潜礁上孤立波传播的数值模拟

Simulation of solitary wave transformation over reef profile

为模拟孤立波在潜礁地形上的传播,建立了基于高阶Boussinesq水波方程的波浪传播数学模型。控制方程采用有限差分方法和有限体积方法混合求解。方程中的对流项用有限体积方法离散,结合HLL黎曼解和二阶TVD-WAF格式求解界面通量,控制单元边界左右变量采用四阶状态插值方法(MUSCL)构筑。方程中其余项则利用传统差分格式近似。通过引入考虑干湿边界的修正黎曼解和波浪破碎指标,实现了对海岸动边界和波浪破碎的处理。应用解析解验证模型并进一步模拟了孤立波在潜礁地形上传播变形,结果表明所建立模型较基于有限差分方法的模型具有巨大优势,适用于潜礁环境下波浪的数值模拟研究,同时也为求解其他类Boussinesq方程提供了参考。

A Boussinesq-type wave model is presented in this paper to simulate the tsunami solitary wave transforma -tion over a reef profile .The governing equation is solved by combining the finite difference method and the finite vol -ume method.The convective flux terms are discretized using the finite volume method , in conjunction with the HLL Riemann Solver and the TVD-WAF scheme to calculate the interface flux .The left and right state of the cell interface is constructed through the fourth-order monotone upstream-centered schemes for conservation laws （MUSCL） method. While for the rest of the terms of the equations , the finite difference approximation is used .By modifying the Riemann Solver to a local wet-dry interface and introducing the wave breaking criterion , time-varying shoreline motion and wave breaking in a surf zone are taken into account .The developed model was verified via analytical solutions and then used to simulate the tsunami solitary wave transformation over a coastal reef .The proposed model is quite advan-tageous over that built on finite difference method and is suitable for modeling wave transformations in a reef environ -ment;meanwhile the proposed hybrid scheme can be used to solve other Boussinesq type equations .