Abstract
Floating body hydrodynamics are typically solved numerically using the boundary element method. The associated code is computationally costly, scaling with the number of mesh panels, and can have accuracy issues at specific frequencies and for thin bodies. In this work, we instead implement a previously-developed matched eigenfunction expansion method to semi-analytically solve the linear potential flow radiation problem for axisymmetric bodies. This method first establishes distinct fluid regions based on the body geometry and expresses the velocity potential as a function of vertical and radial basis functions (eigenfunctions) with unknown coefficients. Eigenfunctions are chosen to automatically enforce several boundary conditions of the problem. The coefficients are found by truncating and solving an infinite linear system representing the matching of potential and radial velocity across fluid region boundaries. This yields a solution for the 3D potential and the hydrodynamic coefficients. We compare the results and computational complexity of the matched eigenfunction expansion method with that of the standard boundary element method. Benefits of the former include 10x faster solve time and lack of meshing, which are particularly appealing in optimization workflows. Our framework will be released as an open-source python package to enable future integration with design tools, implementation of gradients, and democratization of this efficient method. This is a meaningful contribution because prior relevant implementations of the matched eigenfunction expansion method are, to the authors’ knowledge, private and not available open-source or even commercially. Future work will extend this formulation to different kinds of bodies and arrays.
The presentation for this paper at UMERC+METS 2024 can be found here.