In this paper, a hybrid finite-difference and finite-volume numerical scheme is developed to solve the 2-D Boussinesq equations. The governing equations are the extended version of Madsen and Sorensen’s formulations. The governing equations are firstly rearranged into a conservative form. The finite volume method with the HLLC Riemann solver is used to discretize the flux term while the remaining terms are discretized by using the finite difference method. The fourth order MUSCL-TVD scheme is employed to reconstruct the variables at the left and right states of the cell interface. The time marching is performed by using the explicit second-order MUSCL-Hancock scheme with the adaptive time step. The developed model is validated against various experimental measurements for wave propagation, breaking and runup on three dimensional bathymetries.

中文翻译：

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使用混合数值模型对二维扩展Boussinesq方程建模

本文提出了一种有限差分与有限体积混合的数值格式，用于求解二维Boussinesq方程。控制方程是Madsen和Sorensen公式的扩展版本。首先将控制方程重新排列为保守形式。使用HLLC Riemann求解器的有限体积方法来离散通量项，而其余项通过有限差分法来离散化。使用四阶MUSCL-TVD方案来重构单元界面左状态和右状态的变量。通过使用带有自适应时间步长的显式二阶MUSCL-Hancock方案来执行时间行进。所开发的模型已针对各种实验测量结果进行了验证，这些测量结果适用于三维测深仪上的波传播，破裂和加速。