] and Hughes et al [6]. In their work, Berger and Howington [31 show how to define partial fluxes in such a way as to be consistent with the local CG conservation statement.…”

Section: Introductionmentioning

confidence: 99%

“…To be clear, when checking mass balance, we say that a method is consistent, if it enforces mass balance in the same manner that is prescribed by the discrete equations which are solved, this includes using the same set of equations and the same basis functions as the solution itself uses. One important distinction regarding the analyses of both Hughes et al [6] and Berger and Howington [3] is that they are relevant to the primitive form of the continuity equation. Of particular interest here is local conservation with respect to a GWCE-based shallow water equation model.…”

Section: Introductionmentioning

confidence: 99%

“…Of particular interest here is local conservation with respect to a GWCE-based shallow water equation model. So, in light of the work of Hughes et al [6] and Berger and Howington [3], we endeavor to examine the local conservation properties of the GWCE by constructing fluxes that are consistent with the CG statement for the GWCE, which is not an explicit conservation law. In doing so we show that the GWCE is not locally mass conservative, although it is locally conservative with respect to certain quantities.…”

Section: Introductionmentioning

confidence: 99%

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In search of a consistent and conservative mass flux for the GWCE

Massey

Blain

2006

Computer Methods in Applied Mechanics and Engineering

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“…This approach is similar to one proposed by Berger and Howington [3] for conservation laws in primitive form.…”

Section: A Consistent Fluxmentioning

confidence: 85%

“…(17). In a fashion similar to that detailed by Berger et al [3], we consider a nodej and its adjacent neighbors which form the patch Qj. We present in Fig.…”

Section: A Consistent Fluxmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

In search of a consistent and conservative mass flux for the GWCE

Massey

Blain

2006

Computer Methods in Applied Mechanics and Engineering

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Locally conservative groundwater flow in the continuous Galerkin method using 3‐D prismatic patches

Zhao

Lin

et al. 2016

Water Resources Research

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A new procedure has been developed to improve the velocity field computed by the continuous Galerkin finite element method (CG). It enables extending the postprocessing algorithm proposed by Cordes and Kinzelbach (1992) to three‐dimensional (3‐D) models by using prismatic patches for saturated groundwater flow. This approach leverages a dual mesh to preserve local mass conservation and provides interpolated velocities based on consistent fluxes. To develop this 3‐D approach, a triangular conservative patch is introduced by computing not only advection fluxes, but also vertical infiltrations, storage changes, and other sink or source terms. This triangular patch is then used to develop a prismatic patch, which consists of subprisms in two layers. By dividing a single two‐layer patch into two separate one‐layer patches, two dimensional (2‐D) algorithms can be applied to compute velocities. As a consequence, each subelement is able to preserve local mass conservation. A hypothetical 3‐D model is used to evaluate the precision of streamlines and flow rates generated by this approach and the FEFLOW simulation program.

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Implementation and analysis of a partial‐element wetting and drying framework for generalized wave continuity equation‐based hydrodynamic models

Dick

Tromble

Dresback

et al. 2013

Numerical Methods in Fluids

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SUMMARY The ADCIRC hydrodynamic model has been used extensively to predict the effects of storm surge in coastal regions. In an effort to create a more holistic representation of coastal inundation (i.e., the total water level), some recent applications of ADCIRC have focused on modeling coastal river systems. Initial attempts to model river systems with ADCIRC have encountered complications associated with mass balance (artificial increase in mass in the downstream direction) and model instabilities when flow leaves the main channel, which suggests that complications may be attributed to the current treatment of the wet/dry boundary in CG ADCIRC. A new wetting/drying framework has been developed for, and implemented in, the 1D continuous Galerkin ADCIRC code, which is based on the generalized wave continuity equation (GWCE) formulation of the shallow water equations. The new algorithm allows for the inclusion of partially wet elements within the computational domain of ADCIRC, and the focus of this manuscript is flooding‐type wetting/drying processes (e.g., tidal fluctuations and storm surge inundation). The new framework uses a scaling factor, η, placed on the time derivative term in the primitive continuity equation, prior to formulation of the GWCE. Benefits of the new approach include better mass balance and more accurate tracking of the location of the wet/dry interface, compared with the current wetting and drying algorithm.Copyright © 2013 John Wiley & Sons, Ltd.

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Discrete Fluxes and Mass Balance in Finite Elements

Cited by 42 publications

References 7 publications

In search of a consistent and conservative mass flux for the GWCE

In search of a consistent and conservative mass flux for the GWCE

Locally conservative groundwater flow in the continuous Galerkin method using 3‐D prismatic patches

Implementation and analysis of a partial‐element wetting and drying framework for generalized wave continuity equation‐based hydrodynamic models

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