Removing the stiffness of curvature in computing 3-D filaments

Ln this paper, we present a new formulation for computing the motion of a curvature-driven 3-D filament. This new numerical method has none of the high order time step stability constraints that are usually associated with curvature regularization. This result generalizes the previous work of Hou et al. (1994) for 2-D fluid interfaces with surface tension. Applications to 2-D vortex sheets, 3-D motion by curvature, the Kirchhoff rod model, and nearly anti-parallel vortex filaments will be presented to demonstrate the robustness of the method. (C) 1998 Academic Press.