Presidential Young Investigators Award

本文的主要研究目标是实现一个能够准确、高效地求解构成自由曲面的非线性非定常流-体相互作用问题的程序。例如，这些问题是确定部分受约束或自由漂浮的船舶和平台的激励力和反应，以及沿海地区的固定和悬链式管道等水下物体的激励力和反应，由于在精确的自由表面和固体边界条件下求解欧拉流体的精确控制方程的计算困难，目前在这一领域的研究大多集中在线性问题的解决或经验方法上。本文提出的计算流体力学研究计划将从确定几种主要数值方法的相对效率和精度开始，如边界元法、有限差分法、标记单元法和有限元法，用于求解简单边界几何的势理论精确方程。由于最初选择的物体几何形状相当简单，我们也将能够用高阶摄动方法从理论上分析相同的问题，并将结果与数值预测进行比较。

The primary research objective is to implement a program in which the nonlinear and unsteady fluid-body interaction problems that constitutes a free surface are solved accurately and efficiently. Such problems are, for instance, the determination of exciting forces and responses of ships and platforms which are either partially restrained or freely floating, and of submerged bodies, like fixed and catenary pipelines in the coastal areas, Because of the computational difficulties in solving the exact governing equation of an Eulerian fluid subject to exact free-surface and solid-boundary conditions, most of the present research in this area is either concentrated on the solution of linear problems or on empirical methods. The computational hydrodynamics research program proposed here will start with the determination of the relative efficiency and accuracy of several major numerical methods, such as the boundary-element, finite-difference, marker- cell and finite-element methods in solving the exact equations of potential theory for simple boundary geometries. Because of the rather simple body geometries chosen initially, we will be also able to theoretically analyze the same problems by higher-order perturbation methods and compare the results with the numerical predictions.