Study of water waves with submerged obstacles using a vortex method with Helmholtz decomposition
Journal
International Journal for Numerical Methods in Fluids
Journal Volume
60
Journal Issue
2
Pages
119-148
Date Issued
2009
Author(s)
Lin, M.Y.
Abstract
Abstract The present study develops a 2?D numerical scheme that combines the vortex method and the boundary integral method by a Helmholtz decomposition to investigate the interaction of water waves with submerged obstacles. Viscous effects and generation of vorticity on the free surface are neglected. The second kind of Fredholm integral equations that govern the strengths of vortex sheets along boundaries are solved iteratively. Vorticity is convected and diffused in the fluid via a Lagrangian vortex (blob) method with varying cores, using the particle strength exchange method for diffusion, with particle redistribution. A grid?convergence study of the numerical method is reported. The inviscid part of the method and the simulation of the free?surface motion are tested using two calculations: solitary wave propagation in a uniform channel and a moving line vortex in the fluid. Finally, the full model is verified by simulating periodic waves travelling over a submerged rectangular obstacle using nonuniform vortex blobs with a mapping of the redistribution lattice. Overall, the numerical model predicts the vortices' evolution and the free?surface motion reasonably well. Copyright ? 2008 John Wiley & Sons, Ltd.
SDGs
Type
journal article