# Weighted essentially non-oscillatory schemes

@article{Liu1994WeightedEN, title={Weighted essentially non-oscillatory schemes}, author={Xu-Dong Liu and S. Osher and Tony F. Chan}, journal={Journal of Computational Physics}, year={1994}, volume={115}, pages={200-212} }

Abstract 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…

## 2,957 Citations

### The 6th-order weighted ENO schemes for hyperbolic conservation laws

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### Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws

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The basic formulation of ENO and WENO schemes is reviewed, the main ideas in constructing the schemes are outlined and several of recent developments in using the schemes to solve hyperbolic type PDE problems are discussed.

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The numerical experiments show that modifying coefficient ENO scheme is more efficient and of higher accuracy in smooth regions when compared with ENO Scheme.

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Abstract In this paper a new class of finite difference schemes - the Weighted Compact Schemes are proposed. According to the idea of the WENO schemes, the Weighted Compact Scheme is constructed by a…

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A new scheme that combines essentially non-oscillatory (ENO) reconstructions together with monotone upwind schemes for scalar conservation laws interpolants and avoids spurious oscillations while using a simple componentwise extension for solving hyperbolic systems is presented.

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This paper investigates the performance of a class of the hybrid weighted essentially non-oscillatory (WENO) schemes with Lax-Wendroff time discretization procedure using different indicators for hyperbolic conservation laws to reduce computational cost and robustness.

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