Abstract
A novel central weighted essentially non-oscillatory (central WENO; CWENO)-type scheme for the construction of high-resolution approximations to discontinuous solutions to hyperbolic systems of conservation laws is presented. This procedure is based on the construction of a global average weight using the whole set of Jiang–Shu smoothness indicators associated to every candidate stencil. By this device one does not to have to rely on ideal weights, which, under certain stencil arrangements and interpolating point locations, do not define a convex combination of the lower-degree interpolating polynomials of the corresponding sub-stencils. Moreover, this procedure also prevents some cases of accuracy loss near smooth extrema that are experienced by classical WENO and CWENO schemes. These properties result in a more flexible scheme that overcomes these issues, at the cost of only a few additional computations with respect to classical WENO schemes and with a smaller cost than classical CWENO schemes. Numerical examples illustrate that the proposed CWENO schemes outperform both the traditional WENO and the original CWENO schemes.
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Acknowledgements
AB, PM and DZ are supported by Spanish MINECO project MTM2017-83942-P. RB is supported by Fondecyt project 1170473; CRHIAM, project CONICYT/FONDAP/15130015; and CONICYT/PIA/Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal AFB170001. 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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Baeza, A., Bürger, R., Mulet, P. et al. Central WENO Schemes Through a Global Average Weight. J Sci Comput 78, 499–530 (2019). https://doi.org/10.1007/s10915-018-0773-z
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DOI: https://doi.org/10.1007/s10915-018-0773-z