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On the Efficient Computation of Smoothness Indicators for a Class of WENO Reconstructions

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Abstract

Common smoothness indicators used in Weighted Essentially Non-Oscillatory (WENO) reconstructions (Jiang and Shu in J Comput Phys 126:202–228, 1996) have quadratic cost with respect to the order. A set of novel smoothness indicators with linear cost of computation with respect to the order is presented. These smoothness indicators can be used in the context of schemes of the type introduced by Yamaleev and Carpenter (Yamaleev and Carpenter in J Comput Phys 228(11):4248–4272, 2009). The accuracy properties of the resulting non-linear weights are the same as those arising from using the traditional Jiang-Shu smoothness indicators in Yamaleev-Carpenter-type reconstructions. The increase of the efficiency and ease of implementation are shown.

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Acknowledgements

AB, PM and DZ are supported by Spanish MINECO project MTM2017-83942-P. RB is supported by CONICYT/PIA/Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal AFB170001; Fondecyt project 1170473; and CRHIAM, project CONICYT/FONDAP/15130015. PM is also supported by Conicyt (Chile), project PAI-MEC, folio 80150006. DZ is also supported by Conicyt (Chile) through Fondecyt project 3170077.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat de València, 46100, Burjassot, Spain

    Antonio Baeza & Pep Mulet

  2. CI2MA & Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Raimund Bürger

  3. CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    David Zorío

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  1. Antonio Baeza
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  2. Raimund Bürger
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Correspondence to David Zorío.

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Baeza, A., Bürger, R., Mulet, P. et al. On the Efficient Computation of Smoothness Indicators for a Class of WENO Reconstructions. J Sci Comput 80, 1240–1263 (2019). https://doi.org/10.1007/s10915-019-00974-7

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  • DOI: https://doi.org/10.1007/s10915-019-00974-7

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