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Volume 9, Issue 6
An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces

Weidong Shi, Jianjun Xu & Shi Shu

DOI: 10.4208/aamm.OA-2016-0052

Adv. Appl. Math. Mech., 9 (2017), pp. 1364-1382.

Published online: 2017-09

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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 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 equation, semi-Lagrangian method, level-set method, block-structured adaptive mesh, finite difference method.

  • AMS Subject Headings

65L50, 65M06, 65M20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1364, author = {Shi , WeidongXu , Jianjun and Shu , Shi}, title = {An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2017}, volume = {9}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0052}, url = {http://global-sci.org/intro/article_detail/aamm/10183.html} }
TY - JOUR T1 - An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces AU - Shi , Weidong AU - Xu , Jianjun AU - Shu , Shi JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1364 EP - 1382 PY - 2017 DA - 2017/09 SN - 9 DO - http://doi.org/10.4208/aamm.OA-2016-0052 UR - https://global-sci.org/intro/article_detail/aamm/10183.html KW - Convection-diffusion equation, semi-Lagrangian method, level-set method, block-structured adaptive mesh, finite difference method. AB -

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.

Weidong Shi, Jianjun Xu & Shi Shu. (2020). An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces. Advances in Applied Mathematics and Mechanics. 9 (6). 1364-1382. doi:10.4208/aamm.OA-2016-0052
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