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

Part of: Numerical analysis: Ordinary differential equations Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  28 November 2017

Weidong Shi ,
Jianjun Xu  and
Shi Shu
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:weidongshi123@xtu.edu.cn (W. D. Shi), xujianjun@cigit.ac.cn (J. J. Xu), shushi@xtu.edu.cn (S. Shu)
*Corresponding author. Email:weidongshi123@xtu.edu.cn (W. D. Shi), xujianjun@cigit.ac.cn (J. J. Xu), shushi@xtu.edu.cn (S. Shu)
*Corresponding author. Email:weidongshi123@xtu.edu.cn (W. D. Shi), xujianjun@cigit.ac.cn (J. J. Xu), shushi@xtu.edu.cn (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.

Keywords

Convection-diffusion equationsemi-Lagrangian methodlevel-set methodblock-structured adaptive meshfinite difference method

MSC classification

Secondary: 65L50: Mesh generation and refinement 65M06: Finite difference methods 65M20: Method of lines
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 6 , December 2017 , pp. 1364 - 1382
Copyright
Copyright © Global-Science Press 2017 

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