CAJ | 학술논문

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。
위모의고립파재잠초지형상적전파，건립료기우고계Boussinesq수파방정적파랑전파수학모형。공제방정채용유한차분방법화유한체적방법혼합구해。방정중적대류항용유한체적방법리산，결합HLL려만해화이계TVD-WAF격식구해계면통량，공제단원변계좌우변량채용사계상태삽치방법（ MUSCL）구축。방정중기여항칙이용전통차분격식근사。통과인입고필간습변계적수정려만해화파랑파쇄지표，실현료대해안동변계화파랑파쇄적처리。응용해석해험증모형병진일보모의료고립파재잠초지형상전파변형，결과표명소건립모형교기우유한차분방법적모형구유거대우세，괄용우잠초배경하파랑적수치모의연구，동시야위구해기타류Boussinesq방정제공료삼고。
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 .