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 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

Models of non-Boussinesq lock-exchange flow

2011 ◽  
Vol 675 ◽  
pp. 1-26 ◽  
Author(s):  
R. ROTUNNO ◽  
J. B. KLEMP ◽  
G. H. BRYAN ◽  
D. J. MURAKI
Keyword(s):  
Free Boundary ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Water System ◽  
Analytic Solutions ◽  
Analytical Models ◽  
Navier Stokes ◽  
Exchange Flow

Nearly all analytical models of lock-exchange flow are based on the shallow-water approximation. Since the latter approximation fails at the leading edges of the mutually intruding fluids of lock-exchange flow, solutions to the shallow-water equations can be obtained only through the specification of front conditions. In the present paper, analytic solutions to the shallow-water equations for non-Boussinesq lock-exchange flow are given for front conditions deriving from free-boundary arguments. Analytic solutions are also derived for other proposed front conditions – conditions which appear to the shallow-water system as forced boundary conditions. Both solutions to the shallow-water equations are compared with the numerical solutions of the Navier–Stokes equations and a mixture of successes and failures is recorded. The apparent success of some aspects of the forced solutions of the shallow-water equations, together with the fact that in a real fluid the density interface is a free boundary, shows the need for an improved theory of lock-exchange flow taking into account non-hydrostatic effects for density interfaces intersecting rigid boundaries.

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.

scholarly journals Lattice Boltzmann method for 2D flows in curvilinear coordinates

2012 ◽  
Vol 14 (3) ◽  
pp. 772-783 ◽  
Author(s):  
Ljubomir Budinski
Keyword(s):  
Shallow Water ◽  
Lattice Boltzmann ◽  
Shallow Water Equations ◽  
Stokes Equations ◽  
Complex Geometry ◽  
Standard Form ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Equilibrium Distribution Function ◽  
Rectangular Lattice

In order to improve efficiency and accuracy, while maintaining an ease of modeling flows with the lattice Boltzmann approach in domains having complex geometry, a method for modeling equations of 2D flow in curvilinear coordinates has been developed. Both the transformed shallow water equations and the transformed 2D Navier-Stokes equations in the horizontal plane were synchronized with the equilibrium distribution function and the force term in the rectangular lattice. Since the solution of these equations takes place in the classical rectangular lattice environment, boundary conditions are modeled in the standard form of already existing simple methods (bounce-back), not requiring any additional functions. Owing to this and to the fact that the proposed method ensures a more accurate fitting of equations, even to domains of interest having complex geometry, the accuracy of solution is significantly increased, while the simplicity of the standard lattice Boltzmann approach is maintained. For the shallow water equations transformed in curvilinear coordinates, the proposed procedure is verified in three different hydraulic problems, all characterized by complex geometry.

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

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.

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