Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy

@article{Balsara2000MonotonicityPW,
  title={Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy},
  author={Dinshaw S. Balsara and Chi-Wang Shu},
  journal={Journal of Computational Physics},
  year={2000},
  volume={160},
  pages={405-452}
}
In this paper we design a class of numerical schemes that are higher-order extensions of the weighted essentially non-oscillatory (WENO) schemes of G.-S. Jiang and C.-W. Shu (1996) and X.-D. Liu, S. Osher, and T. Chan (1994). Used by themselves, the schemes may not always be monotonicity preserving but coupled with the monotonicity preserving bounds of A. Suresh and H. T. Huynh (1997) they perform very well. The resulting monotonicity preserving weighted essentially non-oscillatory (MPWENO… 
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References

SHOWING 1-10 OF 63 REFERENCES
Accurate Monotonicity-Preserving Schemes with Runge-Kutta Time Stepping
TLDR
A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented, designed to preserve accuracy near extrema and to work well with Runge?Kutta time stepping.
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
TLDR
The construction, analysis, and application of ENO and WENO schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations are described, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil.
Finite-volume implementation of high-order essentially nonoscillatory schemes in two dimensions
We continue the study of the finite-volume application of high-order-ac curate, essentially nonoscillatory shock-capturing schemes to two-dimension al initial-bound ary-value problems. These schemes
Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws
In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation
Weighted essentially non-oscillatory schemes
TLDR
A new version of ENO (essentially non-oscillatory) shock-capturing schemes which is called weighted ENO, where, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, a convex combination of all candidates is used.
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Efficient Implementation of Weighted ENO Schemes
TLDR
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.
A comparison of two formulations for high-order accurate essentially non-oscillatory schemes
The finite volume and finite difference implementations of high-order accurate essentially nonoscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order
...
1
2
3
4
5
...