Recent Progress in Simulations of 3D Vortex Sheets with Surface Tension

Abstract

Numerical simulations of vortex sheets have a long history. The major advantage of the vortex sheet model lies in the efficiency of its boundary integral formulation, which allows us to avoid expensive computations of volumetric equations in some important problems. Although some researchers in computer graphics have exploited this benefit, there seems to be ample room for further improvements to their methods in relation to new results achieved in the applied mathematics community. On the other hand, applied mathematicians also could gain insight into flexible treatment of moving surfaces, which are very common in the current CG community. In this paper, we give an overview of recent progress in numerical simulations of the motion of three-dimensional vortex sheets with surface tension and discuss open problems that interests researchers in both communities referring to important papers from graphics.