一种光滑型TENO非线性加权的WCNS格式

doi:10.7527/S1000-6893.2023.29052

Abstract

Abstract:

Compressible turbulent flow widely exists in the aerospace field， and the coexistence of shock discontinuity and multi-scale turbulence in the flow field poses a challenge for high-precision numerical simulation. To improve the accuracy of complex turbulence simulation， in the framework of the Weighted Compact Nonlinear Scheme （WCNS）， a WCNS-T scheme based on the Targeted Essentially Non-Oscillatory （TENO） weighting strategy is developed， and a smooth S-TENO nonlinear weighting method and its WCNS-ST scheme are further proposed from the perspectives of both numerical convergence and accuracy. The developed WCNS-ST scheme is tested for its ability to capture discontinuous and high-frequency waves through spectral analysis， one-dimensional Lax and Osher-Shu examples， and two-dimensional dual Mach reflection examples. Based on further numerical tests of steady laminar flow past a circular cylinder and unsteady self-adaptive turbulence eddy simulation of a 30P30N multi-element airfoil， the convergence characteristics of the original TENO weighting and the current S-TENO weighting in viscous complex flows， as well as their impact on numerical calculation results， are compared. The results show that the proposed S-TENO nonlinear weighting maintains the dispersion and dissipation characteristics of the original TENO nonlinear weighting and its ability to capture shock waves， significantly improving the problem of excessive nonlinear dissipation in WCNS-JS and WCNS-Z schemes； meanwhile， S-TENO nonlinear weighting significantly eases the convergence difficulties caused by weight discontinuity in the original TENO nonlinear weighting. The above results indicate that the proposed smooth S-TENO nonlinear weighting and its WCNS-ST scheme take into account both accuracy and convergence in numerical simulations of complex flow configurations， making them more suitable for complex engineering applications.

Key words: weighted compact nonlinear scheme, targeted essentially non-oscillatory, nonlinear weighting, compressible turbulence simulation, high-order accurate finite differencing method

CLC Number:

V211.3

Wenchang WU, Yankai MA, Xingsi HAN, Yaobing MIN, Zhenguo YAN. Smooth TENO nonlinear weighting for WCNS scheme[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(8): 129052-129052.

Figures/Tables 16

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非线性加权	时均阻力系数	阻力系数均方根	阻力系数均方根变化/%	CPU计算时间增量/%
WCNS-JS	1.363 27	0.006 42	-3.46	+5.8
WCNS-Z	1.363 89	0.006 41	-3.61	+9.2
WCNS-T	1.364 06	0.009 61	+44.5	+13.0
WCNS-ST	1.364 26	0.006 65	0	+11.4
Linear	1.364 28	0.006 65		0

非线性加权	时均升力系数	时均阻力系数	升力系数误差/%	CPU计算时间增量/%
WCNS-JS	2.36	0.075	-16.9	+3.1
WCNS-Z	2.64	0.074	-7.04	+3.5
WCNS-T	2.80	0.063	-1.41	+6.4
WCNS-ST	2.84	0.066	0	+6.3
Linear	2.82	0.07	-0.7	0
实验结果^［42］	2.84

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Smooth TENO nonlinear weighting for WCNS scheme

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