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TECHNICAL PAPERS

# New Mass-Conserving Algorithm for Level Set Redistancing on Unstructured Meshes

[+] Author and Article Information
Fernando Mut1

Instituto Balseiro,  Universidad Nacional de Cuyo and CNEA, 8400 Bariloche, Argentinafmut@gmu.edu

Gustavo C. Buscaglia2

Instituto Balseiro,  Universidad Nacional de Cuyo and CNEA, 8400 Bariloche, Argentinagustavo@cab.cnea.gov.ar

Enzo A. Dari2

1

Presently at the School of Computational Sciences, George Mason University, 4400 University Drive, MSN 4C7, Fairfax, VA 22030-4444.

2

Also at the Centro Atómico Bariloche, CNEA, and at CONICET, Argentina.

J. Appl. Mech 73(6), 1011-1016 (Feb 01, 2006) (6 pages) doi:10.1115/1.2198244 History: Received April 12, 2005; Revised February 01, 2006

## Abstract

The level set method is becoming increasingly popular for the simulation of several problems that involve interfaces. The level set function is advected by some velocity field, with the zero-level set of the function defining the position of the interface. The advection distorts the initial shape of the level set function, which needs to be re-initialized to a smooth function preserving the position of the zero-level set. Many algorithms re-initialize the level set function to (some approximation of) the signed distance from the interface. Efficient algorithms for level set redistancing on Cartesian meshes have become available over the last years, but unstructured meshes have received little attention. This presentation concerns algorithms for construction of a distance function from the zero-level set, in such a way that mass is conserved on arbitrary unstructured meshes. The algorithm is consistent with the hyperbolic character of the distance equation $(‖∇d‖=1)$ and can be localized on a narrow band close to the interface, saving computing effort. The mass-correction step is weighted according to local mass differences, an improvement over usual global rebalancing techniques.

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Topics: Algorithms , Disks

## Figures

Figure 1

Zalesak’s disk at four different instants: t1=0, t2=157, t3=314, and t4=471. The first one corresponds to the initial state. A uniform unstructured unstretched grid of 80,000 elements was used. Δt=1 and θ=0.5 was set in the transport algorithm.

Figure 2

Zalesak’s disk: Volume and L1-distance evolution for Δt=0.5 and θ=0.5. Comparison between initial and final states (after one revolution). Domain is a uniform unstructured unstretched grid of 80,000 elements.

Figure 3

Zalesak’s disk: Volume and L1-distance evolution for Δt=0.5 and fully implicit scheme (θ=1). Comparison between initial and final states (after one revolution). Domain is a uniform unstructured unstretched grid of 80,000 elements.

Figure 4

Zalesak’s disk: Volume and L1-distance evolution for Δt=2 and Crank-Nicolson scheme. Comparison between initial and final states (after one revolution). Domain meshed with a uniform unstructured unstretched grid of 80,000 elements.

Figure 5

Notched sphere: (a) Volume evolution for Δt=1 and fully implicit scheme. (b) Comparison between initial and final states (t=157) for the runs with and without reinitialization.

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