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An efficient and low-divergence method for generating inhomogeneous and anisotropic turbulence with arbitrary spectra

Published online by Cambridge University Press:  25 August 2023

Hao Guo Open the ORCID record for Hao Guo [Opens in a new window] ,
Peixue Jiang ,
Lin Ye  and
Yinhai Zhu Open the ORCID record for Yinhai Zhu [Opens in a new window]
Hao Guo
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Key Laboratory of CO2 Utilization and Reduction Technology, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Peixue Jiang
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Key Laboratory of CO2 Utilization and Reduction Technology, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Lin Ye
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Key Laboratory of CO2 Utilization and Reduction Technology, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Yinhai Zhu*
Affiliation:
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Key Laboratory of CO2 Utilization and Reduction Technology, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: yinhai.zhu@tsinghua.edu.cn
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Abstract

This paper proposes a low-divergence method to generate inhomogeneous and anisotropic turbulence. Based on the idea of correlation reconstruction, the proposed method uses the Cholesky decomposition matrix to re-establish turbulence correlation functions. This is in contrast with the time-consuming procedure used in conventional methods to solve eigenvalues and eigenvectors in each location required by coordinate transformation, thereby reducing the computational complexity and improving the efficiency of synthetic turbulence generation. The proposed method is based on the classical spectrum-based method that is widely used to generate homogeneous and isotropic turbulence. By adjusting the generation strategy of specific random vectors, inhomogeneous and anisotropic turbulence with a relatively low divergence level can be obtained in practice, with almost no additional computational burden. Two versions of the proposed method are presented: the inverter and shifter versions. Both the versions are highly efficient, easy to implement, and compatible with high-performance computing. This method is also suitable for providing high-quality initial or boundary conditions for scale-resolving turbulence simulations with large grid numbers (such as direct numerical simulations or large eddy simulations); it can be rapidly implemented using various open-source computational fluid dynamics codes or common commercial software.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 970 , 10 September 2023 , A2
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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