The solution of the dam-break problem in the Porous Shallow water Equations

2018 ◽  
Vol 114 ◽  
pp. 83-101 ◽  
Author(s):  
Luca Cozzolino ◽  
Veronica Pepe ◽  
Luigi Cimorelli ◽  
Andrea D'Aniello ◽  
Renata Della Morte ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Dam Break

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

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.

Dam-break computations by a finite volume on dry regions

2021 ◽  
Author(s):  
Farid Boushaba ◽  
Salah Daoudi ◽  
Ahmed Yachouti ◽  
Youssef Regad
Keyword(s):  
Finite Elements ◽  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Equation Model ◽  
Second Order ◽  
Dam Break ◽  
Conservative Form ◽  
Volume Method

Abstract This paper presents numerical solvers, based on the finite volume method. This scheme solves dam break problems on the dry bottom in 2D configuration. The difficulty of the simulation of this type of problem lies in the propagation of shocks on the dry bottom. The equation model used is the shallow water equations written in conservative form. The scheme used is second order in space and time. The method is modified to treat dry bottoms. The validity of the method is demonstrated over the dam break example. A comparison with finite elements shows the weakness and robustness of each method.

scholarly journals Discrete mixed subdomain least squares (DMSLS) meshless method with collocation points for modeling dam-break induced flows

2016 ◽  
Vol 18 (4) ◽  
pp. 702-723 ◽  
Author(s):  
Babak Fazli Malidareh ◽  
Seyed Abbas Hosseini ◽  
Ebrahim Jabbari
Keyword(s):  
Boundary Conditions ◽  
Least Squares ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Meshless Method ◽  
Dam Break ◽  
Collocation Points ◽  
Interior Domain ◽  
Bed Slope ◽  
Squared Residuals

This paper presents a new meshless numerical scheme to overcome the problem of shock waves and to apply boundary conditions in cases of dam-break flows in channels with constant and variable widths. The numerical program solves shallow water equations based on the discrete mixed subdomain least squares (DMSLS) meshless method with collocation points. The DMSLS meshless method is based on the minimization of a least squares functional defined as the weighted summation of the squared residuals of the governing equations over the entire domain and requiring the summation of residual function to be zero at collocation points in boundary subdomains. The collocated discrete subdomain meshless method is applied on the boundary, whereas the collocated discrete least squares meshless technique is applied to the interior domain. The meshless scheme extends for dam-break formulation of shallow water equations. The model is verified by comparing computed results with analytical and experimental data for constant and varying width channels. The developed model is also used to study one-dimensional dam-break problems involving different flow situations by considering changes to the channel width, a bumpy channel with various downstream boundary conditions, and the effects of bed friction and bed slope as source terms on wave propagation. The accuracy of the results is acceptable.

A TVD discretization method for shallow water equations: Numerical simulations of tailing dam break

2017 ◽  
Vol 08 (03) ◽  
pp. 1850001 ◽  
Author(s):  
Chen Luo ◽  
Ke Xu ◽  
Yunsheng Zhao
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Stokes Equations ◽  
Evolutionary Process ◽  
Scientific Basis ◽  
Dam Break ◽  
Tailings Dam ◽  
Dam Breaks ◽  
Tailings Sand ◽  
Downstream Area

In view of the disastrous consequences of tailings dam break and its unique evolutionary process in complex areas, this paper constructs two-dimensional shallow water equations, rheological equations and mathematical models of tailings sand flows on the basis of Navier–Stokes equations (N–S equations). It performs total variation diminishing (TVD) discretization on these equations, develops forward simulation programs in MATLAB2016 and conducts numerical analyses on three kinds of dam breaks (ideal dam break, asymmetric dam break and dam break with obstacles in the downstream area). The results show that TVD discretization is effective in capturing shock waves. According to the analysis on consequences of Huangmailing Tailings Dam break, the author obtains the maximum distance of tailings sand flow, the flow rate of tailings and the time that tailings reach destinations in the downstream area, thereby providing scientific basis for disaster analyses on similar tailings dam breaks and supplying technical support for emergency rescues after disasters.

scholarly journals Deficiency of finite difference methods for capturing shock waves and wave propagation over uneven bottom seabed

2018 ◽  
Vol 7 (3.28) ◽  
pp. 97
Author(s):  
Mohammad Fadhli Ahmad ◽  
Mohd Sofiyan Suliman ◽  
. .
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Source Term ◽  
Finite Difference Methods ◽  
Dam Break ◽  
Numerical Schemes ◽  
Inaccurate Information ◽  
Uneven Bottom

The implementation of finite difference method is used to solve shallow water equations under the extreme conditions. The cases such as dam break and wave propagation over uneven bottom seabed are selected to test the ordinary schemes of Lax-Friederichs and Lax-Wendroff numerical schemes. The test cases include the source term for wave propagation and exclude the source term for dam break. The main aim of this paper is to revisit the application of Lax-Friederichs and Lax-Wendroff numerical schemes at simulating dam break and wave propagation over uneven bottom seabed. For the case of the dam break, the two steps of Lax-Friederichs scheme produce non-oscillation numerical results, however, suffering from some of dissipation. Moreover, the two steps of Lax-Wendroff scheme suffers a very bad oscillation. It seems that these numerical schemes cannot solve the problem at discontinuities which leads to oscillation and dissipation. For wave propagation case, those numerical schemes produce inaccurate information of free surface and velocity due to the uneven seabed profile. Therefore, finite difference is unable to model shallow water equations under uneven bottom seabed with high accuracy compared to the analytical solution.  

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