Mathematical Sciences: Free Surface Boundary Value Problems in Ship Hydrodynamics

本项目的目标是解决小展弦比扁平船理论中的三个重要物理问题。这些问题是：1)高速船的升降计算，2)随时间变化的摄动下近最佳升力/阻力船体的稳定性分析性能，以及3)中速低展弦比平船绕流的计算。前两个问题的求解技术涉及到首席研究员现有工作的扩展，其中混合边值问题用复变量理论重新表述，并用符号处理软件用解析函数的级数展开来求解。由于混合边值问题固有的困难和符号计算的最新发展，这些问题在数学上很有趣。第三个问题需要一种新的装置，它使用匹配的渐近展开，内解满足每个交叉平面上的双体流动，而外解对应于流过一条压源线的流动。

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.