基于CIP方法的孤立波爬坡问题数值模拟

Numerical simulation of solitary wave run-up using a CIP-based model

基于自主研发的紧致插值曲线CIP方法的数学模型,研究孤立波在大陆架上传播及冲击爬升海岸峭壁的数值模拟.在立面二维直角坐标下建立模型,采用高阶差分CIP方法作为流场的基本求解器,利用分步算法离散Navier-Stokes方程,通过多相流理论描述固-液-气之间的相互作用,采用流体体积法(volume of fluid,VOF)类型的具有高精度、紧致的系数权重双曲正切(tangent of hyperbola for interface capturing with slope weighting,THINC-SW)方法改进传统的数学模型,重构了自由面采用浸入边界法(immersed boundary method,IBM)计算固-液边界,避免按照地形边界建立贴边网格的问题.研究孤立波在峭壁前的波形演变及在峭壁上的爬坡高度,比较不同的大陆架水平长度和不同海岸峭壁坡度对孤立波爬高峰值的大小及出现时间的影响,分析孤立波冲击爬坡时的压力分布,为不同海岸地形采取相适应的波浪防护措施提供理论及数据支持.

Numerical simulations of solitary wave propagation through the continental shelf and running up coastal cliffs are performed using a Constrained Interpolation Profile（ CIP）-based model. A two-dimensional Cartesian grid is used in the model,a multiphase flow model is used based on the Navier-Stokes equations adopting a CIP scheme as the base flow solver. The free surface boundary is captured by a volume of fluid（ VOF） type scheme,the tangent of hyperbola for interface capturing with slope weighting（ THINC-SW） scheme. An Immersed Boundary Method（ IBM） is used to calculate the interface of solid-liquid to avoid the problem of the need for building a grid satisfy the geography. The elevation of the free surface and the wave run up the cliff are analyzed.The effect of the length of the continental shelf and the gradient of the cliff on the maximum run-up and its occurrence time are considered,and pressure distribution is also analyzed.