期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 230, 期 10, 页码 3727-3752出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.01.043
关键词
High-order finite-difference methods; Weighted essentially non-oscillatory schemes; Energy estimate; Numerical stability; Artificial dissipation
资金
- LaRC LARSS
A general strategy was presented in 2009 by Yamaleev and Carpenter for constructing energy stable weighted essentially non-oscillatory (ESWENO) finite-difference schemes on periodic domains. ESWENO schemes up to eighth order were developed that are stable in the energy norm for systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain, wherever possible, the WENO stencil biasing properties and satisfy the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L-2 norm. Second-order and third-order boundary closures are developed that are stable in diagonal and block norms, respectively, and achieve third- and fourth-order global accuracy for hyperbolic systems. A novel set of non-uniform flux interpolation points is necessary near the boundaries to simultaneously achieve (1) accuracy, (2) the SBP convention, and (3) WENO stencil biasing mechanics. Published by Elsevier Inc.
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