scholarly journals Momentum Conservative Schemes for Shallow Water Flows

2014 ◽  
Vol 4 (2) ◽  
pp. 152-165 ◽  
Author(s):  
S. R. Pudjaprasetya ◽  
I. Magdalena
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Dam Break ◽  
Staggered Grid ◽  
Conservative Scheme ◽  
Shallow Water Flows ◽  
Advection Term ◽  
Conservative Approximation ◽  
Run Up ◽  
Good Agreement

AbstractWe discuss the implementation of the finite volume method on a staggered grid to solve the full shallow water equations with a conservative approximation for the advection term. Stelling & Duinmeijer [15] noted that the advection approximation may be energy-head or momentum conservative, and if suitable which of these to implement depends upon the particular flow being considered. The momentum conservative scheme pursued here is shown to be suitable for 1D problems such as transcritical flow with a shock and dam break over a rectangular bed, and we also found that our simulation of dam break over a dry sloping bed is in good agreement with the exact solution. Further, the results obtained using the generalised momentum conservative approximation for 2D shallow water equations to simulate wave run up on a conical island are in good agreement with benchmark experimental data.

scholarly journals Momentum Conservative Schemes for Shallow Water Flows

2018 ◽  
Author(s):  
Sri Redjeki Pudjaprasetya ◽  
Ikha Magdalena
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Dam Break ◽  
Shallow Water Flows ◽  
Advection Term ◽  
Generalized Momentum ◽  
Conservative Approximation ◽  
Run Up ◽  
Volume Method ◽  
Good Agreement

We discuss the implementation of the finite volume method on a staggeredgrid to solve the full shallow water equations with a conservative approximation forthe advection term. Stelling & Duinmeijer [15] noted that the advection approximationmay be energy-head or momentum conservative, and if suitable which of these toimplement depends upon the particular flow being considered. The momentum conservativescheme pursued here is shown to be suitable for 1D problems such as transcriticalflow with a shock and dam break over a rectangular bed, and we also found that oursimulation of dam break over a dry sloping bed is in good agreement with the exactsolution. Further, the results obtained using the generalized momentum conservativeapproximation for 2D shallow water equations to simulate wave run up on a conicalisland are in good agreement with benchmark experimental data.

scholarly journals Staggered Conservative Scheme for 2-Dimensional Shallow Water Flows

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 149
Author(s):  
Novry Erwina ◽  
Didit Adytia ◽  
Sri Redjeki Pudjaprasetya ◽  
Toni Nuryaman
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Solitary Wave ◽  
Shallow Water ◽  
Threshold Value ◽  
Staggered Grid ◽  
Conservative Scheme ◽  
Shallow Water Flows ◽  
Run Up ◽  
N Wave

Simulating discontinuous phenomena such as shock waves and wave breaking during wave propagation and run-up has been a challenging task for wave modeller. This requires a robust, accurate, and efficient numerical implementation. In this paper, we propose a two-dimensional numerical model for simulating wave propagation and run-up in shallow areas. We implemented numerically the 2-dimensional Shallow Water Equations (SWE) on a staggered grid by applying the momentum conserving approximation in the advection terms. The numerical model is named MCS-2d. For simulations of wet–dry phenomena and wave run-up, a method called thin layer is used, which is essentially a calculation of the momentum deactivated in dry areas, i.e., locations where the water thickness is less than the specified threshold value. Efficiency and robustness of the scheme are demonstrated by simulations of various benchmark shallow flow tests, including those with complex bathymetry and wave run-up. The accuracy of the scheme in the calculation of the moving shoreline was validated using the analytical solutions of Thacker 1981, N-wave by Carrier et al., 2003, and solitary wave in a sloping bay by Zelt 1986. Laboratory benchmarking was performed by simulation of a solitary wave run-up on a conical island, as well as a simulation of the Monai Valley case. Here, the embedded-influxing method is used to generate an appropriate wave influx for these simulations. Simulation results were compared favorably to the analytical and experimental data. Good agreement was reached with regard to wave signals and the calculation of moving shoreline. These observations suggest that the MCS method is appropriate for simulations of varying shallow water flow.

scholarly journals Analytical Solution of Shallow Water Equations for Ideal Dam-Break Flood along a Wet-Bed Slope

2020 ◽  
Vol 146 (2) ◽  
pp. 06019020 ◽  
Author(s):  
Bo Wang ◽  
Yunliang Chen ◽  
Yong Peng ◽  
Jianmin Zhang ◽  
Yakun Guo
Keyword(s):  
Analytical Solution ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Dam Break ◽  
Bed Slope

A Two-Dimensional Numerical Model for Shallow Water Flows over Variable Topographies

2014 ◽  
Vol 580-583 ◽  
pp. 1793-1798
Author(s):  
Biao Lv ◽  
Shao Xi Li
Keyword(s):  
Numerical Model ◽  
Shallow Water ◽  
Source Term ◽  
Unstructured Grids ◽  
Riemann Solver ◽  
Two Dimensional ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Bed Slope ◽  
Good Agreement

Based on well-balanced Roe’s approximate Riemann solver, a numerical model is developed for the unsteady, two-dimensional, shallow water flow with variable topographies. In this model, an efficient methods are applied to treat the source terms and to satisfy the compatibility condition on unstructured grids. In the method, different components of the bed slope source term are considered separately and the compatible discretization of the components is presented. The newly developed model is verified against analytical solutions and measured date, with good agreement.

scholarly journals Construction, verification of a software for the 2D dam-break flow and some its applications

2007 ◽  
Vol 29 (4) ◽  
pp. 539-550
Author(s):  
Hoang Van Lai ◽  
Nguyen Thanh Don
Keyword(s):  
Shallow Water ◽  
Numerical Method ◽  
Shallow Water Equations ◽  
Theoretical Basis ◽  
Dam Break ◽  
River Delta ◽  
Red River ◽  
Test Cases ◽  
Red River Delta ◽  
Dam Break Flow

In this paper the numerical method for the shallow water equations is studied. The paper consists of 3 sections. In the section 1 the theoretical basis and software IMECI-L2DBREAK for simulation of the 2D dam-break or dyke-break flows is outlined. In the section 2 some results in verification of the IMECH_2DBREAK by the test cases proposed in the big European Hydraulics Laboratories are shown. In the last section some applications of IMECH_2DBREAK for the inundation problem in the Red river delta in the Northern of Vietnam are presented.

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