Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation

作     者：Feng-peng Bai Zhong-hua Yang Wu-gang Zhou 

作者机构：State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University 

出 版 物：《Water Science and Engineering》 (水科学与水工程（英文版）)

年 卷 期：2018年第11卷第1期

页      面：68-74页

核心收录：

学科分类：08[工学] 081501[工学-水文学及水资源] 0815[工学-水利工程] 

基　　金：supported by the National Natural Science Foundation of China(Grants No.51679170 51379157 and 51439007) 

主　　题：Dam-break flow TVD MUSCL-Hancock scheme Slope limiter Numerical accuracy Spurious oscillation 

摘      要：A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.