The improved space-time conservation element and solution element scheme for two-dimensional dam-break flow simulation

摘要

A new numerical scheme, namely space-time conservation element and solution element (CE/SE) method, has been used for the solution of the two-dimensional (2D) dam-break problem. Distinguishing from the well-established traditional numerical methods (such as characteristics, finite difference, finite element, and finite-volume methods), the CE/SE scheme has many non-traditional features in both concept and methodology: space and time are treated in a unified way, which is the most important characteristic for the CE/SE method; the CEs and SEs are introduced, both local and global flux conservations in space and time rather than space only are enforced; an explicit scheme with a stagger grid is adopted. Furthermore, this scheme is robust and easy to implement. In this paper, an improved CE/SE scheme is extended to solve the 2D shallow water equations with the source terms, which usually plays a critical role in dam-break flows. To demonstrate the accuracy, robustness and efficiency of the improved CE/SE method, both 1D and 2D dam-break problems are simulated numerically, and the results are consistent with either the analytical solutions or experimental results.