Journal ArticleDOI
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.About:
This article is published in Journal of Computational Physics.The article was published on 1994-11-01. It has received 3023 citations till now. The article focuses on the topics: Compact stencil & Convex combination.read more
Citations
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Book
Finite Volume Methods for Hyperbolic Problems
TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.
Book ChapterDOI
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
TL;DR: In this paper, the authors describe the construction, analysis, and application of ENO and WENO schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations, where the key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible.
Journal ArticleDOI
Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy
Dinshaw S. Balsara,Chi-Wang Shu +1 more
TL;DR: In this paper, 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. T. Chan (1994) are presented.
Journal ArticleDOI
Weighted ENO Schemes for Hamilton--Jacobi Equations
Guang-Shan Jiang,Danping Peng +1 more
TL;DR: A weighted ENO scheme is presented to approximate the viscosity solution of the Hamilton--Jacobi equation and can be as high as fifth order accurate in the smooth part of the solution.
Journal ArticleDOI
High-order CFD methods: Current status and perspective
Zhijian J Wang,Krzysztof J. Fidkowski,Rémi Abgrall,Francesco Bassi,Doru Caraeni,Andrew Cary,Herman Deconinck,Ralf Hartmann,Koen Hillewaert,H. T. Huynh,Norbert Kroll,Georg May,Per-Olof Persson,Bram van Leer,Miguel R. Visbal +14 more
TL;DR: The 1st International Workshop on High-Order CFD Methods was successfully held in Nashville, Tennessee, on January 7-8, 2012, just before the 50th Aerospace Sciences Meeting as mentioned in this paper.
References
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Journal ArticleDOI
Efficient Implementation of Weighted ENO Schemes
Guang-Shan Jiang,Chi-Wang Shu +1 more
TL;DR: 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.
Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Chi-Wang Shu,Stanley Osher +1 more
TL;DR: Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations.
Journal ArticleDOI
Uniformly high-order accurate nonoscillatory schemes
Ami Harten,Stanley Osher +1 more
TL;DR: 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.
Journal ArticleDOI
ENO schemes with subcell resolution
TL;DR: In this article, the notion of subcell resolution is introduced, which is based on the observation that unlike point values, cell-averages of a discontinuous piecewise-smooth function contain information about the exact location of the discontinuity within the cell.
Journal ArticleDOI
Numerical experiments on the accuracy of ENO and modified ENO schemes
TL;DR: In this article, a modified essentially nonoscillatory (ENO) scheme is proposed, which recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives comparable results with the original ENO schemes for discontinuous problems.
Related Papers (5)
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Chi-Wang Shu,Stanley Osher +1 more