An efficient hybrid multi-resolution WCNS scheme for solving compressible flows

Wang, Zhenming; Zhu, Jun; Wang, Chunwu; Zhao, Ning

doi:10.1016/j.jcp.2022.111877

Cited by 5 publications

(2 citation statements)

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“…The results of MOZ weighting exhibit better resolution compared to Z weighting. Example 5: A Richtmyer-Meshkova instability problem [31] has initial conditions of…”

Section: Two-dimensional Euler Equationsmentioning

confidence: 99%

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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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“…The results of MOZ weighting exhibit better resolution compared to Z weighting. Example 5: A Richtmyer-Meshkova instability problem [31] has initial conditions of…”

Section: Two-dimensional Euler Equationsmentioning

confidence: 99%

“…However, there are still significant non-physical oscillations near strong discontinuities. Wang [31] further improved the efficiency of the WCNS-MR scheme. In the above research, except for the 5-point sub-stencil, the interpolation accuracy of the remaining sub-stencils is very low.…”

Section: Introductionmentioning

confidence: 99%