Piston-Driven Numerical Wave Tank Based on WENO Solver of Well-Balanced Shallow Water Equations

Abstract

A numerical wave tank equipped with a piston type wave-maker is presented for long-duration simulations of long waves in shallow water. Both wave maker and tank are modelled using the nonlinear shallow water equations, with motions of the numerical piston paddle accomplished via a linear mapping technique. Three approaches are used to increase computational efficiency and accuracy. First, the model satisfies the exact conservation property (C-property), a stepping stone towards properly balancing each term in the governing equation. Second, a high-order weighted essentially non-oscillatory (WENO) method is used to reduce accumulation of truncation error. Third, a cut-off algorithm is implemented to handle contaminated digits arising from round-off error. If not treated, such errors could prevent a numerical scheme from satisfying the exact C-property in long-duration simulations. Extensive numerical tests are performed to examine the well-balanced property, high order accuracy, and shock-capturing ability of the present scheme. Correct implementation of the wave paddle generator is verified by comparing numerical predictions against analytical solutions of sinusoidal, solitary, and cnoidal waves. In all cases, the model gives satisfactory results for small-amplitude, low frequency waves. Error analysis is used to investigate model limitations and derive a user criterion for long wave generation by the model.

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Acknowledgements

This research was funded by National Research Foundation of Korea (NRF) grant funded by Korean Government Ministry of Science, ICT & Future Planning (No. 2017R1A2B4007977), and administratively supported by the Institute of Engineering Research at the Seoul National University.

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Correspondence to Jin Hwan Hwang.

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Jung, J., Hwang, J.H. & Borthwick, A.G.L. Piston-Driven Numerical Wave Tank Based on WENO Solver of Well-Balanced Shallow Water Equations. KSCE J Civ Eng 24, 1959–1982 (2020). https://doi.org/10.1007/s12205-020-1875-3

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Keywords

  • Shallow water equations
  • Well-balanced scheme
  • Piston type wave-maker
  • Exact C-property
  • WENO
  • Numerical wave tank