Article: McCaslin JO, Desjardins O; (2014) A Localized Re-initialization Equation for the Conservative Level Set Method. Journal of Computational Physics, 262:408-426
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, ), the FMM solution of this Eikonal equation comes at no additional cost. A metric for the appropriate amount of local reinitialization 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 Zalesak’s 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. (C) 2014 Elsevier Inc. All rights reserved.