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Analysis and removal of spurious pressure oscillations in Boltzmann-equation-based mesoscopic simulation of incompressible turbulence

Published online by Cambridge University Press:  21 February 2025

Yiming Qi Open the ORCID record for Yiming Qi [Opens in a new window] ,
Lian-Ping Wang Open the ORCID record for Lian-Ping Wang [Opens in a new window] ,
Zhaoli Guo  and
Shiyi Chen
Yiming Qi*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China
Lian-Ping Wang*
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
Zhaoli Guo
Affiliation:
Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China
Shiyi Chen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China Eastern Institute for Advanced Study, Eastern Institute of Technology, Ningbo, Zhejiang 315200, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The lattice Boltzmann method has become a popular tool for simulating complex flows, including incompressible turbulent flows; however, as an artificial compressibility method, it can generate spurious pressure oscillations whose impact on the statistics of incompressible turbulence has not been systematically examined. In this work, we propose a theoretical approach to analyse the origin of compressibility-induced oscillations (CIOs) and explore ways to suppress or remove them. We begin by decomposing the velocity field and pressure field each into the solenoidal component and the compressive component, and then study the evolution of these two components analytically and numerically. The analysis yields an evolution equation of the mean-square pressure fluctuation which reveals several coupling effects of the two components. The evolution equation suggests that increasing the bulk-to-shear viscosity ratio can suppress CIOs, which is confirmed by numerical simulations. Furthermore, based on the derived evolution equation and data from the simulation, a model is developed to predict the long-term behaviours of the mean-square pressure fluctuations. In the case of decaying turbulence in a periodic domain, we show that the Helmholtz–Hodge decomposition can be used to obtain the solenoidal components reflecting the true evolution of incompressible turbulent flow, from the mesoscopic artificial compressibility approach. The study provides general theoretical guidelines to understand, suppress and even remove CIOs in other related pseudo-compressibility methods.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Turbulence simulation Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1005 , 25 February 2025 , A9
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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