A stable interface-preserving reinitialization equation for conservative level set method

Abstract

Existing artificial compression based reinitialization approach for conservative level set method has a few drawbacks, like distortion of fluid–fluid interface and formation of unphysical fluid patches away from the interface. In this paper, a novel reinitialization approach has been presented which circumvents these limitations by reformulating the existing reinitialization equation. The new reinitialization equation by design ensures that the interface contour is kept invariant under the action of level set reinitialization. The unphysical patch formation away from the interface is also resolved here by avoiding the use of ill-conditioned contour normal vectors. Owing to the use of much simpler terms, a significant reduction in the numerical computations is achieved with the new reinitialization equation. The new reinitialization equation also enables one to choose a larger time step during the reinitialization iteration, leading to an overall reduction in 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 approach 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.