强非线性波浪-浮体耦合作用模拟的新型高精度CIP重叠网格法

Strongly nonlinear wave-body interaction problem is one of the key research topics in ocean engineering. For numerical simulation of such problem, it is difficult to get enough accuracy in simulating the strongly nonlinear phenomena, i.e., violent free surface, large amplitude structural motion or deformation, etc., especially in the local areas around a floating body. The CIP (Constraint Interpolation Profile) method, coupled with immersed boundary method, has been successfully used to simulate such kind of strongly nonlinear phenomena in a fixed regular Cartesian grid. However, it is difficult to make a high-resolution simulation in the local areas around a floating body. In this study, a new CIP-Overset method with high-accuracy will be developed to make high-resolution simulation of strongly nonlinear wave-body interaction. The overset grid is applied to divide the computational domain into several sub-domains, and an optimal mesh is used for the local areas around a floating body. It can be used to simulate large amplitude structural motion or deformation, and can make a high-resolution simulation in the local areas around a floating body. On the other hand, by using the CIP method, errors of the advection velocity and its phase on the interface between sub-domains can be reduced. Meanwhile, based on the theory of the CIP method, a new interpolation scheme with three-order accuracy is developed for improving the accuracy of information exchanging between sub-domains. It is helpful to get enough accuracy in simulating violent free surface. With the development of the new CIP-Overset method, which is accurate, stable and robust, high-resolution simulation of strongly nonlinear wave-body interaction can be expected.

强非线性波浪-浮体相互作用机理是当前海洋工程领域亟待解决的重点、难点问题之一。应用数值方法研究该问题的难点是：准确模拟自由面剧烈砰击、浮体大幅度运动或变形等强非线性现象，并实现浮体边界区域流场高精度计算。笛卡尔直角网格系统中，CIP法结合浸入边界法，可成功模拟上述强非线性现象，但难以高精度模拟浮体边界区域流场。为此，本项目研究将重叠网格系统引入CIP法。基于重叠网格系统，将计算区域划分成若干个子区域，优化浮体边界区域网格，准确模拟浮体大幅度运动或变形，实现浮体边界区域流场高精度计算。基于CIP法，有效控制子区域交界面处对流速度值及其相位差，并开发具有三阶精度的插值算法，提高子区域之间流场信息交换的精度，准确模拟强非线性自由面运动。充分结合CIP法和重叠网格系统的各自优点，探索并发展一种精度高、稳定性好、鲁棒性强的新型CIP重叠网格法，为更好地揭示强非线性波浪-浮体相互作用机理奠定算法基础。

强非线性波浪-浮体相互作用机理是当前海洋工程领域亟待解决的重点、难点问题之一。应用数值方法研究该问题的难点是：准确模拟自由面剧烈砰击、浮体大幅度运动或变形等强非线性现象，并实现浮体边界区域流场高精度计算。笛卡尔直角网格系统中，CIP法结合浸入边界法，可成功模拟上述强非线性现象，但难以高精度模拟浮体边界区域流场。为此，本项目研究将重叠网格系统引入CIP法。基于重叠网格系统，将计算区域划分成若干个子区域，优化浮体边界区域网格，准确模拟浮体大幅度运动或变形，并实现浮体边界区域流场高精度计算。基于CIP法，有效控制子区域交界面处对流速度值及其相位差，并开发三阶精度的插值算法，提高子区域之间流场信息交换的精度，准确模拟强非线性自由面运动。充分结合CIP法和重叠网格系统的各自优点，探索并发展一种精度高、稳定性好、鲁棒性强的新型CIP重叠网格法。.本项目首先基于“bounding box”和X-ray射线法原理，并结合叉树数据结构，自主研发了一种简单、高效的重叠网格生成算法。通过二维简单/复杂几何形状、三维简单/复杂几何形状系列算例测试表面，本项目开发的算法可实现高效的寻点、挖洞操作，并快速生产重叠网格；以此为基础，完成了新型CIP重叠网格法的开发，并开展了系列算法精度验证工作，例如：1）数值造波验证，算例结果表明本项目开发的新型算法可实现波浪准确模拟，同试验数据对比，波面数值平均误差小于10%；2）强非线性聚焦波-浮体耦合模拟验证，结果显示浮体运动平均误差小于15%；3）船舶甲板上浪砰击模拟验证，同模型试验数据对比，船舶运动平均误差小于15%，典型位置处波浪砰击压力平均误差小于20%。同时，针对新型CIP重叠网格算法开展了并行优化研究，在576核集群上测试表明，并行加速比体现线性特性。通过本项目研究，形成了一套具有自主知识产权的新型CIP重叠网格算法，可实现强非线性波浪-浮体耦合问题精细模拟，为更好地揭示强非线性波浪-浮体相互作用机理奠定算法基础。