期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 51, 期 2, 页码 864-893出版社
SIAM PUBLICATIONS
DOI: 10.1137/110848104
关键词
hyperbolic conservation laws; ENO scheme; exponential polynomials; interpolation; approximation order; flux function
资金
- National Research Foundation of Korea (NRF) [2012R1A1A2004518, 2009-0093827]
- Ministry of Education, Science, and Technology
- National Research Foundation of Korea [2012R1A1A2004518] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
This study proposes modified essentially nonoscillatory (ENO) schemes that can improve the performance of the classical ENO schemes. The key ideas of our approach consist of the following two approaches. First, the interpolation method is implemented by using exponential polynomials with shape (or tension) parameters such that they can be tuned to the characteristics of given data, yielding better approximation than the classical ENO schemes at the same computational cost. Second, we present a new smoothness measurement that can evaluate the local smoothness of a function inside a stencil such that it enables the identification of the smoothest one, while avoiding the inclusion of discontinuous points in the stencil. Some numerical experiments are provided to demonstrate the performance of the proposed schemes.
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