Mathematical Sciences: Free Surface Boundary Value Problems in Ship Hydrodynamics

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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.