Geometric Reinitialization for Capillary Flows: a Comparative Study with State-of-the-Art Conservative Level-Set Methods

TL;DR

The paper presents a complete Conservative Level-Set solver for incompressible two-phase flows with capillary forces and introduces a novel geometric reinitialization method. It benchmark-tests PDE-based, geometric, and projection-based reinitializations on 3D cases: rising bubble, capillary-driven capillary migration, and Rayleigh-Plateau instability, detailing robustness and accuracy across metrics such as volume preservation, surface area, and interface shape. The key finding is that the two-parameter geometric reinitialization offers competitive accuracy with strong robustness and less parameter tuning compared to the four-parameter PDE-based approach, while the projection-based method generally underperforms for complex 3D interfacial dynamics. The work provides practical guidance for selecting reinitialization strategies in CLS-based simulations and highlights the geometric method’s potential for complex multi-physics problems where interface fidelity and volume conservation are critical.

Abstract

Simulations of immiscible 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, rely on Eulerian representations of the fluids and interface and require reinitialization methods to ensure volume conservation and accurate ST force modeling. This work focuses on the complete description of a CLS solver and proposes a novel geometric reinitialization method, based on the level-set literature. It includes a quantitative and objective comparison of this new geometric method to two reinitialization approaches: the PDE-based reinitialization proposed in the original CLS method and a simple projection-based approach. This comparison tackles three 3D application cases: the rise of a bubble, the capillary migration of a droplet, and the Rayleigh-Plateau instability development in a capillary jet. The PDE-based and geometric methods lead to high-quality, spatially-converged results in good agreement with benchmark and analytic solutions, while the projection-based reinitialization fails to capture complex 3D interfacial dynamics. The results also highlight the robustness of the novel geometric method which offers a two-parameter framework in comparison to the PDE-based method that necessitates a case-dependent selection of four parameters.

Figures (17)

• Figure 1: PDE-based reinitialization process flow diagram
• Figure 2: Distance property described in Equation \ref{['eq:d_abs']}.
• Figure 3: Geometric reinitialization flow diagram
• Figure 4: Geometric redistanciation for quadrilateral and adaptively refined (right) meshes compared to the method of Mut2006 and Ausas2011 for simplex meshes (left).
• Figure 5: 2D cross-section view in the x-y plane of the initial state of the rising bubble case