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潜礁上孤立波传播的数值模拟

DOI: 10.3969/j.issn.1006??7043.201212107

Keywords: Boussinesq 水波方程, 孤立波, 有限体积, 有限差分, 潜礁

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Abstract:

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。

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