Large-eddy simulation of wall-bounded turbulent flow with high-order discrete unified gas-kinetic scheme

Zhang, Rui; Zhong, Chengwen; Liu, Sha; Zhuo, Congshan

doi:10.1186/s42774-020-00051-w

Cited by 15 publications

(6 citation statements)

References 57 publications

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“…Similarly, the discrete unified gas-kinetic scheme (DUGKS) proposed by Guo et al [95,96] is capable of multiscale flow simulations in all Knudsen regimes by adopting the discrete solution of the kinetic equation along a characteristic line. After a decade of development and improvement, the UGKS and DUGKS have gained great success in solving multiscale transport problems, such as radiative transfer [97][98][99][100], phonon transport [101,102], plasma physics [42,103,104], neutron transport [105,106], multicomponent and multiphase flow [107][108][109][110][111], granular flow [112][113][114], and turbulent flow [115][116][117].…”

Section: Unified Gas-kinetic Scheme For High-speed Flowsmentioning

confidence: 99%

GKS and UGKS for High-Speed Flows

Zhu

Zhong

2021

Aerospace

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The gas-kinetic scheme (GKS) and the unified gas-kinetic scheme (UGKS) are numerical methods based on the gas-kinetic theory, which have been widely used in the numerical simulations of high-speed and non-equilibrium flows. Both methods employ a multiscale flux function constructed from the integral solutions of kinetic equations to describe the local evolution process of particles’ free transport and collision. The accumulating effect of particles’ collision during transport process within a time step is used in the construction of the schemes, and the intrinsic simulating flow physics in the schemes depends on the ratio of the particle collision time and the time step, i.e., the so-called cell’s Knudsen number. With the initial distribution function reconstructed from the Chapman–Enskog expansion, the GKS can recover the Navier–Stokes solutions in the continuum regime at a small Knudsen number, and gain multi-dimensional properties by taking into account both normal and tangential flow variations in the flux function. By employing a discrete velocity distribution function, the UGKS can capture highly non-equilibrium physics, and is capable of simulating continuum and rarefied flow in all Knudsen number regimes. For high-speed non-equilibrium flow simulation, the real gas effects should be considered, and the computational efficiency and robustness of the schemes are the great challenges. Therefore, many efforts have been made to improve the validity and reliability of the GKS and UGKS in both the physical modeling and numerical techniques. In this paper, we give a review of the development of the GKS and UGKS in the past decades, such as physical modeling of a diatomic gas with molecular rotation and vibration at high temperature, plasma physics, computational techniques including implicit and multigrid acceleration, memory reduction methods, and wave–particle adaptation.

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Section: Unified Gas-kinetic Scheme For High-speed Flowsmentioning

confidence: 99%

GKS and UGKS for High-Speed Flows

Zhu

Zhong

2021

Aerospace

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“…2017; Zhang et al. 2020), microflows (Liu, Bai & Zhong 2015; Zhu & Guo 2017), compressible flows (Peng et al. 2016; Chen et al.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, some deterministic methods based on the discrete velocity method (Broadwell 1964), such as the gas-kinetic unified algorithm (Li & Zhang 2004;Li et al 2015), unified gas-kinetic scheme (UGKS) (Xu & Huang 2010;Huang, Xu & Yu 2012), discrete unified gas-kinetic scheme (DUGKS) (Guo, Xu & Wang 2013;Guo, Wang & Xu 2015) and conserved discrete unified gas kinetic scheme (CDUGKS) (Liu et al 2018;Chen et al 2019), have been proposed. These deterministic methods have been proven to simulate accurately the gas flow in various flow regimes from rarefied to continuum, and have been applied successfully to a variety of flow problems in different flow regimes, such as turbulent flows (Wang, Wang & Guo 2016;Bo et al 2017;Zhang et al 2020), microflows (Liu, Bai & Zhong 2015;Zhu & Guo 2017), compressible flows (Peng et al 2016;Chen et al 2020) and multiphase flows (Zhang, Yan & Guo 2018;Yang, Zhong & Zhuo 2019), providing a reliable numerical scheme for the accurate calculation of base flow in the stability analysis of rarefied flow.…”

