A moving mesh WENO method for one-dimensional conservation laws
View/ Open
Issue Date
2012-10-01Author
Yang, Xiaobo
Huang, Weizhang
Qiu, Jianxian
Publisher
Society for Industrial and Applied Mathematics
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
In this paper, we develop an efficient moving mesh weighted essentially nonoscillatory (WENO) method for one-dimensional hyperbolic conservation laws. The method is based on the quasi-Lagrange approach of the moving mesh strategy in which the mesh is considered to move continuously in time. Several issues arising from the implementation of the scheme, including mesh smoothness, mesh movement restriction, and computation of transformation relations, and their effects on the accuracy of the underlying scheme have been addressed. Particularly, it is found that a least squares smoothing can be used to effectively smooth the mesh, and the transformation relations can be computed using either high order finite differences or WENO applied to some geometric conservation laws. Moreover, mesh movement can cause WENO schemes to become unconditionally unstable. A simple strategy is used to restrict the mesh movement and recover the stability. Numerical results are presented to demonstrate the accuracy and shock-capturing ability of the new scheme.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/110856381.
Collections
Citation
Yang, Xiaobo., Huang, Weizhang., Qiu, Jianxian. "A moving mesh WENO method for one-dimensional conservation laws." SIAM J. Sci. Comput., 34(4), A2317–A2343. (27 pages). http://dx.doi.org/10.1137/110856381.
Items in KU ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
We want to hear from you! Please share your stories about how Open Access to this item benefits YOU.