Modelling coastal water waves using a depth-integrated, non-hydrostatic model with shock-capturing ability

Fang, Kezhao; Liu, Zhongbo; Zou, Zhili

doi:10.1080/00221686.2014.948503

Cited by 14 publications

(10 citation statements)

References 31 publications

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“…It represents the first application of a finite element based discretisation method for multi-layer non-hydrostatic modelling based upon the approach of Stelling and Zijlema (2003) in coastal and ocean domains. In the restricted case of depth-integrated applications (a single layer in our model) which has been adopted extensively for nonhydrostatic studies (Walters, 2005;Yamazaki et al, 2009;Wei and Jia, 2014;Fang et al, 2015), this work represents the first application of the discontinuous Galerkin finite element (DG-FE) method. More generally, we believe this work also represents one of the first demonstrations of a multi-layer approach combined with an unstructured mesh in the horizontal.…”

Section: And Thementioning

confidence: 99%

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Multi-layer non-hydrostatic free surface modelling using the discontinuous Galerkin method

2019

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A multi-layer non-hydrostatic version of the unstructured mesh, discontinuous Galerkin finite element based coastal ocean model, Thetis, is developed. This is accomplished using the PDE solver framework, Firedrake, which is used to automatically produce the code for the discretised model equations in a rapid and efficient manner. The motivation for this work is a need to accurately simulate dispersive nearshore free surface processes. In order to resolve both frequency dispersion and non-linear effects accurately, additional non-hydrostatic terms are included in the layer-integrated hydrostatic equations, producing a form similar to the layered non-linear shallow water equations, but with extra vertical velocities at the layer interfaces. An implementation process is adopted to easily handle the inter-layer connection, i.e. the governing equations are transformed into a depth-integrated system through the introduction of depth-averaged variables. The model is verified and validated through comparisons against several idealised and experimentally-based test cases. All the comparisons demonstrate good agreement, showing that the developed non-hydrostatic model has excellent capabilities in representing coastal wave phenomena including shoaling, refraction and diffraction of dispersive short waves, as well as propagation, run-up and inundation of non-linear tsunami waves.

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Section: And Thementioning

confidence: 99%

“…A sketch of the experimental set-up may be found in (Fang et al, 2015), along with details of the six transects along which free-surface elevations are recorded and compared against our numerical results.…”

Section: Wave Propagation Over An Elliptical Shoalmentioning

confidence: 99%

Multi-layer non-hydrostatic free surface modelling using the discontinuous Galerkin method

2019

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“…Summing all Eqs. (24) at the end of the CP problem, we get ( ) ( ) ). This means that the non-hydrostatic step does not affect the global mass balances.…”

Section: Model Properties Preservation Of the Local And Global Mass Bmentioning

confidence: 99%

“…22,23 Only a few non-hydrostatic models are equipped with this shock-capturing feature. 18,24,25 In the NLSWEs applications involving fast transitions between wet and dry surfaces, e.g., coastal flooding and run-up of tsunamis, an accurate modeling of wetting/drying (WD) processes plays an important role. Several WD numerical techniques have been proposed, [26][27][28] but generally these are affected by several drawbacks, e.g., the mass imbalance and the high computational costs due to additional relationships to include in the numerical procedure at the transition wet/dry surface.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2017

FMRIJ

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Due to the enormous damages and losses of human lives in the inundated regions, the simulation of the propagation of tsunamis in coastal areas has received an increasing interest of the researchers. We present a 2D depth-integrated, non-hydrostatic shallow waters solver to simulate the propagation of tsunamis, solitary waves and surges in coastal regions. We write the governing continuity and momentum equations in conservative form and discretize the domain with unstructured triangular Generalized Delaunay meshes. We apply a fractional-time-step procedure, where two problems (steps) are consecutively solved. In the first and in the second step, we hypothesize a hydrostatic and a non-hydrostatic distribution of the pressure, respectively. Several literature models, which solve the same set of equations, are based on a fractional-time-step procedure. In the hydrostatic step of these literature solvers, the flow field does not satisfy the depthintegrated continuity equation, since the momentum equations are solved independently of the continuity equation. In both steps of the proposed numerical scheme, the computed flow field satisfies the depth-integrated continuity equation discretized in each computational cell. This is obtained by solving together the governing equations, according to the different numerical procedures adopted in the steps of the algorithm. Wet/dry problems are implicitly embedded in the proposed numerical solver. We present several model applications where analytical or measured reference solutions are available. The computational effort required by the proposed procedure is investigated.

