Finite volume simulation of viscous free surface waves using the Cartesian cut cell approach
Finite volume simulation of viscous free surface waves using the Cartesian cut cell approach
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DOI：
10.1002/fld.2079
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发表时间：
2009
影响因子：
1.8
通讯作者：
W. Bai;C. Mingham;D. Causon;L. Qian
中科院分区：
文献类型：
--
作者：
W. Bai;C. Mingham;D. Causon;L. Qian
介绍了笛卡尔割元法在二维粘性自由表面流动数值模拟中的应用。采用任意拉格朗日-欧拉方法更新半拉格朗日格式中的移动自由水面，其中在每个时间步使用空间二阶精度的有限体积方法基于欧拉描述求解流场。切割单元法被用来跟踪自由表面和固体边界跨越一个固定的背景笛卡尔网格覆盖整个流体，空气和固体区域。在这种方法中，充满空气和固体的单元没有显式计算，并且除了流体单元之外，切割单元和合并单元根据相应的边界条件单独处理。为了验证本数值方法的有效性，首先对不同低雷诺数下圆柱绕流和矩形容器中波浪晃动进行了实验研究。进一步的数值计算结果得到了规则波和波浪通过潜堤的传播。该模型还被应用于水下圆柱受迫振荡辐射波的数值模拟。结果表明，本文所建立的数值模型采用笛卡尔割元法求解波浪场是高效的，并能自动生成边界拟合网格。这些功能是特别有用的移动边界问题，在一个更大的计算域和较长的模拟时间。版权所有© 2009约翰威利父子有限公司。
The application of the Cartesian cut cell approach in the numerical simulation of two‐dimensional viscous free surface flows is described. The Arbitrary Lagrangian–Eulerian method is adopted to update the moving free water surface in a semi‐Lagrangian scheme, in which a finite volume method of second‐order accuracy in space is used for solving the flow field based on an Eulerian description at each time step. The cut cell approach is employed to track the free surface and solid boundaries across a stationary background Cartesian grid covering the whole fluid, air and solid regions. In this approach, the cells full of air and solid are not calculated explicitly, and apart from the fluid cells, cut cells and merged cells are treated separately in terms of corresponding boundary conditions. In order to validate the present numerical method, current flow past a circular cylinder at various low Reynolds numbers and wave sloshing in a rectangular container are tested first. Further numerical results are obtained for the propagation of regular waves and a wave passing over a submerged dike. The model is also applied to the simulation of radiation waves induced by a forced oscillating submerged circular cylinder. The results indicate that the present numerical model using the Cartesian cut cell approach is highly efficient for solving the wave fields, and fully automatic for generating boundary fitted meshes. These features are particularly useful for moving boundary problems in a larger computational domain and with a longer simulation time. Copyright © 2009 John Wiley & Sons, Ltd.