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… 

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References

SHOWING 1-10 OF 12 REFERENCES

ENO schemes with subcell resolution

Multi-Dimensional ENO Schemes for General Geometries

A class of shock-capturing schemes which are designed to compute cell-averages to high-order accuracy and based on an adaptive selection of stencil for each cell so as to avoid spurious oscillations near discontinuities while achieving high order of accuracy away from them.

Uniformly High-Order Accurate Nonoscillatory Schemes. I

A uniformly second-order approximation of hyperbolic conservation laws is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.

Efficient Implementation of Weighted ENO Schemes

A new way of measuring the smoothness of a numerical solution is proposed, emulating the idea of minimizing the total variation of the approximation, which results in a fifth-order WENO scheme for the caser= 3, instead of the fourth-order with the original smoothness measurement by Liuet al.

Numerical experiments on the accuracy of ENO and modified ENO schemes

In this paper we make further numerical experiments assessing an accuracy degeneracy phenomena reported by A. Rogerson and E. Meiburg (this issue, 1990). We also propose a modified ENO scheme, which

A numerical study of the convergence properties of ENO schemes

We report numerical results obtained with finite difference ENO schemes for the model problem of the linear convection equation with periodic boundary conditions. For the test function sin(x), the

Uniformly high order accuracy essentially non-oscillatory schemes III

The construction and the analysis of essentially non-oscillatoryshockcapturingmethodsfortheapproximation ofhyper-bolicconservationlaws and the resulting schemes are highly nonlinear.

Commun

  • Pure Appl. Math. 46, 1
  • 1986

J. Comput. Phys

  • J. Comput. Phys
  • 1978