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

Massey, Thomas C.; Blain, Cheryl Ann

doi:10.1016/j.cma.2005.02.013

Cited by 11 publications

(3 citation statements)

References 17 publications

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“…Three different metrics were utilized for the assessment of mass balance performance of the new and old algorithms for the test cases. These metrics consist of instantaneous global mass balance, instantaneous local (elemental) mass balance, and average elemental mass balance over one forcing cycle using a finite volume‐type mass balance approach, for example, . Note that the accumulation terms were multiplied by η for partially wet elements under the new algorithm for all mass balance calculations presented in this document.…”

Section: Testingmentioning

confidence: 99%

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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Section: Testingmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…Despite these encouraging applications and the ongoing research involved in improving the method, it remains plagued by two caveats. GWCEbased models are subject to advective instabilities (Kolar et al 1994) and the GWCE form sacrifices the primitive continuity equation; thus, the primitive form is no longer satisfied in a discrete sense, which implies continuity (or mass) imbalances (Dawson et al 2006;Massey and Blain 2006), rendering the method less suitable for coupling with transport equations, let alone for long time integrations (more than several years) in which conservation is crucial.…”

Section: Introductionmentioning

confidence: 99%

Tracer Conservation for Three-Dimensional, Finite-Element, Free-Surface, Ocean Modeling on Moving Prismatic Meshes

White

Legat

Deleersnijder

2008

Monthly Weather Review

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Large-scale free-surface ocean models designed to run over climatic time scales are required to globally conserve the volume and any tracer up to machine precision. In addition, local consistency is critical and requires that the discrete tracer equation preserve constants in a closed domain and if there is no tracer source or sink. Local consistency, together with monotonicity, will ensure that no spurious tracer extrema occur. A three-dimensional, finite-element, shallow-water model is presented. The mesh is unstructured in the horizontal, extruded in the third dimension, and made up of multiple layers of prisms. In addition, the mesh is allowed to move in the vertical and adapts itself to the free-surface motions. It is shown that achieving consistency requires a discrete compatibility between the tracer and continuity equations. In addition, to ensure global tracer conservation in a consistent way, a discrete compatibility between the tracer, continuity, and free-surface elevation equations must be fulfilled. It is suggested that this compatibility constraint, together with the use of a numerically stable scheme, severely restricts the choice of usable finite-element spatial discretizations. A consistent and conservative time-stepping algorithm is described for which a unique time step is used. It is suggested that future research is needed in order to design a consistent and conservative split-explicit algorithm. Some illustrative test cases are presented in which the method is shown to satisfy all conservation properties. A few experiments in which consistency breaks down are carried out, and the consequences of this breakdown process are investigated.

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“…The wave-equation formulation was first proposed by Lynch and Gray, [19] to correctly handle the wave propagation issues. This wave equation formulation, on the other hand, appears to have several issues, such as advective instabilities and mass conservation [ [20] , [21] ]. This problem with the first option regarding the formulation of the wave equation, led to further research on the second option, determining the correct discretization using finite element method to solve primitive equations without using modified formulations or stabilization.…”

Section: Introductionmentioning

confidence: 99%

A novel technique for implementing the finite element method in a shallow water equation

Swastika,

Fakhruddin,

Al Hazmy

et al. 2023

MethodsX

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

Cited by 11 publications

References 17 publications

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

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

Tracer Conservation for Three-Dimensional, Finite-Element, Free-Surface, Ocean Modeling on Moving Prismatic Meshes

A novel technique for implementing the finite element method in a shallow water equation

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