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A new framework to construct third‐order weighted essentially nonoscillatory weights using weight limiter functions
Author(s) -
Parvin Sabana,
Kumar Dubey Ritesh
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.4926
Subject(s) - classification of discontinuities , nonlinear system , mathematics , benchmark (surveying) , smoothness , limiter , third order , polygon mesh , spurious relationship , simple (philosophy) , weight function , scheme (mathematics) , flux limiter , mathematical analysis , mathematical optimization , computer science , geometry , telecommunications , philosophy , statistics , physics , theology , geodesy , epistemology , quantum mechanics , geography
A new simple and generic framework is proposed to construct nonlinear weights for third‐order weighted essentially nonoscillatory scheme (WENO) reconstructions. It is done by imposing necessary conditions on nonlinear weights to get a nonoscillatory WENO scheme. These conditions give further insight into the required structure of nonlinear weights to design third‐order WENO schemes. This new framework for WENO weights is completely different from the existing prevailing approaches. Several nonlinear weights using different functions of a smoothness parameter (termed as weight limiter functions) are proposed and analyzed. These new weights by construction guarantee for third‐order accurate nonoscillatory scheme. Numerical results for various benchmark test problems are given and compared with WENO‐JS3 wnd WENO‐Z3 scheme. Computational results show that WENO schemes using proposed weights achieves third‐order accuracy for smooth solution and resolves discontinuities without spurious oscillations.