A consistent solution of the reinitialization equation in the conservative level-set method

TL;DR

This paper introduces a new re-initialization method for the conservative level-set function that ensures second-order convergence and preserves interface integrity during re-initialization.

Contribution

It proposes a novel discretization consistent with re-initialization, guaranteeing second-order convergence and avoiding artificial deformations in interface simulations.

Findings

Achieves second-order convergence of interface curvature.

Prevents artificial deformations during multiple re-initializations.

Ensures consistency between re-initialization and advection equations.

Abstract

In this paper, a new re-initialization method for the conservative level-set function is put forward. First, it has been shown that the re-initialization and advection equations of the conservative level-set function are mathematically equivalent to the re-initialization and advection equations of the localized signed distance function. Next, a new discretization for the spatial derivatives of the conservative level-set function has been proposed. This new discretization is consistent with the re-initialization procedure and it guarantees a second-order convergence rate of the interface curvature on gradually refined grids. The new re-initialization method does not introduce artificial deformations to stationary and non-stationary interfaces, even when the number of re-initialization steps is large.