Level-Set field re-initialization: A computational model with finite element method on complicated domains

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Scientific computing

Background:

• Level-Set (LS) methods are crucial for simulating interfaces in fluid dynamics.
• Accurate re-initialization of the LS field is essential for maintaining simulation fidelity.
• Existing methods face challenges with complex geometries and higher-order approximations.

Purpose of the Study:

• To introduce a proficient re-initialization method for the LS field within the Finite Element Method (FEM) framework.
• To develop a technique that preserves the signed distance (SD) property of the LS field.
• To integrate this method with FEM for complex domains and higher-degree polynomials.

Main Methods:

• The proposed method utilizes an Eulerian-Lagrange multiplier technique for re-initialization.
• It is based on geometric re-initialization principles.
• The scheme is integrated with the FEM, supporting higher-degree polynomial approximations.

Main Results:

• Numerical benchmark tests demonstrate the method's effectiveness and efficiency.
• The technique successfully preserves the LS field's mass.
• High performance is achieved in simulations on complex domains.

Conclusions:

• The developed re-initialization method is proficient for LS field simulations using FEM.
• It offers an efficient way to maintain the SD property and mass conservation.
• The method is suitable for complex geometries and higher-degree polynomial approximations in FEM.