scholarly journals Simulation of Ocean Circulation of Dongsha Water Using Non-Hydrostatic Shallow-Water Model

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2832 ◽  
Author(s):  
Shin-Jye Liang ◽  
Chih-Chieh Young ◽  
Chi Dai ◽  
Nan-Jing Wu ◽  
Tai-Wen Hsu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Free Surface ◽  
Hydrostatic Pressure ◽  
Velocity Field ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Shallow Water Model

A two-dimensional non-hydrostatic shallow-water model for weakly dispersive waves is developed using the least-squares finite-element method. The model is based on the depth-averaged, nonlinear and non-hydrostatic shallow-water equations. The non-hydrostatic shallow-water equations are solved with the semi-implicit (predictor-corrector) method and least-squares finite-element method. In the predictor step, hydrostatic pressure at the previous step is used as an initial guess and an intermediate velocity field is calculated. In the corrector step, a Poisson equation for the non-hydrostatic pressure is solved and the final velocity and free-surface elevation is corrected for the new time step. The non-hydrostatic shallow-water model is verified and applied to both wave and flow driven fluid flows, including solitary wave propagation in a channel, progressive sinusoidal waves propagation over a submerged bar, von Karmann vortex street, and ocean circulations of Dongsha Atolls. It is found hydrostatic shallow-water model is efficient and accurate for shallow water flows. Non-hydrostatic shallow-water model requires 1.5 to 3.0 more cpu time than hydrostatic shallow-water model for the same simulation. Model simulations reveal that non-hydrostatic pressure gradients could affect the velocity field and free-surface significantly in case where nonlinearity and dispersion are important during the course of wave propagation.

On the necessity of non-hydrostatic pressure models for free surface flow over complex topography

2020 ◽  
Author(s):  
Isabel Echeverribar ◽  
Pilar Brufau ◽  
Pilar García-Navarro
Keyword(s):  
Free Surface ◽  
Hydrostatic Pressure ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Finite Volume Scheme ◽  
Complex Topography ◽  
Source Terms ◽  
Pressure Correction ◽  
Wide Range

<p><span><strong>There is a wide range of geophysical flows, such as flow in open channels and rivers, tsunami and flood modeling, that can be mathematically represented by the non-linear shallow water 1D equations involving hydrostatic pressure assumptions as an approximation of the Navier Stokes equations. In this context, special attention must be paid to bottom source terms integration and numerical corrections when dealing with wet/dry fronts or strong slopes in order to obtain physically-based solutions (Murillo and García-Navarro, 2010) in complex and realistic cases with irregular topography. However, although these numerical corrections have been developed in recent years achieving not only more robust models but also more accurate results, they still might find a limit when dealing with specific scenarios where vertical information or disspersive effects become crucial. This work presents a 1D shallow water model that introduces vertical information by means of a non-hydrostatic pressure correction when necessary. In particular, the pressure correction method (Hirsch, 2007) is applied to a 1D finite volume scheme for a rectification of the velocity field in free surface scenarios. It is solved by means of an implicit scheme, whereas the depth-integrated shallow water equations are solved using an explicit scheme. It is worth highlighting that it preserves all the advantages and numerical fixes aforementioned for the pure shallow water system. Computations with and without non-hydrostatic corrections are compared for the same cases to test the validity of the conventional hydrostatic pressure assumption at some scenarios involving complex topography.</strong></span></p><p><span>[1] J. Murillo and P. Garcia-Navarro, Weak solutions for partial differential equations with source terms: application to the shallow water equations, Journal of Computational Physics, vol. 229, iss. 11, pp. 4327-4368, 2010.</span></p><p><span>[2] C. Hirsch, Numerical Computation of Internal and External flows: The fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann, 2007.</span></p>

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

scholarly journals A FINITE ELEMENT METHOD FOR STORM SURGE AND TIDAL COMPUTATION

1984 ◽  
Vol 1 (19) ◽  
pp. 82 ◽  
Author(s):  
Y. Coeffe ◽  
S. Dal Secco ◽  
P. Esposito ◽  
B. Latteux
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shallow Water ◽  
Storm Surge ◽  
Incident Wave ◽  
Shallow Water Equations ◽  
Implicit Scheme ◽  
Wave Condition ◽  
Recent Developments ◽  
Element Method

The paper reports the current progress in developing a finite element method for the shallow water equations. Some recent developments as the implementation of a semi implicit scheme or the use of an incident wave condition are described. Different realistic applications are presented concerning tidal and storm surge simulations.

A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries

2000 ◽  
Vol 23 (4) ◽  
pp. 359-372 ◽  
Author(s):  
Mourad Heniche ◽  
Yves Secretan ◽  
Paul Boudreau ◽  
Michel Leclerc
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Dimensional Finite Element

scholarly journals Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation

2020 ◽  
Vol 28 (2) ◽  
pp. 93-114
Author(s):  
Stelian Ion ◽  
Stefan-Gicu Cruceanu ◽  
Dorin Marinescu
Keyword(s):  
Initial Data ◽  
Shallow Water ◽  
Global Solution ◽  
Riemann Problem ◽  
Hyperbolic System ◽  
Shallow Water Equations ◽  
Local Existence ◽  
Water Model ◽  
Constructive Approach ◽  
Shallow Water Model

AbstractWe investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be “small enough”). One di culty for the extended solution arises from the double degeneracy of the hyperbolic system describing the model. Another di culty is given by the fact that the construction of the solution assumes solving an equation which has no global solution. Finally, we present some cases to illustrate the existence and non-existence of the solution.

scholarly journals A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Alia Al-Ghosoun ◽  
Ashraf S. Osman ◽  
Mohammed Seaid
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Shallow Water ◽  
Finite Volume ◽  
Second Order ◽  
Static Deformation ◽  
Wave Runup ◽  
Content Type ◽  
Element Method

Purpose The purpose of this study is twofold: first, to derive a consistent model free-surface runup flow problems over deformable beds. The authors couple the nonlinear one-dimensional shallow water equations, including friction terms for the water free-surface and the two-dimensional second-order solid elastostatic equations for the bed deformation. Second, to develop a robust hybrid finite element/finite volume method for solving free-surface runup flow problems over deformable beds. The authors combine the finite volume for free-surface flows and the finite element method for bed elasticity. Design/methodology/approach The authors propose a new model for wave runup by static deformation on seabeds. The model consists of the depth-averaged shallow water system for the water free-surface coupled to the second-order elastostatic formulation for the bed deformation. At the interface between the water flow and the seabed, transfer conditions are implemented. Here, hydrostatic pressure and friction forces are considered for the elastostatic equations, whereas bathymetric forces are accounted for in the shallow water equations. As numerical solvers, the authors propose a well-balanced finite volume method for the flow system and a stabilized finite element method for elastostatics. Findings The developed coupled depth-averaged shallow water system and second-order solid elastostatic system is well suited for modeling wave runup by deformation on seabeds. The derived coupling conditions at the interface between the water flow and the bed topography resolve well the condition transfer between the two systems. The proposed hybrid finite volume element method is accurate and efficient for this class of models. The novel technique used for wet/dry treatment accurately captures the moving fronts in the computational domain without generating nonphysical oscillations. The presented numerical results demonstrate the high performance of the proposed methods. Originality/value Enhancing modeling and computations for wave runup problems is at an early stage in the literature, and it is a new and exciting area of research. To the best of our knowledge, solving wave runup problems by static deformation on seabeds using a hybrid finite volume element method is presented for the first time. The results of this research study, and the research methodologies, will have an important influence on a range of other scientists carrying out research in related fields.

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