基于二维浅水方程的滑坡体兴波数值模型

A numerical model for landslide-generated waves based on two-dimensional shallow water equations

基于有限体积方法和结构化网格,建立了海底滑坡引起的波浪传播数值模型。模型控制方程为考虑了海床随时间变化的二维浅水方程。采用中心迎风格式计算控制体界面数值通量,采用线性重构技术、局部海床高程处理技术和全隐式离散底摩阻项,保证了格式的和谐性、守恒性和水深非负性,有效处理了海岸动边界问题。时间积分采用具有强稳定性质的二阶龙格-库塔方法 (ssp RK)。针对滑坡体兴波经典算例开展数值模拟,将计算结果与解析解、实验结果及其他模型计算结果进行比较和分析。结果表明,对于所考虑的计算工况,模型能较合理地模拟滑坡兴波的产生、传播和爬高过程。

Based on the finite-volume method and a structured mesh system, a numerical model for simulating land- slide-generated waves is developed. The governing equations are the two-dimensional nonlinear shallow water （NLSW） equations with the consideration of a dynamic seabed. The central upwind scheme is used to compute the numerical interface flux. The second-order MUSCL method for variables reconstruction, local bed modification and implicit treatment to bottom friction are used to ensure the properties of well-balanced, conservative and non-negative water depth, as well as the ability to deal with the moving shoreline. The second-order Runge-Kutta method with Strong Stability Preserving （SSP） is adopted to perform the time marching. A series of benchmark cases are simulated and the numerical results are compared with the analytical solution, experimental data and numerical results from other models. It is found the present model can simulate the generation, propagation and runup of the landslide-generated waves for the considered cases with reasonable accuracy.