A clebsch method for free-surface vortical flow simulation

College, USA Fig. 1. Various free-surface vortical flow phenomena simulated using our Clebsch method (left to right): reconnection of vortex bubble rings, horseshoe vortex with free ends attached to the water surface, wake vortex formation in a paddling propulsion, turbulent free-surface vortices behind a bunny in tidal wave.

We propose a novel Clebsch method to simulate the free-surface vortical flow. At the center of our approach lies a level-set method enhanced by a wavefunction correction scheme and a wave-function extrapolation algorithm to tackle the Clebsch method's numerical instabilities near a dynamic interface. By combining the Clebsch wave function's expressiveness in representing vortical structures and the level-set function's ability on tracking interfacial dynamics, we can model complex vortex-interface interaction problems that exhibit rich free-surface flow details on a Cartesian grid. We showcase the efficacy of our approach by simulating a wide range of new free-surface flow phenomena that were impractical for previous methods, including horseshoe vortex, sink vortex, bubble rings, and free-surface wake vortices.