Section: Introductionmentioning

confidence: 99%

A novel linear stability analysis method for plane Couette flow considering rarefaction effects

Zou

Zhong

et al. 2023

J. Fluid Mech.

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Following the stability analysis method in classic fluid dynamics, a linear stability equation (LSE) suitable for rarefied flows is derived based on the Bhatnagar–Gross–Krook (BGK) equation. The global method and singular value decomposition method are used for modal and non-modal analysis, respectively. This approach is validated by results obtained from Navier–Stokes (NS) equations. The modal analysis shows that LSEs based on NS equations (NS-LSEs) begin to fail when the Knudsen number ( $Kn$ ) increases past $\sim$ 0.01, regardless of whether a slip model is used. When $Kn\geq 0.01$ , the growth rate of the least stable mode is generally underestimated by the NS-LSEs. Under a fixed wavenumber, the pattern (travelling or standing wave) of the least stable mode changes with $Kn$ ; when the mode presents the same pattern, the growth rate decreases almost linearly with increasing $Kn$ ; otherwise, rarefaction effects may not stabilize the flow. The characteristic lengths of the different modes are different, and the single-scale classic stability analysis method cannot predict multiple modes accurately, even when combined with a slip model and even for continuum flow. However, non-modal analysis shows that this error does not affect the transient growth because modes with small growth rates offer little contribution to the transient growth. In rarefied flow, as long as the Mach number ( $Ma$ ) is large enough, transient growth will occur in some wavenumber ranges. The rarefaction effect plays a stabilizing role in transient growth. The NS-LSEs-based method always overestimates the maximum transient growth.

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“…With the information of the Knudsen number incorporated in the construction of the interface flux, the DUGKS exhibits the capability of properly modeling a wide range of fluid flows ranging from the continuum regime to the free-molecule regime [ 32 ]. Over the past decade, the DUGKS has proven its excellent performance in predicting microscale gas flows [ 33 , 34 ], multicomponent gas flows [ 35 , 36 ], turbulent flows [ 37 , 38 , 39 ], compressible flows [ 40 , 41 , 42 ], radiative heat transfer [ 43 , 44 ], and so forth [ 45 ]. A comparative study [ 46 ] has demonstrated the stability superiority of the DUGKS over that of the LB method in terms of nearly incompressible flows.…”

Section: Introductionmentioning

confidence: 99%

Free-Energy-Based Discrete Unified Gas Kinetic Scheme for van der Waals Fluid

Yang

Zhuo

et al. 2022

Entropy

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The multiphase model based on free-energy theory has been experiencing long-term prosperity for its solid foundation and succinct implementation. To identify the main hindrance to developing a free-energy-based discrete unified gas-kinetic scheme (DUGKS), we introduced the classical lattice Boltzmann free-energy model into the DUGKS implemented with different flux reconstruction schemes. It is found that the force imbalance amplified by the reconstruction errors prevents the direct application of the free-energy model to the DUGKS. By coupling the well-balanced free-energy model with the DUGKS, the influences of the amplified force imbalance are entirely removed. Comparative results demonstrated a consistent performance of the well-balanced DUGKS despite the reconstruction schemes utilized. The capability of the DUGKS coupled with the well-balanced free-energy model was quantitatively validated by the coexisting density curves and Laplace’s law. In the quiescent droplet test, the magnitude of spurious currents is reduced to a machine accuracy of 10−15. Aside from the excellent performance of the well-balanced DUGKS in predicting steady-state multiphase flows, the spinodal decomposition test and the droplet coalescence test revealed its stability problems in dealing with transient flows. Further improvements are required on this point.

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Large-eddy simulation of wall-bounded turbulent flow with high-order discrete unified gas-kinetic scheme

Cited by 15 publications

References 57 publications

GKS and UGKS for High-Speed Flows

GKS and UGKS for High-Speed Flows

A novel linear stability analysis method for plane Couette flow considering rarefaction effects

Free-Energy-Based Discrete Unified Gas Kinetic Scheme for van der Waals Fluid

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