光滑型TENO非线性加权六阶低耗散WCNS-CU6-ST格式

doi:10.7527/S1000-6893.2024.30598

Abstract

Abstract:

The flow environment of spacecraft involves complex flow phenomena such as shock waves and turbulence. The coexistence of shock wave discontinuities and multiscale turbulent structures in the flow field poses significant challenges to high-order accurate numerical simulations. To effectively reduce numerical dissipation in turbulence simulations， a sixth-order central/fifth-order upwind linear hybrid interpolation was developed under the framework of Weighted Compact Nonlinear Scheme （WCNS）. Considering the high-resolution shock capturing characteristics， the scale separation strategy in the TENO scheme is used to develop nonlinear weight functions. For the numerical convergence of the numerical scheme， a smooth S-TENO nonlinear weight function is further developed. Through Approximate Dispersion Relations （ADR）， one-dimensional convection problems， and self-adaptive turbulence eddy simulation of three-dimensional channel， it was found that the linear stencil using a sixth-order central/fifth-order upwind linear hybrid interpolation stencil can significantly reduce the numerical dissipation of the scheme， thereby improving the prediction accuracy of channel flow and transonic flow past an airfoil. The proposed smooth S-TENO nonlinear weight not only maintains the good dispersion and dissipation properties of the original TENO nonlinear weight， but also significantly improves the numerical convergence in the cases of shock wave/turbulent boundary layer interaction when transonic flow past an airfoil， thus improving the accuracy of computational results. The numerical results indicate that the optimized sixth-order low-dissipation WCNS-CU6-ST scheme based on smooth S-TENO weight can achieve both low numerical dissipation and good convergence， which is helpful to improve the accuracy of simulations in complex shock/turbulence problems.

Key words: high-order accurate numerical scheme, finite differencing method, nonlinear weight function, shock capturing, turbulence simulation, numerical dissipation, numerical convergence

CLC Number:

V211.3

Wenchang WU, Xingsi HAN, Yaobing MIN, Zhenguo YAN, Yankai MA. Sixth-order low-dissipation WCNS-CU6-ST scheme based on smooth TENO nonlinear weight[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(S1): 730598.

Figures/Tables 11

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Sixth-order low-dissipation WCNS-CU6-ST scheme based on smooth TENO nonlinear weight

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