New High-Order Hybrid Cell-Edge and Cell-Node Weighted Compact Nonlinear Schemes

Deng, Xiaogang; Mao, Meiliang; Jiang, Yi; Liu, Huayong

doi:10.2514/6.2011-3857

Cited by 43 publications

(21 citation statements)

References 6 publications

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“…15) In the positivity limiter procedure, 16) the first-order positivity preserving flux of Lax-Friedrich is blended with the original AWENO flux for the region where the particle density possibly becomes negative. 9) For time advancement, the third-order total variation diminishing Runge-Kutta scheme 17) was employed.…”

Section: Methodsmentioning

confidence: 99%

Computational Analysis of Compressible Gas-Particle-Multiphase Turbulent Mixing Layer in Euler-Euler Formulation

Terakado

Nagata

Nonomura

et al. 2016

AEROSPACE TECHNOLOGY JAPAN

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Effects of solid particles in the gas-particle multiphase compressible turbulent mixing layer were investigated by direct numerical simulation, compared with the single phase turbulent mixing layer of which the net density ratio (sum of gas and particle densities) was set to be the same as the multiphase case. Here, the situation of solid rocket motor was considered, so that the Mach number and the density (temperature) ratio were set to be high and far from unity, respectively, and the solid particles were distributed only in one side of the mixing layer for the initial condition. Three-dimensional compressible gas-particle-multiphase Navier-Stokes equations in the Euler-Euler formulation were solved with an alternative weighted essentially non-oscillatory scheme with a positivity preserving limiter of the particle density for the multiphase flow computation. It was found that the existence of solid particles leads to the sparse structures of turbulence and suppresses the fine scale turbulent structures, especially for the JET side, which corresponds to the side where particles were initially distributed and the gas density was low. The growth rate of the mixing layer thickness for multiphase flow became smaller due to the change in flow. The change in flow structures also affected the properties of acoustic waves. The Mach wave like structures do not appear for the initially particle existing side for the multiphase flow due to the suppression of fine scale turbulent structures, compared with single phase flow.

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Section: Methodsmentioning

confidence: 99%

Computational Analysis of Compressible Gas-Particle-Multiphase Turbulent Mixing Layer in Euler-Euler Formulation

Terakado

Nagata

Nonomura

et al. 2016

AEROSPACE TECHNOLOGY JAPAN

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“…Nevertheless, it is well known that the abovementioned schemes can fail when applied to flow problems involving severe discontinuities, motivating several recent studies that focused on improving the robustness of these schemes [18,19,20,21]. For the finite difference WENO scheme, Zhang et al [18] and Hu et al [19] proposed flux-limiting methods to enforce positivity-preserving properties.…”

Section: Accepted Manuscriptmentioning

confidence: 97%

“…Nonomura et al [20] proposed a new cell-edge-and cell-node-type explicit finite difference scheme and confirmed that this scheme improves the positivity of the WCNS; however, they found that negative pressures still occur in extremely severe situations. Deng et al [21] proposed another cell-edge-and cell-node-type explicit difference ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T scheme for improving the WCNS robustness; however, they did not sufficiently verify whether the scheme preserves the positivity of both density and pressure for severe benchmark problems.…”

Section: Accepted Manuscriptmentioning

confidence: 98%

“…Previous studies by Nonomura et al [20] and Deng et al [21] suggested that use of fluxes on both the cell edge and cell node in the central finite differencing step is essential for improving the WCNS robustness. Therefore, we developed a new cell-node-and cell-edge-type alternate central compact scheme (ACCS) with a control parameter for robustness.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…We now consider the 1D Mach 3 shock entropy wave interaction problem [2,5,6,12,20,21,28]. are shown in Fig.…”

Section: D Problem With High-frequency Structures Behind a Moving Shmentioning

confidence: 99%

See 2 more Smart Citations

A new central compact finite difference formula for improving robustness in weighted compact nonlinear schemes

Sumi

Kurotaki

2015

Computers & Fluids

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A third‐order compact nonlinear scheme for compressible flow simulations

Tian

Wang

Zhang

et al. 2020

Numerical Methods in Fluids

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Summary Reynolds‐averaged Navier‐Stokes simulations based on second‐order numerical methods are widely used by commercial codes and work as dominating tools for most industrial applications. They, however, suffer from limitations in accurate and reliable predictions of skin‐friction drag and aerodynamic heating, as well as in simulations of complex flows such as large‐scale separation and transition. A remedy for this is the development of high‐order schemes, by which numerically induced dissipation and dispersion errors of low‐order schemes can be effectively reduced. Weighted compact nonlinear schemes (WCNSs) are a family of high‐resolution nonlinear shock‐capturing methods. A stencil‐selection procedure is introduced in the proposed work with an aim to improve the nonlinear weight of the third‐order WCNS. By using the approximate dispersion relation analysis, it is demonstrated that the new scheme has reduced dissipation and dispersion errors, compared with WCNSs using two typical nonlinear weights. Improvements are also achieved by the new scheme in numerical tests such as the double Mach reflection problem and the Rayleigh‐Taylor instability simulation, which are characterized by strong shock discontinuities and rich small scales, respectively. The new scheme is therefore highly favored in the simulation of flow problems involving strong discontinuities and multiscales phenomena.

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New High-Order Hybrid Cell-Edge and Cell-Node Weighted Compact Nonlinear Schemes

Cited by 43 publications

References 6 publications

Computational Analysis of Compressible Gas-Particle-Multiphase Turbulent Mixing Layer in Euler-Euler Formulation

Computational Analysis of Compressible Gas-Particle-Multiphase Turbulent Mixing Layer in Euler-Euler Formulation

A new central compact finite difference formula for improving robustness in weighted compact nonlinear schemes

A third‐order compact nonlinear scheme for compressible flow simulations

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