Continuous, discontinuous and coupled discontinuous–continuous Galerkin finite element methods for the shallow water equations

Dawson, Clint; Westerink, Joannes J.; Feyen, Jesse; Pothina, Dharhas

doi:10.1002/fld.1156

Cited by 96 publications

(59 citation statements)

References 49 publications

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“…The cyclonic wind data were derived from the Holland formulation (Holland, 1980) using the best track estimate of Hudhud obtained from the Joint Typhoon Warning Center database. The hydrodynamic depth-averaged model AD-CIRC applies the continuous Galerkin finite-element method to solve shallow water equations for water levels and vertically integrated momentum equations for velocity (Kolar et al, 1994;Atkinson et al, 2004;Luettich and Westerink, 2004;Dawson et al, 2006;Westerink et al, 2008;Kubatko et al, 2009;Tanaka et al, 2011). The model utilizes an unstructured mesh and allows for refinement in areas where the solution gradients are the highest.…”

Section: Modelling Systemmentioning

confidence: 99%

Wave–current interaction during Hudhud cyclone in the Bay of Bengal

Volvaiker¹,

Vethamony²,

Antony³

et al. 2017

Nat. Hazards Earth Syst. Sci.

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Abstract. The present work describes the interaction between waves and currents utilizing a coupled ADCIRC+SWAN model for the very severe cyclonic storm Hudhud, which made landfall at Visakhapatnam on the east coast of India in October 2014. Model-computed wave and surge heights were validated with measurements near the landfall point. The Holland model reproduced the maximum wind speed of ≈ 54 m s −1 with the minimum pressure of 950 hPa. The modelled maximum surge of 1.2 m matches with the maximum surge of 1.4 m measured off Visakhapatnam. The two-way coupling with SWAN showed that waves contributed ≈ 0.25 m to the total water level during the Hudhud event. At the landfall point near Visakhapatnam, the East India Coastal Current speed increased from 0.5 to 1.8 m s −1 for a short duration (≈ 6 h) with net flow towards the south, and thereafter reversed towards the north. An increase of ≈ 0.2 m in H s was observed with the inclusion of model currents. It was also observed that when waves travelled perpendicular to the coast after crossing the shelf area, with current towards the southwest, wave heights were reduced due to wave-current interaction; however, an increase in wave height was observed on the left side of the track, when waves and currents opposed each other.

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Section: Modelling Systemmentioning

confidence: 99%

Wave–current interaction during Hudhud cyclone in the Bay of Bengal

Volvaiker¹,

Vethamony²,

Antony³

et al. 2017

Nat. Hazards Earth Syst. Sci.

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“…It was originally developed by Luettich et al [2] and Luettich and Westerink [7] and subsequently improved by many researchers [9][10][11][12][13][14]. In ADCIRC, the SWEs are formulated using the traditional hydrostatic pressure and Boussinesq approximations and have been discretized in space using the Galerkin finite element method and in time using the finite difference method.…”

Section: Introductionmentioning

confidence: 99%

CaMEL and ADCIRC Storm Surge Models—A Comparative Study

Akbar

Luettich

Fleming³

et al. 2017

JMSE

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Abstract:The Computation and Modeling Engineering Laboratory (CaMEL), an implicit solver-based storm surge model, has been extended for use on high performance computing platforms. An MPI (Message Passing Interface) based parallel version of CaMEL has been developed from the previously existing serial version. CaMEL uses hybrid finite element and finite volume techniques to solve shallow water conservation equations in either a Cartesian or a spherical coordinate system and includes hurricane-induced wind stress and pressure, bottom friction, the Coriolis effect, and tidal forcing. Both semi-implicit and fully-implicit time stepping formulations are available. Once the parallel implementation is properly validated, CaMEL is evaluated against ADCIRC, an established storm surge model, using a hindcast of storm surge due to Hurricane Katrina. Observed high water marks are used to verify that both models have comparable accuracy. The effects of time step on the stability and accuracy of the models are investigated and indicate that the semi-and fully-implicit solvers in CaMEL allow the use of larger timesteps than ADCIRC's explicit and semi-implicit solvers. However, ADCIRC outperforms CaMEL in parallel scalability and execution wall clock times. Wall times of CaMEL improve significantly when the largest stable time step sizes are used in respective models, although ADCIRC still is faster.Keywords: shallow water equation; storm surge; parallel model; hybrid finite volume and finite element method; implicit matrix-free solver; spherical coordinate system

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“…Significant progress in the application of DG methods to the SWE has been achieved in the last few years [15,16,17,18,19,20,21,22,23,24,25]. However, two issues relevant in many applications, namely preserving steady-states at rest with variable bathymetry and properly handling flooding and drying, have not been addressed in previous work, with the exception of [17] where a moving mesh was used to deal with dry areas in a one-dimensional setting; the extension to two space dimensions does not seem to be straightforward.…”

Section: Introductionmentioning

confidence: 99%

A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying

Ern

Piperno

Djadel

2007

Numerical Methods in Fluids

114

110

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SUMMARYWe build and analyze a Runge-Kutta Discontinuous Galerkin method to approximate the one-and two-dimensional Shallow-Water Equations. We introduce a flux modification technique to derive a wellbalanced scheme preserving steady-states at rest with variable bathymetry and a slope modification technique to deal satisfactorily with flooding and drying. Numerical results illustrating the performance of the proposed scheme are presented.

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Continuous, discontinuous and coupled discontinuous–continuous Galerkin finite element methods for the shallow water equations

Cited by 96 publications

References 49 publications

Wave–current interaction during Hudhud cyclone in the Bay of Bengal

Wave–current interaction during Hudhud cyclone in the Bay of Bengal

CaMEL and ADCIRC Storm Surge Models—A Comparative Study

A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying

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