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

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. © 2017 World Scientific Publishing Company.