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<p>This study proposed a numerical model based on a hybrid scheme using finite-difference and finite-volume methods to simulate nonlinear wave propagation from deep to shallow water. Six shock-capturing-type reconstruction schemes, namely the second-order Monotonic Upwind Scheme for Conservation Laws (MUSCL), the second-order MUSCL–Total Variation Diminishing (TVD) scheme with the van Leer limiter, the standard fourth-order MUSCL–TVD scheme with the Minmod limiter, the improved fourth-order MUSCL–TVD scheme, the fifth-order Weighted Essentially Non-oscillatory (WENO) scheme, and the fifth-order TVD scheme with the Superbee slope limiter, were used to discretize the flux terms in the governing equations. Regular wave propagation in water of uniform depth, and over a submerged bar or a slope, was simulated using these schemes. Comparison of numerical results with theoretical solutions or experimental data illustrates the simulation performance of the six reconstruction schemes.</p>

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Comparison of Shock-Capturing-Type Reconstruction Schemes in a Numerical Model for Nonlinear Wave Propagation

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Pengbo Zheng,
  • Hongsheng Zhang,
  • Qingyuan Liu,
  • Dali Xu,
  • Lingting Kong,
  • Haiqing Jia

摘要

This study proposed a numerical model based on a hybrid scheme using finite-difference and finite-volume methods to simulate nonlinear wave propagation from deep to shallow water. Six shock-capturing-type reconstruction schemes, namely the second-order Monotonic Upwind Scheme for Conservation Laws (MUSCL), the second-order MUSCL–Total Variation Diminishing (TVD) scheme with the van Leer limiter, the standard fourth-order MUSCL–TVD scheme with the Minmod limiter, the improved fourth-order MUSCL–TVD scheme, the fifth-order Weighted Essentially Non-oscillatory (WENO) scheme, and the fifth-order TVD scheme with the Superbee slope limiter, were used to discretize the flux terms in the governing equations. Regular wave propagation in water of uniform depth, and over a submerged bar or a slope, was simulated using these schemes. Comparison of numerical results with theoretical solutions or experimental data illustrates the simulation performance of the six reconstruction schemes.