### A New Mass-Conserving Algorithm For Level Set Redistancing On Unstructured Meshes.

#### 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 zerolevel

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 (k rd k= 1) and can be localized

on a narrow band close to the interface, saving computing effort. The mass-rebalancing

step is weighted according to local mass differences, an improvement over usual global rebalancing

techniques.

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 zerolevel

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 (k rd k= 1) and can be localized

on a narrow band close to the interface, saving computing effort. The mass-rebalancing

step is weighted according to local mass differences, an improvement over usual global rebalancing

techniques.

#### Full Text:

PDF

Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**