Numerical model for the shallow water equations on a curvilinear grid with the preservation of the Bernoulli integral

A new horizontal two-dimensional mathematic scheme namely space-time Conservation Element and Solution Element (CE-SE) is introduced in this paper. The CE-SE method has some features which space and time are unified and treated on the same footing, both local and global flux are enforced conservation. The proposed model is applied to solve the 2-D shallow water equations in the triangular mesh, and tested by using the field data in Yangzi River. It shows that the hydraulics characters in natural rivers which are with complex boundaries and topography can be well simulated by using this new method.

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Simulation of Shallow Flows in Nonuniform Open Channels

Journal of Fluids Engineering ◽

10.1115/1.2829593 ◽

2008 ◽

Vol 130 (1) ◽

Cited By ~ 4

Author(s):

Qiuhua Liang

Keyword(s):

Numerical Model ◽

Shallow Water ◽

Shallow Water Equations ◽

Open Channels ◽

Immersed Boundary ◽

Source Terms ◽

Irregular Domain ◽

New Formulation ◽

Irregular Bed Topography ◽

Transcritical Flows

This paper presents a new formulation of the 2D shallow water equations, based on which a numerical model (referred to as NewChan) is developed for simulating complex flows in nonuniform open channels. The new shallow water equations mathematically balance the flux and source terms and can be directly applied to predict flows over irregular bed topography without any necessity for a special numerical treatment of source terms. The balanced governing equations are solved on uniform Cartesian grids using a finite-volume Godunov-type scheme, enabling automatic capture of transcritical flows. A high-order numerical scheme is achieved using a second-order Runge–Kutta integration method. A very simple immersed boundary approach is used to deal with an irregular domain geometry. This method can be easily implemented in a Cartesian model and does not have any influence on computational efficiency. The numerical model is validated against several benchmark tests. The computed results are compared with analytical solutions, previously published predictions, and experimental measurements and excellent agreements are achieved.

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A numerical model for simulation of near-shore waves and wave induced currents using the depth-averaged non-hydrostatic shallow water equations with an improvement of wave energy dissipation

Tạp chí Khoa học và Công nghệ Biển ◽

10.15625/1859-3097/20/2/15087 ◽

2020 ◽

Vol 20 (2) ◽

pp. 155-172

Author(s):

Phung Dang Hieu ◽

Phan Ngoc Vinh

Keyword(s):

Numerical Model ◽

Shallow Water ◽

Wave Height ◽

Shallow Water Equations ◽

Wave Breaking ◽

Water Model ◽

Height Distribution ◽

Time Duration ◽

Wave Energy Dissipation ◽

Near Shore

This study proposes a numerical model based on the depth-integrated non-hydrostatic shallow water equations with an improvement of wave breaking dissipation. Firstly, studies of parameter sensitivity were carried out using the proposed numerical model for simulation of wave breaking to understand the effects of the parameters of the breaking model on wave height distribution. The simulated results of wave height near the breaking point were very sensitive to the time duration parameter of wave breaking. The best value of the onset breaking parameter is around 0.3 for the non-hydrostatic shallow water model in the simulation of wave breaking. The numerical results agreed well with the published experimental data, which confirmed the applicability of the present model to the simulation of waves in near-shore areas.

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MAPPING TIDAL CURRENTS AND RESIDUAL CURRENTS BY USE OF COASTAL ACOUSTIC TOMOGRAPHY

Proceedings of International Conference "Managinag risks to coastal regions and communities in a changinag world" (EMECS'11 - SeaCoasts XXVI) ◽

10.31519/conferencearticle_5b1b94407213d3.12732916 ◽

2017 ◽

Author(s):

Xiao-Hua Zhu ◽

Ze-Nan Zhu ◽

Xinyu Guo ◽

...

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Mean Amplitude ◽

Momentum Equation ◽

Tidal Currents ◽

Acoustic Tomography ◽

Mean Values ◽

Residual Currents ◽

Water Depths ◽

Deep Area

A coastal acoustic tomography (CAT) experiment for mapping the tidal currents in the Zhitouyang Bay was successfully carried out with seven acoustic stations during July 12 to 13, 2009. The horizontal distributions of tidal current in the tomography domain are calculated by the inverse analysis in which the travel time differences for sound traveling reciprocally are used as data. Spatial mean amplitude ratios M2 : M4 : M6 are 1.00 : 0.15 : 0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, velocity amplitudes of M4 measured by CAT agree well with those of M4 predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area where water depths are larger than 60 m is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. Dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents.

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