Volume 11 Issue 1
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Feng-peng Bai, Zhong-hua Yang, Wu-gang Zhou. 2018: Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation. Water Science and Engineering, 11(1): 68-74. doi: 10.1016/j.wse.2017.09.004
Citation: Feng-peng Bai, Zhong-hua Yang, Wu-gang Zhou. 2018: Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation. Water Science and Engineering, 11(1): 68-74. doi: 10.1016/j.wse.2017.09.004
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Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation

doi: 10.1016/j.wse.2017.09.004

  • State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China

Funds:  This work was supported by the National Natural Science Foundation of China (Grants No. 51679170, 51379157, and 51439007).
  • Received Date: 2017-01-14
  • Rev Recd Date: 2017-03-13
    Abstract
  • 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.

     

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