Volume 8 Issue 3
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Article Navigation >  Water Science and Engineering  > 2015  >  8(3): 239-247
Jing Yin, Jia-wen Sun, Zi-feng Jiao. 2015: A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations. Water Science and Engineering, 8(3): 239-247. doi: 10.1016/j.wse.2015.06.003
Citation: Jing Yin, Jia-wen Sun, Zi-feng Jiao. 2015: A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations. Water Science and Engineering, 8(3): 239-247. doi: 10.1016/j.wse.2015.06.003
shu

A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations

doi: 10.1016/j.wse.2015.06.003

  • a National Marine Environment Monitoring Center, State Oceanic Administration, Dalian 116023, PR China

  • b State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, PR China

Funds:  This work was supported by the National Natural Science Foundation of China (Grant No. 51579034) and the Open Fund of the Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences (Grant No. KLOCW1502).
Corresponding author.
More Information
  • Corresponding author: Jing Yin
  • Received Date: 2014-10-22
  • Rev Recd Date: 2015-06-23
    Abstract
  • A total variation diminishing-weighted average flux (TVD-WAF)-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer (HLL) Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth-order monotone upstream-centered scheme for conservation laws (MUSCL). The time marching scheme based on the third-order TVD Runge-Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.

     

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