A Parameter-free ε-adaptive Algorithm for Improving High-Order Weighted Compact Nonlinear Schemes

Zheng, Shichao; Deng, Xiaogang; Wang, Dongfang; Zeng, Mingyong

doi:10.3850/978-981-11-2730-4_0233-cd

Cited by 1 publication

(11 citation statements)

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“…For the WENO-Z scheme with q = 2, if = Ω(h 4 ), it can also achieve optimal order accuracy regardless of critical points, otherwise the scheme will lose accuracy at critical points above first-order (n cp > 1) [6]. This conclusion also applies to the WCNS scheme [18]. This adaptive algorithm chooses the low power-function of grid spacing for to make it large enough to cover up the difference of smoothness indicators near critical points, thus avoiding loss of accuracy.…”

Section: Discussion Onmentioning

confidence: 83%

“…To further attenuate numerical oscillations, another kind of -adaptive algorithm based on smoothness indicators is developed [16][17][18]. A recently proposed parameter-free -adaptive algorithm [18] has the following form adp = β ave β min β std (15) where…”

Section: Discussion Onmentioning

confidence: 99%

“…To achieve high-order accuracy in smooth regions and suppress numerical oscillations near discontinuities, should be chosen according to following two criteria [12,18] (1) In smooth regions, the smoothness indicator β k of each sub-stencil is uniformly small.…”

Section: New -Adaptive Algorithmsmentioning

confidence: 99%

“…Since then, a series of improved and optimized schemes [6][7][8][9][10][11] were developed based on these two representative works. Meanwhile, some researchers [4,6,[12][13][14][15][16][17][18] paid attention to the small quantity in weight functions to further improve the performance of schemes.…”

Section: Introductionmentioning

confidence: 99%

“…However, this adaptive algorithm contains four free empirical parameters to be manually adjusted in practical computations, which hinders the application and popularization of the algorithm. Recently, Zheng et al [18] proposed a parameter-free -adaptive algorithm, which can help reduce numerical dissipation in smooth regions, suppress numerical oscillations near discontinuities, and lessen susceptibility to flux functions and interpolation variables. Unfortunately, these adaptive algorithms will inevitably lose accuracy near critical points due to the large relative disparity in smoothness indicators of sub-stencils.…”

Section: Introductionmentioning

confidence: 99%

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A New ϵ-Adaptive Algorithm for Improving Weighted Compact Nonlinear Scheme with Applications

et al. 2022

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To improve the resolution and accuracy of the high-order weighted compact nonlinear scheme (WCNS), a new ϵ-adaptive algorithm based on local smoothness indicators is proposed. The new algorithm introduces a high-order global smoothness indicator to adjust the value of ϵ according to the local flow characteristics. Specifically, the algorithm increases ϵ in smooth regions, which can help cover up the disparity in smoothness indicators of sub-stencils and make the nonlinear scheme approach the background linear scheme. As a result, optimal order accuracy can be achieved in smooth regions, including critical points. While near discontinuities, the algorithm decreases ϵ, thereby strengthening the stencil selection mechanism and further attenuating spurious oscillations. Meanwhile, the new algorithm makes nonlinear schemes scale-invariant of flow variables. The results of approximate dispersion relation (ADR) show that the new algorithm can greatly reduce spectral errors of nonlinear schemes in the medium and low wavenumber range without inducing instability. Numerical results indicate that the new algorithm can significantly improve resolution of small-scale structures and suppress numerical oscillations near discontinuities with only a minor increment in computational cost.

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Section: Discussion Onmentioning

confidence: 83%