Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules

Zhang, Yue; Zhu, Li-Guo; Wang, Ruijie

doi:10.1103/physreve.97.053306

Cited by 54 publications

(50 citation statements)

References 56 publications

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“…An implicit DUGKS [26] for simulating of steady flow in all flow regions was constructed with an implicit macroscopic prediction technique [27]. Up to now, DUGKS has been applied to many fields, such as compressible flow [28,29], multi-phase flow [30,31], multi-component flow [32], complex motion (with immerse boundary method) [33], radiative transfer [34], etc.…”

Section: Introductionmentioning

confidence: 99%

Large-eddy Simulation of Wall-bounded Turbulent Flow with High-order Discrete Unified Gas-Kinetic Scheme

Zhang

Zhong²,

Liu

et al. 2020

Preprint

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In this paper, we introduce the incompressible discrete Maxwellian equilibrium distribution function and external forces into the two-stage third-order Discrete Unified Gas-Kinetic Scheme (DUGKS) for simulating low-speed incompressible turbulent flows with forcing term. The Wall-Adapting Local Eddy-viscosity (WALE) and Vreman sub-grid models for Large-Eddy Simulations (LES) of wall-bounded turbulent flows are coupled within the present framework. In order to simulate the three-dimensional turbulent flows associated with great computational cost, a parallel implementation strategy for the present framework is developed, and is validated by three canonical wall-bounded turbulent flows, viz., the fully developed turbulent channel flow at a friction Reynolds number (Re) about 180, the turbulent plane Couette flow at a friction Re number about 93 and three-dimensional lid-driven cubical cavity flow at a Re number of 12000. The turbulence statistics are computed by the present approach with both WALE and Vreman models, and their predictions match precisely with each other. Especially, the predicted flow physics of three-dimensional lid-driven cavity are consistent with the description from abundant literatures. While, they have small discrepancies in comparison to the Direct Numerical Simulation (DNS) due to the relatively low grid resolution. The present numerical results verify that the present two-stage third-order DUGKS-based LES method is capable for simulating inhomogeneous wall-bounded turbulent flows and getting reliable results with relatively coarse grids.

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Section: Introductionmentioning

confidence: 99%

Large-eddy Simulation of Wall-bounded Turbulent Flow with High-order Discrete Unified Gas-Kinetic Scheme

Zhang

Zhong²,

Liu

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The discrete unified gas-kinetic scheme (DUGKS) is developed by Guo el al. is also a multiscale scheme [5,19], and has been successfully applied in the field of micro flow [20,21], gas mixture [22], gas-particle multiphase flow [23], phonon transport [24], radiation [25], etc. The general synthetic iteration scheme was first proposed by Wu et al for the steady state solution of the linearized kinetic eqaution [6], and is recently extended to the simulation of nonlinear kinetic equation and diatomic gas [26,27].…”

Section: Introductionmentioning

confidence: 99%

A Unified Gas-kinetic Scheme for Micro Flow Simulation Based on Linearized Kinetic Equation

Liu

2020

Preprint

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The flow regime of micro flow varies from collisionless regime to hydrodynamic regime according to the Knudsen number. On the kinetic scale, the dynamics of micro flow can be described by the linearized kinetic equation. In the continuum regime, hydrodynamic equations such as linearized Navier-Stokes equations and Euler equations can be derived from the linearized kinetic equation by the Chapman-Enskog asymptotic analysis. In this paper, based on the linearized kinetic equation we are going to propose a unified gas kinetic scheme scheme (UGKS) for micro flow simulation, which is an effective multiscale scheme in the whole micro flow regime. The important methodology of UGKS is the following. Firstly, the evolution of microscopic distribution function is coupled with the evolution of macroscopic flow quantities. Secondly, the numerical flux of UGKS is constructed based on the integral solution of kinetic equation, which provides a genuinely multiscale and multidimensional numerical flux. The UGKS recovers the linear kinetic solution in the rarefied regime, and converges to the linear hydrodynamic solution in the continuum regime. An outstanding feature of UGKS is its capability of capturing the accurate viscous solution even when the cell size is much larger than the kinetic kinetic length scale, such as the capturing of the viscous boundary layer with a cell size ten times larger than the particle mean free path. Such a multiscale property is called unified preserving (UP) which has been studied in \cite{guo2019unified}. In this paper, we are also going to give a mathematical proof for the UP property of UGKS.

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“…Under this flow condition, there are strong gradients of the macroscopic variables and the species show disjoint behaviour. The profile of a shock wave for a monoatomic gas mixture is a well-studied problem both experimentally [12] [23] and numerically [30] [40] [37] [43], etc. The work by Kosuge et al [30] , which is based on the Boltzmann transport equation, is considered a standard benchmark and all numerical studies compare with it.…”

Section: Introductionmentioning

confidence: 99%

Derivation and numerical comparison of Shakhov and Ellipsoidal Statistical kinetic models for a monoatomic gas mixture

Todorova

Steijl

2019

European Journal of Mechanics - B/Fluids

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Gas mixtures are important for many practical applications. Extending kinetic model equations of the Bhatnagar-Gross-Krook (BGK) type from a single-species gas to a multi-species gas mixture presents a number of significant challenges. First, obtaining the correct species diffusions, viscous stresses as well as heat conduction in the continuum limit requires a careful design of the collision terms in the kinetic equations. Secondly, the derived model collision terms need to guarantee positivity of the macroscopic fields. In the present work, two new kinetic models are introduced and compared: an approach based on the Shakhov kinetic model and an approach involving an anisotropic Gaussian equilibrium function. The two new models are capable of modelling a binary mixture of monoatomic gases, with updated definitions for the relaxation parameters and target species velocities and temperature. Both methods account for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The key contribution of the models is the exact recovery of the Fick, Newton and Fourier laws in the continuum limit, while preserving positive temperature fields and crucial properties of the Boltzmann equation. The profile of a normal shock wave is inspected under various flow conditions to numerically validate the two models. The results show improvement upon comparison with a model, which has two correct transport coefficients, and demonstrate the ability to reliably model inert gas mixtures.

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Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules

Cited by 54 publications

References 56 publications

Large-eddy Simulation of Wall-bounded Turbulent Flow with High-order Discrete Unified Gas-Kinetic Scheme

Large-eddy Simulation of Wall-bounded Turbulent Flow with High-order Discrete Unified Gas-Kinetic Scheme

A Unified Gas-kinetic Scheme for Micro Flow Simulation Based on Linearized Kinetic Equation

Derivation and numerical comparison of Shakhov and Ellipsoidal Statistical kinetic models for a monoatomic gas mixture

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