Dora algorithm in the calculation of shallow water wave equation

Abstract

With the development of global water conservancy facilities, flood prevention, water environment, shipping and other large-scale engineering technologies, the shallow water problem has become a serious problem in various countries. One-dimensional shallow water wave model and two-dimensional shallow water wave model can only be applied to solve large engineering problems, due to the limitations of computer technology and data technology. Dora algorithm is a relatively new algorithm, mainly to solve the dynamic equations, which is relatively more physical significance, because it is less limited and more stable. Compared with traditional algorithms, Dora's algorithm is that it can solve the problem of initial water depth is zero. In the numerical simulation of dam rupture, Dora algorithm does not have numerical shocks in intermittent waves, which is enough to show that the algorithm can effectively simulate the movement of dam break waves. Dora's algorithm is absolutely stable. The Dora algorithm uses either the block-wise operator method or the step-wise method. The Dora algorithm solves the problem of water depth being zero when solving the St. Vennan equation. No special treatment is required to simulate flood movements in the mainstream, such as dam breaks. The paper mainly focuses on the Dora algorithm and the advantage comparison of the algorithm and the traditional algorithm. The final results show that the algorithm can satisfy the one-dimensional shallow water wave equation and solve the situation without water depth. Whether it is one-dimensional or two-dimensional shallow water wave models, they are able to well simulate the long straight open channel constant flow for the curve constant flow. For the water level, the simulation results of the one-dimensional shallow water wave equation are not accurate, and the two-dimensional shallow water wave model can be closer to the experimental value of the dam break.