Review of level-set reinitialization methods in computational mechanics and materials science
Abstract
The level-set (LS) method has been widely spread since its introduction in 1988. One of its main features is that interfaces are represented through signed distance functions, and the distance property eases the smoothing of discontinuities across an interface, and the computation of normal vectors and mean curvatures. This property can be lost whenever the LS function is evolved, for instance, through an LS transport equation. Numerous studies proposing so-called LS reinitialization methods to restore the distance property have been published since 1988. This paper is a review of numerical developments on LS reinitialization in the past decade (2014-2024). LS reinitialization methods are classified into three categories: direct methods which geometrically compute distances, local indirect methods which solve the Eikonal equation point-by-point, and global indirect methods which solve the Eikonal equation for all points at once. The review focuses on numerical methods and investigates the following questions. Can it be implemented in a parallel computing environment with nearly optimal scalability? Can it be used with any approximation method, and is it compatible with unstructured grids? Can it be extended to reach higher-order convergence rates? Can it be combined with mass change error attenuation techniques? Does it involve any numerical parameters that may affect its robustness? Is it limited only to some applications? Through a quantitative and qualitative analysis of the past decade's literature, this review paper proposes novel insights on LS reinitialization. Research on direct methods should focus on parallel efficiency and robust higher-order distance computation techniques. More attention should be given to local indirect methods, especially regarding parallel and higher-order algorithms for unstructured grids. Control parameters for global indirect methods should be better determined or eliminated. More research is needed on the issue of blind spots in two-phase problems involving moving contact lines and their elimination.
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