Mathematical Sciences: Free Surface Boundary Value Problems in Ship Hydrodynamics

本课题旨在解决低纵横比平船理论中三个重要的物理问题。这些问题包括：1)高速船舶的纵倾和纵倾计算；2)在时间相关扰动下接近最佳升力/阻力船体的稳定性分析性能；3)中速行驶的低展弦比平船的气流计算。前两个问题的解决技术涉及主要研究者现有工作的扩展，其中混合边值问题以复变量理论的形式重新表述，并通过使用符号操作软件的解析函数的级数展开来解决。由于混合边值问题固有的困难和符号计算的最新发展，这些问题在数学上是有趣的。第三个问题需要一种新的方法，它使用匹配渐近展开，内部解满足每个交叉平面上的双体流，外部解对应流过一系列压力源。

The objectives of this project is to solve three physically important problems in low-aspect ratio flat ship theory. These problems are 1) the calculation of the rise and trim of a high speed vessel, 2) the performance of a stability analysis for near optimal lift/drag hulls under time dependent perturbations and 3) the calculation of the flow past a low-aspect ratio flat ship traveling at moderate speeds. The solution techniques for the first two problems involve an extension of existing work by the principal investigator where mixed boundary value problems are reformulated in terms of complex variable theory and solved by a series expansion in terms of analytic functions using symbolic manipulation software. These problems are mathematically interesting because of the inherent difficulty of mixed boundary value problems and the recent developments in symbolic computation. The third problem requires a novel apparoach that uses matched asymptotic expansions, with the inner solution satisfying a double body flow in each cross plane, and the outer solution corresponding to the flow past a line of pressure sources.