一种基于幅值和波数的耗散控制方法

doi:10.7527/S1000-6893.2022.26589

Abstract

Abstract:

The shock capture scheme can adaptively control the dissipation according to the smoothness of the local flow field to suppress the small-scale non-physical fluctuations and resolve large-scale flow structures. In order to better identify the small-scale non-physical fluctuations produced in the shock capture process， and then more accurately control dissipation， this paper proposes a dissipation control method based on amplitude and wavenumber of the local flow field. For problems with strong unsteadiness， such as shock-dominated or isotropic turbulence problems， according to the one-dimensional unsteady Euler equation， the relationship between different physical quantities at small scales is derived， and the threshold of the small-scale fluctuation amplitude are determined by numerical experiments or Kolmogorov scale theory. Finally， based on Fourier analysis and the threshold of the small-scale fluctuation amplitude， the relationship between the magnitude of the dissipation， and the amplitude and wavenumber of the local flow field is established. In order to obtain the shock-capturing capability， the scheme is hybridized with the TENO（Targeted Essentially Non-Oscillatory） scheme to form a hybrid scheme. A series of benchmark examples involving shocks or turbulence show that this scheme produces small-scale nonphysical fluctuations with lower wavenumbers， smaller amplitudes， and better resolution of large-scale flow structures during computations.

Key words: Kolmogorov scale, compressible flow, isotropic turbulence, dissipation control, shock capture scheme

CLC Number:

V211.3

Huangsheng WEI, Zhu HUANG, Guang XI. A dissipation control method based on amplitude and wavenumber[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(4): 126589-126589.

Figures/Tables 16

Fig. 1

Table 1

Coefficients of numerical flux of sub-stencils

$k$	$c i - 2$	$c i - 1$	$c i$	$c i + 1$	$c i + 2$	$c i + 3$
$0$		- $16$	$56$	$26$
$1$			$26$	$56$	- $16$
$2$	$26$	- $76$	$116$
$3$			$312$	$1312$	- $512$	- $112$

Table 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

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Fig. 10

Fig. 11

Fig. 12

Fig. 13

Table 2

Table 3

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算例	TENO使用比例/%
算例	TENO	中心-TENO	尺度可控
正激波	100.00	9.23	2.37
激波密度波	100.00	7.62	7.14
二维黎曼	100.00	4.40	2.99
瑞利泰勒	100.00	4.46	2.18
双马赫	100.00	6.88	1.15
衰减湍流	100.00	31.68	0.10

算例	CPU时间/s
算例	TENO	中心-TENO	尺度可控
正激波	37.7	14.1	9.0
激波密度波	44.2	13.3	14.8
二维黎曼	2 088.6	531.3	534.0
瑞利泰勒	1 683.2	497.4	469.5
双马赫	2 325.7	721.9	603.8
衰减湍流	2 727.8	2 006.4	1 475.5

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A dissipation control method based on amplitude and wavenumber

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References 37

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