Three-level order-adaptive weighted essentially non-oscillatory schemes

Classical fifth-order weighted essentially non-oscillatory (WENO) schemes are based on reconstructions from three consecutive second-order polynomials. They give a third-order accurate scheme when two consecutive polynomials are smooth and one is non-smooth. This situation means losing one order of...

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Autores principales:	A. Arun Govind Neelan, Manoj T. Nair, Raimund Bürger
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	WENO ENO High resolution schemes Order-adaptive schemes Finite volume method Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/3f7023a379e04e95bbb0aa84deec14e2
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spelling	oai:doaj.org-article:3f7023a379e04e95bbb0aa84deec14e22021-11-18T04:51:19ZThree-level order-adaptive weighted essentially non-oscillatory schemes2590-037410.1016/j.rinam.2021.100217https://doaj.org/article/3f7023a379e04e95bbb0aa84deec14e22021-11-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2590037421000510https://doaj.org/toc/2590-0374Classical fifth-order weighted essentially non-oscillatory (WENO) schemes are based on reconstructions from three consecutive second-order polynomials. They give a third-order accurate scheme when two consecutive polynomials are smooth and one is non-smooth. This situation means losing one order of accuracy if compared with a fourth-order scheme. In classical WENO schemes, weighting functions that determine the weights for the polynomials and that eventually define the reconstruction are directly related to a smoothness indicator. This property may lead to a non-zero residual of a very small value in the Taylor expansion. To handle this situation a weighting procedure that does not directly rely on the smoothness indicator is presented. Once the smooth polynomials are determined, the smoothness indicator has no role in the further steps, which are taken care of by a new switch function. Contrary to other approaches this switch function does not involve any conditional statements. A tuning parameter is also included so that the resulting order-adaptive property can be adjusted to specific requirements. The performance of the resulting schemes for cell-average and point-value reconstructions is studied. In addition, the effect of the choice of numerical flux or Riemann solver on these reconstruction strategies is analysed. Numerical tests for the Euler equations of gas dynamics in one and two space dimensions are presented. Improvements in resolution and the stability are found when compared with the conventional WENO techniques.A. Arun Govind NeelanManoj T. NairRaimund BürgerElsevierarticleWENOENOHigh resolution schemesOrder-adaptive schemesFinite volume methodMathematicsQA1-939ENResults in Applied Mathematics, Vol 12, Iss , Pp 100217- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	WENO ENO High resolution schemes Order-adaptive schemes Finite volume method Mathematics QA1-939
spellingShingle	WENO ENO High resolution schemes Order-adaptive schemes Finite volume method Mathematics QA1-939 A. Arun Govind Neelan Manoj T. Nair Raimund Bürger Three-level order-adaptive weighted essentially non-oscillatory schemes
description	Classical fifth-order weighted essentially non-oscillatory (WENO) schemes are based on reconstructions from three consecutive second-order polynomials. They give a third-order accurate scheme when two consecutive polynomials are smooth and one is non-smooth. This situation means losing one order of accuracy if compared with a fourth-order scheme. In classical WENO schemes, weighting functions that determine the weights for the polynomials and that eventually define the reconstruction are directly related to a smoothness indicator. This property may lead to a non-zero residual of a very small value in the Taylor expansion. To handle this situation a weighting procedure that does not directly rely on the smoothness indicator is presented. Once the smooth polynomials are determined, the smoothness indicator has no role in the further steps, which are taken care of by a new switch function. Contrary to other approaches this switch function does not involve any conditional statements. A tuning parameter is also included so that the resulting order-adaptive property can be adjusted to specific requirements. The performance of the resulting schemes for cell-average and point-value reconstructions is studied. In addition, the effect of the choice of numerical flux or Riemann solver on these reconstruction strategies is analysed. Numerical tests for the Euler equations of gas dynamics in one and two space dimensions are presented. Improvements in resolution and the stability are found when compared with the conventional WENO techniques.
format	article
author	A. Arun Govind Neelan Manoj T. Nair Raimund Bürger
author_facet	A. Arun Govind Neelan Manoj T. Nair Raimund Bürger
author_sort	A. Arun Govind Neelan
title	Three-level order-adaptive weighted essentially non-oscillatory schemes
title_short	Three-level order-adaptive weighted essentially non-oscillatory schemes
title_full	Three-level order-adaptive weighted essentially non-oscillatory schemes
title_fullStr	Three-level order-adaptive weighted essentially non-oscillatory schemes
title_full_unstemmed	Three-level order-adaptive weighted essentially non-oscillatory schemes
title_sort	three-level order-adaptive weighted essentially non-oscillatory schemes
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/3f7023a379e04e95bbb0aa84deec14e2
work_keys_str_mv	AT aarungovindneelan threelevelorderadaptiveweightedessentiallynonoscillatoryschemes AT manojtnair threelevelorderadaptiveweightedessentiallynonoscillatoryschemes AT raimundburger threelevelorderadaptiveweightedessentiallynonoscillatoryschemes
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Three-level order-adaptive weighted essentially non-oscillatory schemes

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