Application of Local Polynomial Collocation Method to the Simulation of 3D Liquid Sloshing

局部多項式配點法在三維水槽盪漾問題之數值模擬應用研究

吳南靖(Nan-Jing Wu) ； 蕭士俊(Shih-Chun Hsiao) ； 吳漢倫(Han-Lun Wu)

《海洋工程學刊》 15卷2期 (2015/06) Pp. 67-83

https://doi.org/10.6266/JCOE.2015.1502.01

摘要

波浪現象可視為勢流的一種，其控制方程式為拉普拉斯方程式（Laplace equation），而水面必須同時滿足運動與動力兩條邊界條件。本文採用Wu and Chang（2011）提出之拉格朗日觀點（Lagrangian aspect）的離散方法，對水面邊界條件進行時間上的離散。在每一時間步，必須做一次拉普拉斯方程式之數值求解，並採用Wu and Tsay（2013）之局部多項式配點法求解方程式。此方法最初只能適用於二維之物理問題，因此本文延續前人研究，將此方法擴展至三維，並以此建立一套可模擬三維自由液面勢流場之數值模式，用來模擬搖晃水槽內非線性水波盪漾。

關鍵字

搖晃水槽 ； 多項式有限配點法 ； 無網格 ； 水波盪漾

並列摘要

In this paper a mesh-free numerical model for simulating 3-D free-surface potential flows is established. A time-marching scheme in Lagrangian aspect is chosen for the boundary conditions of the moving and deforming free surface while a local polynomial collocation method is applied for solving the Laplace equation at each time step. This collocation method is employed because the governing equation is satisfied on boundaries as well as boundary conditions are so the partial derivatives of the solution are calculated accurately. The trajectories of free-surface nodes can thus be predicted precisely due to the accurate estimation of the partial derivatives of velocity potential, which represent components of the velocity vector at that specific node. The numerical model is applied to the simulation of free surface waves in the liquid sloshing of both rectangular and cylindrical swaying tanks. Fairly good agreements are observed in the comparison of numerical results with experimental data.

並列關鍵字

swaying tank ； polynomial collocation method ； meshless ； liquid sloshing