An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws

Borges, Rafael Brandão de Rezende; Carmona, Monique; Costa, Bruno; Don, Wai Sun

doi:10.1016/j.jcp.2007.11.038

Cited by 1,149 publications

(1,038 citation statements)

References 8 publications

(35 reference statements)

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“…ence of scales of distinct weights at non-smooth parts of the solution. As pointed out by Borges et al [6], for a smooth function, increasing the value of q in Eq. (12) decreases the correction of the WENO-Z weights to the ideal weights d k , making the scheme closer to the optimal central scheme.…”

Section: Weighted Essentially Non-oscillatory Schemesmentioning

confidence: 75%

“…The method combines the idea of the step-by-step construction of a higher order WENO scheme [10] and the properties of s 5 introduced by Borges et al [6]. For completeness, two important properties of s 5 are listed here:…”

Section: The New Methodsmentioning

confidence: 99%

“…Let us have a look at a numerical example of a discontinuous function [6] uð0; xÞ ¼ f ðxÞ ¼ ÀsinðpxÞ À 1 2…”

Section: ðIþ3þà1=2mentioning

confidence: 99%

“…A mapping function is proposed by Henrick et al [5] to obtain the optimal order near critical points. Borges et al [6] devise a new set of WENO weights that satisfies the necessary and sufficient conditions for fifth-order convergence given by Henrick et al [5] and enhances the accuracy at critical points. A class of higher than fifth order weighted essentially non-oscillatory schemes are designed by Balsara and Shu in [7].…”

Section: Introductionmentioning

confidence: 99%

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Improvement of Weighted Essentially Non-Oscillatory Schemes Near Discontinuities

Shen

Zha

2009

19th AIAA Computational Fluid Dynamics

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a b s t r a c tIn this article, we analyze the fifth-order weighted essentially non-oscillatory (WENO-5) scheme and show that, at a transition point from smooth region to a discontinuity point or vice versa, the accuracy order of WENO-5 is decreased to third order. A new method is proposed to overcome this drawback by introducing fourth-order fluxes combined with high order smoothness indicator. Numerical examples show that the new method is more accurate near discontinuities with accuracy improved to fourth order.

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Section: Weighted Essentially Non-oscillatory Schemesmentioning

confidence: 75%

Section: The New Methodsmentioning

confidence: 99%

“…Let us have a look at a numerical example of a discontinuous function [6] uð0; xÞ ¼ f ðxÞ ¼ ÀsinðpxÞ À 1 2…”

Section: ðIþ3þà1=2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improvement of Weighted Essentially Non-Oscillatory Schemes Near Discontinuities

Shen

Zha

2009

19th AIAA Computational Fluid Dynamics

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“…A mapping function is proposed by Henrick et al [10] to obtain the optimal order near critical points. Borges et al [11] devised a new set of WENO weights that satisfies the necessary and sufficient conditions for fifth-order convergence proposed by Henrick et al [10] and enhances the accuracy at critical points. Wang and Chen [12] proposed optimized WENO schemes for linear waves with discontinuity.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Drag Prediction Using RANS models and DDES for the DLR-F6 Configuration Using High Order Schemes

Gan

Shen

Zha

2016

54th AIAA Aerospace Sciences Meeting

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This paper compares the accuracy and robustness of steady state RANS, unsteady RANS, and DDES turbulence models with high order schemes for predicting the drag of the DLR-F6 configuration. The implicit time marching method with unfactored Gauss-Seidel line relaxation is used with a 5th order WENO finite difference scheme for Navier-Stokes equations. The viscous terms are discretized using a 4th order conservative central differencing. The effect of grid size on the accuracy of drag prediction by using the different turbulent models are conducted on the coarse, medium and fine mesh models at the same angle of attack. The coarse mesh has about 10 drag counts deviation from the experiment, the medium mesh has 28 counts, and the fine mesh has about 15 counts difference. The RANS method achieves almost the same results as URANS and DDES at angle of attack of 0.49• . The DDES have the least deviation from the experimental drag result and the closest pressure distribution to the experiment in the trailing edge separation zone. However, since the DDES uses the same mesh as the RANS model in this paper, the DDES results should not be considered as conclusive.

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Computational Electromagnetic‐Aerodynamics

Shang¹

2016

Computational Electromagneticaerodynamics

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An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws

Cited by 1,149 publications

References 8 publications

Improvement of Weighted Essentially Non-Oscillatory Schemes Near Discontinuities

Improvement of Weighted Essentially Non-Oscillatory Schemes Near Discontinuities

Comparison of Drag Prediction Using RANS models and DDES for the DLR-F6 Configuration Using High Order Schemes

Computational Electromagnetic‐Aerodynamics

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