Radial Basis Function Methods in Fluid-Structure Interaction

Abstract

This thesis focuses on the use of a number of radial basis function (RBF) methods in computational fluid-structure interaction (FSI). RBF provide a general interpolation framework and have been applied in a number of different ways in various areas of FSI, including bi-directional fluid-structure coupling, mesh or point cloud motion, and in the numerical solution of PDE themselves. This thesis presents novel techniques in all three of these areas. Firstly, an efficiency improvement to the state-of-the-art in RBF mesh motion. Secondly, improvement and simplification of the handing of both moving and static boundaries in RBF-Finite Difference (RBF-FD) methods for numerically solving PDE. Lastly, a partitioned FSI solver is developed using a new coupling method, which extends the current applicability of RBF-FD to a more general class of FSI problems.