A Simple Implementation of the Semi-Lagrangian Level-Set Method

A Simple Implementation of the Semi-Lagrangian Level-Set Method

Year:    2017

Author:    Weidong Shi, Jian-Jun Xu, Shi Shu

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 104–124

Abstract

Semi-Lagrangian (S-L) methods have no CFL stability constraint, and are more stable than the Eulerian methods. In the literature, the S-L method for the level-set re-initialization equation was complicated, which may be unnecessary. Since the re-initialization procedure is auxiliary, we propose to use the first-order S-L scheme coupled with a projection technique to improve the accuracy at the grid points just adjacent to the interface. Standard second-order S-L method is used for evolving the level-set convection equation. The implementation is simple, including on the block-structured adaptive mesh. The efficiency of the S-L method is demonstrated by extensive numerical examples including passive convection of interfaces with corners/kinks/large deformation under given velocity fields, a geometrical flow with topological changes, simulations of bubble/ droplet dynamics in incompressible two-phase flows. In terms of accuracy it is comparable to the other existing methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2015.m1305

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 104–124

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Semi-Lagrangian method level-set method interface motion two-phase flow bubble/ droplet dynamics block-structured adaptive mesh.

Author Details

Weidong Shi

Jian-Jun Xu

Shi Shu

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