Improved weighted compact nonlinear scheme for implicit large-eddy simulations

Ma, Yankai; Yan, Zhenguo; Liu, Huayong; Min, Yaobing; Zhu, Hehua

doi:10.1016/j.compfluid.2022.105412

Cited by 6 publications

(1 citation statement)

References 44 publications

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“…Another branch of nonlinear weighted schemes is the weighted compact nonlinear scheme (WCNS) [7,[17][18][19], which is the scheme the current research is based on. It was summarized to have a series of advantages over the WENO schemes [2].…”

Section: Introductionmentioning

confidence: 99%

Improvement of Z-Weighted Function Based on Fifth-Order Nonlinear Multi-Order Weighted Method for Shock Capturing of Hyperbolic Conservation Laws

Bai,

Yan,

Mao

et al. 2024

Entropy

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Based on a 5-point stencil and three 3-point stencils, a nonlinear multi-order weighted method adaptive to 5-3-3-3 stencils for shock capturing is presented in this paper. The form of the weighting function is the same as JS (Jiang–Shu) weighting; however, the smoothness indicator of the 5-point stencil adopts a special design with a higher-order leading term similar to the τ in Z weighting. The design maintains that the nonlinear weights satisfy sufficient conditions for the scheme to avoid degradation even near extreme points. By adjusting the linear weights to a specific value and using the τ in Z weighting, the method can be degraded to Z weighting. Analysis of linear weights shows that they do not affect the accuracy in the smooth region, and they can also adjust the resolution and discontinuity-capturing capability. Numerical tests of different hyperbolic conservation laws are conducted to test the performance of the newly designed nonlinear weights based on the weighted compact nonlinear scheme. The numerical results show that there are no obvious oscillations near the discontinuity, and the resolution of both the discontinuity and smooth regions is better than that of Z weights.

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