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
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An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces
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One‐ and two‐step semi‐Lagrangian integrators for arbitrary Lagrangian–Eulerian‐finite element two‐phase flow simulations
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