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

Umer Siddiqui1, Fahim Raees1

  • 1Department of Mathematics, NED University of Engineering and Technology, Karachi, Pakistan.

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Summary
This summary is machine-generated.

This study presents an efficient re-initialization method for the Level-Set (LS) field using the Finite Element Method (FEM). The technique preserves the signed distance property and mass, proving effective for complex domains and higher-degree polynomials.

Keywords:
Finite element method (FEM)Lagrange multiplier methodLevel-set (LS) methodNon-uniform gridsRe-initialization scheme for the Level-Set (LS) methodRe-initialization, and multiphase flow

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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.