Aspects of nonlinear simulations using shallow-water models based on the wave continuity equation

Kolar, Randall L.; Westerink, Joannes J.; Cantekin, M. E.; Blain, Cheryl Ann

doi:10.1016/0045-7930(94)90017-5

Cited by 132 publications

(101 citation statements)

References 20 publications

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“…α 1 u n+1 +α 0 u n +α −1 u n−1 ∆t + u n+1 · ∇u n+1 + c b u n+1 − ν∇ · ∇u n+1 = −∇h n+1 − ∇p n+1 + κ∇η n+1 + c s V n+1 − C n+1 (5) where both u and h are unknowns at time step n + 1. For the first order time accurate scheme, α 1 = 1.0, α 0 = −1.0 and α −1 = 0.0 and for second order time accurate scheme α 1 = 1.5, α 0 = −2.0 and α −1 = 0.5.…”

Section: Camel Model Approachmentioning

confidence: 99%

“…Figure 1 demonstrates the terminology used here in CaMEL to describe H , h , and Z . Details about the wind stress, bottom friction, tidal forcing, and Coriolis terms can be found in [2][3][4][5][6]. Problem Description (to be used for CaMEL only; consult ADCIRC Theory Guide [7] for ADCIRC description).…”

Section: Introductionmentioning

confidence: 99%

“…Typically storm surge models are used to simulate the storm surge by solving shallow water equations (SWEs). The momentum balance includes acceleration, wind stress, atmospheric pressure, tidal effects, Coriolis acceleration due to planetary rotation, friction drag at the sea floor, lateral mixing, wave-current interactions, and other potential forces and accelerations [1][2][3][4][5][6]. One must mathematically formulate the physical phenomena accurately and solve the resulting equations numerically with efficient algorithms.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Camel Model Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CaMEL and ADCIRC Storm Surge Models—A Comparative Study

Akbar

Luettich

Fleming³

et al. 2017

JMSE

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show abstract

“…Oahu ADCIRC solves a variant of the two-dimensional, depth-integrated (2DDI) shallow-water equations for water levels and the 2DDI momentum equations for currents (Kolar et al 1994, Luettich and Westerink 2004, Dawson et al 2006. ADCIRC was applied with a 1 sec timestep.…”

Section: Kauaimentioning

confidence: 99%

HAKOU v3: SWIMS Hurricane Inundation Fast Forecasting Tool for Hawaii

Smith¹,

Anderson²,

Taflanidis³

et al. 2012

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“…Two methods of mitigating the errors are presented in Kolar et al [11]. In the first, it is shown that if , the numerical parameter in the generalized wave continuity equation, is increased so that its value is one or two orders of magnitude larger than the bottom friction, then mass conservation is greatly improved.…”

Section: Introductionmentioning

confidence: 99%

Normal Flow Boundary Conditions in Shallow Water Models — Influence on Mass Conservation and Accuracy

Kolar¹,

Gray²,

Westerink³

1994

Computational Methods in Water Resources X

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Finite element solution of the shallow water wave equations has found increasing use by researchers and practitioners in the modeling of oceans and coastal areas. Wave equation models, most of which use equal-order, C 0 interpolants for both the velocity and the surface elevation, successfully eliminate spurious oscillation modes without resorting to artificial or numerical damping. An important question for both primitive equation and wave equation models is the interpretation of boundary conditions. Analysis of the characteristics of the governing equations shows that a single condition at each boundary is sufficient. Yet there is not a consensus in the literature as to what that boundary condition must be or how it should be implemented in a finite element code. Traditionally (partly because of limited data) surface elevation is specified at open ocean boundaries while the normal flux is specified as zero at land boundaries. In most finite element wave equation models, both of these boundary conditions are implemented as essential conditions. Our recent work focuses on alternate ways to numerically implement normal flow boundary conditions with an eye toward improving the mass-conserving properties of wave equation models. In particular, we have found that treating normal fluxes as natural conditions with the flux interpreted as external to the computational domain results in a mass conservative scheme for all parameter values. Use of generalized functions in the finite element formulation shows this is a natural interpretation. A series of twodimensional experiments demonstrates that this interpretation also improves the accuracy of primitive equation models by eliminating some of the spurious oscillation modes. BACKGROUND

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Aspects of nonlinear simulations using shallow-water models based on the wave continuity equation

Cited by 132 publications

References 20 publications

CaMEL and ADCIRC Storm Surge Models—A Comparative Study

CaMEL and ADCIRC Storm Surge Models—A Comparative Study

HAKOU v3: SWIMS Hurricane Inundation Fast Forecasting Tool for Hawaii

Normal Flow Boundary Conditions in Shallow Water Models — Influence on Mass Conservation and Accuracy

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