A singular-value decomposition (SVD)-based generalized finite difference (GFD) method for close-interaction moving boundary flow problems

Abstract

In this paper, we present a study on a singular-value decomposition (SVD)-based generalized finite difference (GFD) method and a nodal selection scheme for moving body/boundary flow problems formulated on a hybrid Cartesian cum meshfree grid system. The present study shows that the SVD-based method is more robust and accurate than the conventional least-squares-based GFD scheme. A nodal selection scheme is also introduced to overcome the problem of numerical instability associated with the clustering of computational nodes. Such nodal clustering occurs dynamically when moving bodies or boundaries approach within close proximity of each other, resulting in the overlap of their meshfree grids. The nodal scheme is applied to close-interaction flow problems as exemplified by the squeezing action of a circular cylinder through a very narrow slot and the close proximity bypass interaction of two oscillating circular cylinders. Copyright © 2008 John Wiley & Sons, Ltd.