|Water Science and Engineering 2018, 11(1) 68-74 DOI: https://doi.org/10.1016/j.wse.2017.09.004 ISSN: 1674-2370 CN: 32-1785/TV|
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Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation
Feng-peng Bai, Zhong-hua Yang*, Wu-gang Zhou
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
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.
|Keywords： Dam-break flow TVD MUSCL-Hancock scheme Slope limiter Numerical accuracy Spurious oscillation|
|Received 2017-01-14 Revised 2017-03-13 Online: 2018-01-31|
This work was supported by the National Natural Science Foundation of China (Grants No. 51679170, 51379157, and 51439007).
|Corresponding Authors: firstname.lastname@example.org (Zhong-hua Yang)|
|About author: email@example.com (Zhong-hua Yang)|
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