A Geometric Reinitialization for Conservative Level-Set Methods in the Context of Capillary Flows

Abstract

Simulations of immiscible two-phase flows involving surface tension (ST) require a robust high-fidelity framework. State-of-the-art multi-phase models, such as the Conservative Level-Set (CLS) approach, use Eulerian representations of the fluids and their interface, and require reinitialization methods to ensure volume conservation and accurate ST force modeling. This work proposes a new geometric reinitialization strategy for CLS formulations as an alternative to the typical PDE-based reinitialization methods. Building on the geometric reinitialization developed in context of level-set frameworks, the proposed method is an extension to the CLS approach within an open-source finite element framework that allows for fully distributed and adaptively refined, two- and three-dimensional meshes. This extension enables application of the geometric reinitialization method to large-scale three-dimensional problems with strongly deforming interfaces, including breakup. The method is quantitatively compared to two established reinitialization approaches: the PDE-based reinitialization proposed in the original CLS method and a simple projection-based approach. The assessment comprises three 3D application cases of increasing complexity: the capillary migration of a droplet, the rise of a bubble, and the Rayleigh-Plateau instability development in a capillary jet. The geometric method leads to high-quality, spatially-converged results in good agreement with benchmark and reference solutions. It robustly and accurately recovers expected interface topology-based metrics (e.g., the volume, surface area and sphericity), and relevant flow quantities. In addition, the proposed method has only two parameters and is robust across parameter choices and cases.