High-order level set reinitialization for multiphase flow simulations based on unstructured grids

Reinitialization is essential to maintaining the accuracy of the level set method at capturing interfaces. In this paper, a high-order reinitialization method for the level set function which has previously been developed for structured grids was extended to unstructured grids. The proposed method involves constructing a stencil of an unstructured grid to define a high-order polynomial that approximates a piecewise segment of the interface. Then, the closest point method is adopted to estimate the signed distance function at grid points. The proposed method was validated by solving some benchmark problems of static cases and then the evolution of moving interfacial problems subject to prescribed velocity fields for various grid resolutions consisting of triangular elements. The accuracy of the proposed method was evaluated for computing geometric quantities such as the normal vector and curvature field. The proposed method proved to have high-order accuracy for estimating not only the signed distance function but also geometric quantities for a smooth interface. Finally, a local correction procedure was developed to apply the proposed method to level set problems involving the interface with kinks. The proposed method can accurately estimate normal vector and curvature fields including singularities both for static cases and for dynamic cases where an interface experiences topological changes.