An improved weighted essentially non-oscillatory scheme with a new smoothness indicator

Ha, Youngsoo; Kim, Chang Ho; Lee, Yeon Ju; Yoon, Jungho

doi:10.1016/j.jcp.2012.06.016

Cited by 138 publications

(96 citation statements)

References 21 publications

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“…Before proceeding, we must observe that there are many variants of the WENO reconstructions described above (for example in [61][62][63][64]) and this investigation is by no means exhaustive. The different variants of the WENO reconstructions have all been developed as a response to demands of either different orders of accuracy [65,66] or reduced computational expense.…”

Section: Weno Reconstructionsmentioning

confidence: 99%

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

Maulik

San

2017

Fluids

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Solving two-dimensional compressible turbulence problems up to a resolution of 16, 384 2 , this paper investigates the characteristics of two promising computational approaches: (i) an implicit or numerical large eddy simulation (ILES) framework using an upwind-biased fifth-order weighted essentially non-oscillatory (WENO) reconstruction algorithm equipped with several Riemann solvers, and (ii) a central sixth-order reconstruction framework combined with various linear and nonlinear explicit low-pass spatial filtering processes. Our primary aim is to quantify the dissipative behavior, resolution characteristics, shock capturing ability and computational expenditure for each approach utilizing a systematic analysis with respect to its modeling parameters or parameterizations. The relative advantages and disadvantages of both approaches are addressed for solving a stratified Kelvin-Helmholtz instability shear layer problem as well as a canonical Riemann problem with the interaction of four shocks. The comparisons are both qualitative and quantitative, using visualizations of the spatial structure of the flow and energy spectra, respectively. We observe that the central scheme, with relaxation filtering, offers a competitive approach to ILES and is much more computationally efficient than WENO-based schemes.

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Section: Weno Reconstructionsmentioning

confidence: 99%

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

Maulik

San

2017

Fluids

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“…It measures the regularity of the solution on each three-point substencil S k ( j) by estimating the approximate magnitude of its derivatives. Specifically, the smoothness indicator β k in [10] …”

Section: Smoothness Indicatormentioning

confidence: 99%

“…(3.5) is applied to f j−1/2 in a symmetric way. The readers are referred to the article [10] for more details.…”

Section: Smoothness Indicatormentioning

confidence: 99%

“…Remark 3.1 When constructing the global smoothness measurement, the WENO-NS uses an additional contribution term which measures the solution smoothness on the stencil S 1 ( j) [10]. However, instead of using this measurement, the proposed method adjusts the contribution of each substencil.…”

Section: A New Nonlinear Weightmentioning

confidence: 99%

“…The WENO-M and WENO-Z schemes are devised through a novel utilization of the known smoothness indicators of WENO-JS. Very recently, another version of a smoothness indicator based on L 1 -norm has been proposed in [10]. This WENO scheme (WENO-NS) has the fifth order accuracy and yields an improved behavior in compared to other fifth-order WENO schemes, but finding optimal internal parameters in WENO-NS weights is rather complicated.…”

Section: Introductionmentioning

confidence: 99%

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Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes

Kim

Yoon

2015

J Sci Comput

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This paper is concerned with fifth-order weighted essentially non-oscillatory (WENO) scheme with a new smoothness indicator. As the so-called WENO-JS scheme (Jiang and Shu in J Comput Phys 126:202-228, 1996) provides the third-order accuracy at critical points where the first and third order derivatives do not becomes zero simultaneously, several fifth-order WENO scheme have been developed through modifying the known smoothness indicators of WENO-JS. Recently a smoothness indicator based on L 1 -norm has been proposed by Ha et al. (J Comput Phys 232:68-86, 2013) (denoted by WENO-NS). The aim of this paper is twofold. Firstly, we further improve the smoothness indicator of WENO-NS and secondly, using this measurement, we suggest new nonlinear weights by simplifying WENO-NS weights. The proposed WENO scheme provides the fifth-order accuracy, even at critical points. Some numerical experiments are provided to demonstrate that the present scheme performs better than other WENO schemes of the same order.

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Third‐order WENO scheme with a new smoothness indicator

Gande

Rathod

Rathan

2017

Numerical Methods in Fluids

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Summary In this article, we have devised a new reference smoothness indicator for third‐order weighted essentially non‐oscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially non‐oscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the third‐order convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on three‐point stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier third‐order WENO schemes like WENO‐JS and WENO‐Z. Copyright © 2017 John Wiley & Sons, Ltd.

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An improved weighted essentially non-oscillatory scheme with a new smoothness indicator

Cited by 138 publications

References 21 publications

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes

Third‐order WENO scheme with a new smoothness indicator

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