Further improvement of weighted compact nonlinear scheme using compact nonlinear interpolation

Yan, Zhenguo; Liu, Huayong; Ma, Yankai; Mao, Meiliang; Deng, Xiaogang

doi:10.1016/j.compfluid.2017.06.028

Cited by 20 publications

(10 citation statements)

References 34 publications

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“…In 2008, two group [14,15] explored higher order WCNS and expanded the scheme to the ninth order, respectively. To further improve the resolution of the WCNS, Yan and Liu [17] developed the Y-type nonlinear weights and proposed a new seventh order compact nonlinear interpolation method based on the same stencil as the fifth order WENO scheme. To recover the optimal numerical resolution in smooth flow field, Zhang etc.…”

Section: Introductionmentioning

confidence: 99%

An Improved Third-order HWCNS for Compressible Flow Simulation on Curvilinear Grids

Cheng

Tang

Liu

et al. 2021

Preprint

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Due to the very high requirements on the quality of computational grids, stability property and computational efficiency, the application of high-order schemes to complex flow simulation is greatly constrained. In order to solve these problems, the third-order hybrid cell-edge and cell-node weighted compact nonlinear scheme(HWCNS3) is improved by introducing a new nonlinear weighting mechanism. The new scheme uses only the central stencil to reconstruct the cell boundary value, which makes the convergence of the scheme more stable. The application of the scheme to Euler equation on curvilinear grids is also discussed. Numerical results show that the new HWCNS3 achieves the expected order in smooth region, captures discontinuities sharply without obvious oscillation, has higher resolution than the original one and preserves freestream and vortex on curvilinear grids.

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Section: Introductionmentioning

confidence: 99%

An Improved Third-order HWCNS for Compressible Flow Simulation on Curvilinear Grids

Cheng

Tang

Liu

et al. 2021

Preprint

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“…Recently a class of weighted compact nonlinear schemes (WCNS's) as high order accurate shock-capturing schemes have been widely adopted to investigate compressible flows with shock waves and discontinuities [19,20,21,22,23,24,25]. The WCNS's first proposed by Deng and Zhang [19] and developed in [20,21,22,26] integrate WENO interpolation into the cell-centered compact schemes.…”

Section: Introductionmentioning

confidence: 99%

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

Jiang

Chen

Zhang

et al. 2020

Preprint

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The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe CFL restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization and a fifth-order WCNS is used for the spatial discretization. The designed semi-implicit WCNS is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed method.

show abstract

Section: Introductionmentioning

confidence: 99%

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

Jiang

Chen

Zhang

et al. 2020

Preprint

View full text Add to dashboard Cite

The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe Courant-Friedrichs-Levy (CFL) restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization of the split components and a fifth-order WCNS is used for the spatial discretizationof flux derivatives. The high order IMEX method is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressibleregimes are given to demonstrate the advantages of the designed IMEX WCNS.

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Further improvement of weighted compact nonlinear scheme using compact nonlinear interpolation

Cited by 20 publications

References 34 publications

An Improved Third-order HWCNS for Compressible Flow Simulation on Curvilinear Grids

An Improved Third-order HWCNS for Compressible Flow Simulation on Curvilinear Grids

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

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