An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces
Year: 2017
Author: Weidong Shi, Jianjun Xu, Shi Shu
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1364–1382
Abstract
A new Semi-Lagrangian scheme is proposed to discretize the surface convection-diffusion equation. The other involved equations including the level-set convection equation, the re-initialization equation and the extension equation are also solved by S-L schemes. The S-L method removes both the CFL condition and the stiffness caused by the surface Laplacian, allowing larger time step than the Eulerian method. The method is extended to the block-structured adaptive mesh. Numerical examples are given to demonstrate the efficiency of the S-L method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0052
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1364–1382
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Convection-diffusion equation semi-Lagrangian method level-set method block-structured adaptive mesh finite difference method.
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