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“…Numerous shock-capturing procedures, in the framework of the Finite Volumes (FV), Finite Elements (FE) and Finite Differences (FD) schemes, have been proposed for the solution of the hydrostatic NLSWEs [22,23]. Only a few non-hydrostatic models are equipped with this shock-capturing feature [18,24,25].…”

Section: Introductionmentioning

confidence: 99%

Simulation of the Propagation of Tsunamis in Coastal Regions by a Two-Dimensional Non-Hydrostatic Shallow Water Solver

Aricò¹

2017

FMRIJ

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During the last years, great effort has been addressed by several authors to simulate the propagation of solitary waves/ tsunamis, tides or surges, due to the tremendous damages and losses of human lives in the inundated rural and residential areas. Tsunamis are sea waves usually generated by undersea landslides and earthquakes. They can be regarded as long/solitary waves with small amplitude and long wavelength, travelling with high speed over long distances. Approaching the coast, their amplitude increases, becoming potentially destructive. The propagation of tsunami in coastal regions can be studied by investigating the shoaling and breaking of solitary waves over inclined bottoms [1]. Chanson [2] asserted that the front of tsunamis over dry plains becomes a shock wave, and presented a similarity between the propagation of the tsunamis over dry coastal areas and the classical dam-break problems. Generally, 3D simulations of the processes described as above, e.g., by RANS models [3], or Smoothed Particle Hydrodynamics methods [4], or Volume of Fluids methods [5], require very high computational costs. For these reasons, a significant amount of literature based on depthintegrated equations has been published for simulations of long waves/tsunamis propagation. Generally, the two modeling approaches proposed in literature are the Boussinesq-Type Models (BTMs) and the Non-Hydrostatic Nonlinear Shallow Water Equations (NLSWEs) models.The classical formulation of the BTMs [6] involves weak nonlinearity and dispersion. High-order BTMs have been proposed to overcome these difficulties, but suffer from complex numerical discretization, which leads to high computational efforts [7,8]. Generally, the BTMs also suffer from the inclusion, in the governing equations, of extra terms, based on empirical considerations, introduced for the simulation of wave breaking with the associated energy dissipation, and wetting/drying transition [8].Hereafter, we call "hydrostatic NLSWEs" and "non-hydrostatic NLSWEs" (or "dynamic NLSWEs") respectively the NLSWEs with hydrostatic and non-hydrostatic (or dynamic) pressure distribution. Due to simplicity and accuracy, the hydrostatic AbstractDue to the enormous damages and losses of human lives in the inundated regions, the simulation of the propagation of tsunamis in coastal areas has received an increasing interest of the researchers. We present a 2D depth-integrated, nonhydrostatic shallow waters solver to simulate the propagation of tsunamis, solitary waves and surges in coastal regions. We write the governing continuity and momentum equations in conservative form and discretize the domain with unstructured triangular Generalized Delaunay meshes. We apply a fractionaltime-step procedure, where two problems (steps) are consecutively solved. In the first and in the second step, we hypothesize a hydrostatic and a non-hydrostatic distribution of the pressure, respectively. Several literature models, which solve the same set of equations, are based on a fractional-time-step procedure. In th...

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Modelling coastal water waves using a depth-integrated, non-hydrostatic model with shock-capturing ability

Cited by 14 publications

References 31 publications

Multi-layer non-hydrostatic free surface modelling using the discontinuous Galerkin method

Multi-layer non-hydrostatic free surface modelling using the discontinuous Galerkin method

Untitled

Simulation of the Propagation of Tsunamis in Coastal Regions by a Two-Dimensional Non-Hydrostatic Shallow Water Solver

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