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

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.

Author Details

Weidong Shi

Jianjun Xu

Shi Shu

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