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为高效数值求解扩展型Boussinesq水波方程,采用一种近似变换方法,将动量方程中的混合导数项变换为纯空间导数项,建立了一种基于原始变量的新的守恒形式方程。对守恒形式方程中的通量项采用基于二阶迎风TVD格式的有限体积方法进行求解,时间导数项采用具有TVD性质的三阶龙格-库塔多步积分方法进行时间积分,剩余项采用中心差分方法进行计算,发展了扩展型Boussinesq水波方程的一种简单高效的混合有限体积/有限差分求解方法。该方法具有数值格式构造过程简单、无需可调参数、数值稳定性强等优点。利用典型波浪传播算例对数值模型进行了验证,计算结果与文献实验数据吻合良好。
In order to efficiently and efficiently solve the extended Boussinesq wave equation, an approximate transformation method is adopted to transform the mixed derivative term in the momentum equation into the pure space derivative term. A new conservative form equation based on the original variables is established. The flux term in the conservation equation is solved by the finite volume method based on the second-order upwind TVD scheme. The time derivative term is time-integrated using the third-order Runge-Kutta multi-step integration method with the TVD property. The remaining terms are centered Differential method to develop a simple and efficient mixed finite volume / finite difference method for solving the extended Boussinesq wave equation. The method has the advantages of simple format construction process, no adjustable parameters and strong numerical stability. The numerical model is verified by a typical wave propagation example. The calculated results are in good agreement with the experimental data in the literature.