The first decade of unified gas kinetic scheme

Zhu, Yajun; Xu, Kun

doi:10.48550/arxiv.2102.01261

Cited by 2 publications

(2 citation statements)

References 101 publications

(169 reference statements)

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“…On the other hand, the gas kinetic scheme (GKS) has made a great progress in recent years. 24 However, it is noted that most of GKS-based methods are constructed by using the Maxwellian distribution function, which makes the derivation and implementation very complicated.…”

Section: Introductionmentioning

confidence: 99%

A combined flux reconstruction and lattice Boltzmann flux solver for inviscid compressible flow simulation

Qin

et al. 2022

Numerical Methods in Fluids

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A numerical method, which combines the high order flux reconstruction (FR) and the lattice Boltzmann flux solver (LBFS), has been developed to solve inviscid compressible flows in this article. Extensive research has shown that LBFS has absorbed the advantages of both finite volume method (FVM) and lattice Boltzmann method (LBM). On one hand, compared with FVM, FR can achieve arbitrary high order accuracy and is compact for parallel computing by avoiding wide stencils on meshes, which shows FR is a better choice than FVM. On the other hand, different from the discrete velocity Boltzmann equation based methods, the present method, that is, FR‐LBFS, solves the Euler equations essentially, and then the calculation efficiency can be improved. In FR‐LBFS, the common inviscid flux at the cell interface is evaluated by the local reconstruction of the lattice Boltzmann equation (LBE) solution from macroscopic flow variables at solution points. Unlike the traditional flux solution at the interface where the nonlinear convective terms have to be considered in the computation, the feature of linear convection term in LBE can make it easier to calculate flux in the current method. Furthermore, by considering real physical effects in LBM, the positive density and pressure can be achieved in the case of strong shocks and discontinuities. Some typical inviscid problems, including the advection of density perturbation, sod shock tube, Riemann problem for two‐dimensional gas dynamics, supersonic flow in a convergent nozzle with a ramp, subsonic flow around a cylinder, and transonic flow over a NACA0012 airfoil, are simulated to demonstrate the accuracies and robustness of the proposed FR‐LBFS.

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Section: Introductionmentioning

confidence: 99%

A combined flux reconstruction and lattice Boltzmann flux solver for inviscid compressible flow simulation

Qin

et al. 2022

Numerical Methods in Fluids

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“…The time step in UGKS doesn't need to be less than the particle collision time, which makes the scheme highly efficient in continuum flow regime. Besides the neutral gas flow, the UGKS has been successfully applied to many other transport problems, such as radiation, photon transport, plasma, etc [31,32,54,28,69]. In particular, an effective multiscale scheme based on the UGKS for the disperse dilute gasparticle system has been proposed [30].…”

Section: Introductionmentioning

confidence: 99%

Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow

Yang,

Liu,

et al. 2021

Preprint

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In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the disperse dilute gas-particle multiphase flow is proposed. In this study, the gas phase is always in the hydrodynamic regime. However, the particle phase covers different flow regimes from particle trajectory crossing to the hydrodynamic wave interaction with the variation of local particle phase Knudsen number. The UGKWP is an appropriate method for the capturing of the multiscale transport mechanism in the particle phase through its coupled wave-particle formulation. In the regime with intensive particle collision, the evolution of solid particle will be followed by the analytic wave with quasi-equilibrium distribution; while in the rarefied regime the non-equilibrium particle phase will be captured through particle tracking and collision, which plays a decisive role in recovering particle trajectory crossing behavior. The gas phase in the multiphase system is assumed to be stay in the continuum flow regime, and its evolution is mainly controlled by the Navier-Stokes equations with the interaction with particle phase. The gas-kinetic scheme (GKS) is employed for the simulation of gas flow. In the highly collision regime for the particles, no particles will be sampled in UGKWP and the wave formulation for solid particle with the hydrodynamic gas phase will reduce the system to the two-fluid Eulerian model. On the other hand, in the collisionless regime for the solid particle, the free transport of solid particle will be followed in UGKWP, and coupled system will return to the Eulerian-Lagrangian formulation for the gas and particle. The scheme will be tested for in all flow regimes, which include the non-equilibrium particle trajectory crossing, the particle concentration under different Knudsen number, and the dispersion of particle flow with the variation of Stokes number. A experiment of shock-induced particle bed fluidization is simulated and the results are compared with experimental measurements. These numerical solutions validate suitability of the proposed scheme for the simulation of gas-particle multiphase flow.

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The first decade of unified gas kinetic scheme

Cited by 2 publications

References 101 publications

A combined flux reconstruction and lattice Boltzmann flux solver for inviscid compressible flow simulation

A combined flux reconstruction and lattice Boltzmann flux solver for inviscid compressible flow simulation

Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow

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