A Novel Reinitialization Scheme for Conservative Level Set Method

TL;DR

This paper introduces a new reinitialization scheme for the conservative level set method that improves interface accuracy, mass conservation, and computational efficiency by reformulating the reinitialization equation.

Contribution

The proposed reinitialization approach reformulates the equation to prevent interface distortion, reduce unphysical patches, and enhance mass conservation and computational efficiency.

Findings

Significant improvement in mass conservation.

Ability to use larger time steps during reinitialization.

Effective on complex unstructured meshes.

Abstract

Existing artificial compression based reinitialization scheme for conservative level set method has a few drawbacks, like distortion of fluid-fluid interface, unphysical patch formation away from the interface and lack of mass conservation. In this paper, a novel reinitialization approach has been presented which circumvents these limitations by reformulating the reinitialization equation. With the reformulated procedure, the present approach is able to reinitialize the level set function without causing any unwanted movement of the interface contour. The unphysical patch formation away from the interface is also resolved here by avoiding the use of ill-conditioned contour normal vectors. As a result of this measure, there is a significant improvement in the mass conservation property. In addition, the simplified form of the new reinitialization equation enables one to choose a much larger time step during the reinitialization iteration. Moreover, the new formulation also helps in reducing the amount of numerical computations per time step, leading to an overall reduction in the computational efforts. In order to evaluate the performance of the present formulation, a set of test problems involving reinitialization of stationary level set functions is carried out first. Then, the efficacy of the proposed reinitialization scheme is demonstrated using a set of standard two-dimensional scalar advection based test problems and incompressible two-phase flow problems. Finally, the ability to deal with complex mesh types is demonstrated by solving a test problem on an unstructured mesh consisting of finite volume cells having triangular and quadrilateral shapes.