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Improved third‐order weighted essentially nonoscillatory schemes with new smoothness indicators
Author(s) -
Li Chen,
Guo Qilong,
Sun Dong,
Liu Pengxin,
Zhang Hanxin
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4872
Subject(s) - smoothness , mathematics , third order , interpolation (computer graphics) , nonlinear system , euler equations , dissipation , polynomial , order (exchange) , scheme (mathematics) , euler's formula , polynomial interpolation , mathematical analysis , linear interpolation , frame (networking) , computer science , physics , telecommunications , quantum mechanics , thermodynamics , philosophy , theology , finance , economics
Summary In this article, we present two improved third‐order weighted essentially nonoscillatory (WENO) schemes for recovering their design‐order near first‐order critical points. The schemes are constructed in the framework of third‐order WENO‐Z scheme. Two new global smoothness indicators, τ L 3 and τ L 4 , are devised by a nonlinear combination of local smoothness indicators ( IS k ) and reference values ( IS G ) based on Lagrangian interpolation polynomial. The performances of the proposed schemes are evaluated on several numerical tests governed by one‐dimensional linear advection equation or one‐ and two‐dimensional Euler equations. Numerical results indicate that the presented schemes provide less dissipation and higher resolution than the original WENO3‐JS and subsequent WENO3‐N scheme.