In this paper we introduce a new version of ENO (essentially non-oscillatory) shock-capturing schemes which we call weighted ENO. The main new idea is that, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, we use a convex combination of all candidates to achieve the essentially non-oscillatory property, while additionally obtaining one order of improvement in accuracy. The resulting weighted ENO schemes are based on cell averages and a TVD Runge-Kutta time discretization. Preliminary encouraging numerical experiments are given. © 1994 Academic Press. All rights reserved.
CITATION STYLE
Liu, X. D. (1994). Weighted essentially non-oscillatory schemes. Journal of Computational Physics, 115(1), 200–212. https://doi.org/10.1006/jcph.1994.1187
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