Abstract In this study, we developed a fully dispersive Boussinesq-type wave model in the modelling framework of the public-domain Boussinesq model, FUNWAVE-TVD. The model adopts the fully dispersive Boussinesq equations of Karambas and Memos (2009) and uses a finite-volume and finite-difference TVD-type scheme. A well-balanced conservative form of the governing equations is derived to facilitate the hybrid numerical scheme. Flux terms were computed by the MUSCL-TVD scheme up to the fourth-order accuracy within the Riemann solver. The third-order Strong Stability-Preserving (SSP) Runge–Kutta scheme was used for time stepping. The convolution integral terms were estimated by the numerical evaluation and the spatial derivative terms were computed by the finite difference scheme. Wave breaking is predicted by locally switching the Boussinesq equations to nonlinear shallow water equations with a Froude number criterion. The model is validated against the linear wave theory and various experiments to examine the capability of the model in simulating wave dispersion, shoaling, breaking, refraction, diffraction, and run-up.

中文翻译：

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基于有限体积和有限差分 TVD 型方案的 2DH 全色散弱非线性 Boussinesq 型模型

摘要 在这项研究中，我们在公共域 Boussinesq 模型 FUNWAVE-TVD 的建模框架中开发了一个完全色散的 Boussinesq 型波模型。该模型采用 Karambas 和 Memos (2009) 的完全色散 Boussinesq 方程，并使用有限体积和有限差分 TVD 类型的方案。导出控制方程的良好平衡的保守形式以促进混合数值方案。通量项由 MUSCL-TVD 方案计算，在黎曼求解器内达到四阶精度。三阶强稳定性保持 (SSP) Runge-Kutta 方案用于时间步进。卷积积分项通过数值评估估计，空间导数项通过有限差分方案计算。通过使用 Froude 数标准将 Boussinesq 方程局部转换为非线性浅水方程来预测波浪破裂。该模型针对线性波浪理论和各种实验进行了验证，以检验模型在模拟波浪色散、浅滩、破碎、折射、绕射和爬高方面的能力。