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An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces

Published online by Cambridge University Press:  28 November 2017

Weidong Shi*
Affiliation:
School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan, Hunan 411105, China Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, China
Jianjun Xu*
Affiliation:
Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, China
Shi Shu*
Affiliation:
School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan, Hunan 411105, China
*
*Corresponding author. Email:[email protected] (W. D. Shi), [email protected] (J. J. Xu), [email protected] (S. Shu)
*Corresponding author. Email:[email protected] (W. D. Shi), [email protected] (J. J. Xu), [email protected] (S. Shu)
*Corresponding author. Email:[email protected] (W. D. Shi), [email protected] (J. J. Xu), [email protected] (S. Shu)
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Abstract

A new Semi-Lagrangian scheme is proposed to discretize the surface convection-diffusion equation. The other involved equations including the 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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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