Discrete unified gas kinetic scheme for a reformulated BGK–Vlasov–Poisson system in all electrostatic plasma regimes

Liu, Hongtao; Shi, Feng; Wan, Jie; He, Xiaoming; Cao, Yong

doi:10.1016/j.cpc.2020.107400

Cited by 17 publications

(13 citation statements)

References 51 publications

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“…With this consideration, a new conserved DUGKS has been proposed [124] as well, where the conservative flow variables are updated from the macroscopic conservation law instead of by taking moments of the auxiliary distribution function as in the original DUGKS. Regardless of the quadrature rule in velocity space, the conservation law is always satisfied on the macroscopic level in the conserved DUGKS, which could benefit in the numerical calculations where conservation is of much importance, such as for highly nonequilibrium flow and plasma physics [48,104,125]. Following these conservation laws, we can see from Equation (33) that the evolution mainly depends on the microscopic flux F ij across cell interfaces.…”

Section: Basic Algorithmmentioning

confidence: 99%

“…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%

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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: Basic Algorithmmentioning

confidence: 99%

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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“…Very recently, Liu et al further developed an improved DUGKS which has the asymptotic properties in terms of both Kn and D , based on the BGK-Vlasov equation and a reformulated Poisson equation (RPE) [100]. The RPE reads in dimensionless form as,…”

Section: Plasmamentioning

confidence: 99%

Progress of discrete unified gas-kinetic scheme for multiscale flows

Guo

2021

Adv. Aerodyn.

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Multiscale gas flows appear in many fields and have received particular attention in recent years. It is challenging to model and simulate such processes due to the large span of temporal and spatial scales. The discrete unified gas kinetic scheme (DUGKS) is a recently developed numerical approach for simulating multiscale flows based on kinetic models. The finite-volume DUGKS differs from the classical kinetic methods in the modeling of gas evolution and the reconstruction of interface flux. Particularly, the distribution function at a cell interface is reconstructed from the characteristic solution of the kinetic equation in space and time, such that the particle transport and collision effects are coupled, accumulated, and evaluated in a numerical time step scale. Consequently, the cell size and time step of DUGKS are not passively limited by the particle mean-free-path and relaxation time. As a result, the DUGKS can capture the flow behaviors in all regimes without resolving the kinetic scale. Particularly, with the variation of the ratio between numerical mesh size scale and kinetic mean free path scale, the DUGKS can serve as a self-adaptive multiscale method. The DUGKS has been successfully applied to a number of flow problems with multiple flow regimes. This paper presents a brief review of the progress of this method.

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“…The purpose of this work is to extend the UGKWP method to the field of multiscale gas mixture and plasma simulations. The proposed UGKWP method shares the same multiscale property with the UGKS [16] and DUGKS [17,18]. The scheme preserves the collisionless limit in the rarefied regime, and the corresponding NS and MHD solvers in the comtinuum flow regime.…”

Section: Introductionmentioning

confidence: 99%

“…The deterministic discrete ordinate method (DVM) has great advantages in the simulation of low speed and small temperature variation flow due to the absence of statistical noise [9]. In the past decade, many deterministic numerical methods have been developed for multi-species gas mixture [10][11][12][13][14], as well as plasma transport [15][16][17][18]. On the other hand, when dealing with the high speed and 3D flow, the stochastic particle method shows great advantages in terms of memory reduction and computation efficiency.…”

Section: Introductionmentioning

confidence: 99%

Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

Liu

2021

Adv. Aerodyn.

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In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) methods to the multi-species gas mixture and multiscale plasma transport. The construction of the scheme is based on the direct modeling on the mesh size and time step scales, and the local cell’s Knudsen number determines the flow physics. The proposed scheme has the multiscale and asymptotic complexity diminishing properties. The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale, and preserve the asymptotic Euler, Navier-Stokes, and magnetohydrodynamics (MHD) when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path. The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number. In the continuum regime, the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver. In the UGKWP, the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables, and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale. For plasma transport, the current scheme provides a smooth transition from particle-in-cell (PIC) method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime. In the continuum limit, the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time. In the highly magnetized regime, the cell size and time step are not restricted by the Debye length and plasma cyclotron period. The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.

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Discrete unified gas kinetic scheme for a reformulated BGK–Vlasov–Poisson system in all electrostatic plasma regimes

Cited by 17 publications

References 51 publications

GKS and UGKS for High-Speed Flows

GKS and UGKS for High-Speed Flows

Progress of discrete unified gas-kinetic scheme for multiscale flows

Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

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