Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 269, Issue -, Pages 329-354Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2014.03.032
Keywords
WENO scheme; Smoothness indicator; Hyperbolic conservation law; Euler equation
Funding
- NSFC [11172299]
- 973 Program [2012CB224806]
- CAS Program for Cross & Cooperative Team of the Science & Technology Innovation
- National Natural Science Foundation of China [21376243]
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In this work, a new smoothness indicator that measures the local smoothness of a function in a stencil is introduced. The new local smoothness indicator is defined based on the Lagrangian interpolation polynomial and has a more succinct form compared with the classical one proposed by Jiang and Shu [12]. Furthermore, several global smoothness indicators with truncation errors of up to 8th-order are devised. With the new local and global smoothness indicators, the corresponding weighted essentially non-oscillatory (WENO) scheme can present the fifth order convergence in smooth regions, especially at critical points where the first and second derivatives vanish (but the third derivatives are not zero). Also the use of higher order global smoothness indicators incurs less dissipation near the discontinuities of the solution. Numerical experiments are conducted to demonstrate the performance of the proposed scheme. (C) 2014 Elsevier Inc. All rights reserved.
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