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An efficient 3D iterative interface-correction reinitialization for the level set method. (English) Zbl 1521.76384

Summary: The level set (LS) method is a popular approach to represent interfaces owing to its smooth description of interfaces, accurate interface information and the convenience of applying to 3D, but it suffers from severe mass loss/gain mainly due to the reinitialization. To address this problem, an efficient 3D iterative interface-correction reinitialization for the LS method is proposed to maintain mass conservation and capture the accurate interface by keeping zero-level-set undisturbed. The standard reinitialization is executed as an outer iteration process to reconstruct LS functions and the operation of fixing the interface location is performed as an inner iteration process. The inner iteration firstly determines displacement errors of zero-level-set interpolation points and then redistribute these errors iteratively to adjacent nodes. The disturbed interface can return to its original position when the displacement errors tend to zero. This method requires only a small number of inner iterations without additional constraint equations and complex coupling operations. The novel approach exhibits excellent properties of mass conservation and interface preservation with the low-cost computing. Several benchmark examples are carried out to illustrate the accuracy and efficiency of the new method. The simulation results indicate that the proposed scheme is found to be highly reliable and accurate.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76Txx Multiphase and multicomponent flows

Software:

A-SLEIPNNIR
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Full Text: DOI

References:

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