A localized re-initialization equation for the conservative level set method

Abstract

The conservative level set methodology for interface transport is modified to allow for localized level set re-initialization. This approach is suitable to applications in which there is a significant amount of spatial variability in level set transport. The steady-state solution of the modified re-initialization equation matches that of the original conservative level set provided an additional Eikonal equation is solved, which can be done efficiently through a fast marching method (FMM). Implemented within the context of the accurate conservative level set method (ACLS) (Desjardins et al., 2008, [6]), the FMM solution of this Eikonal equation comes at no additional cost. A metric for the appropriate amount of local re-initialization is proposed based on estimates of local flow deformation and numerical diffusion. The method is compared to standard global re-initialization for two test cases, yielding the expected results that minor differences are observed for Zalesakʼs disk, and improvements in both mass conservation and interface topology are seen for a drop deforming in a vortex. Finally, the method is applied to simulation of a viscously damped standing wave and a three-dimensional drop impacting on a shallow pool. Negligible differences are observed for the standing wave, as expected. For the last case, results suggest that spatially varying re-initialization provides a reduction in spurious interfacial corrugations, improvements in the prediction of radial growth of the splashing lamella, and a reduction in conservation errors, as well as a reduction in overall computational cost that comes from improved conditioning of the pressure Poisson equation due to the removal of spurious corrugations.