An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations

Sun, Weiwei; Jiang, Song; Xu, Kun; Shu, Li

doi:10.1016/j.jcp.2015.09.002

Cited by 60 publications

(49 citation statements)

References 21 publications

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“…The unified gas-kinetic scheme (UGKS) was initially developed for the problems in the field of rarefied gas dynamics [29,30], and has also been successfully applied to problems in radiative transfer under the finite volume framework [23,24,25,26,27,28]. In this section, we review the basic idea of the UGKS using the example of the multidimensional linear transport equation in a purely scattering medium.…”

Section: Review Of the Ugks For The Linear Transport Equationmentioning

confidence: 99%

“…Another approach towards releasing the stiffness issue in the diffusive regime is to develop asymptotic-preserving (AP) DOM [19,20,21,22,23,24,25,26,27,28] . One of the examples is the unified gas-kinetic scheme (UGKS), which couples the particles' transport and collision process using a multiscale flux function obtained from the integral solution of the kinetic model equation.…”

Section: Introductionmentioning

confidence: 99%

“…The cell size and time step are not restricted by the mean free path and mean collision time. It was developed initially in the field of rarefied gas dynamics [29,30,31] and has been applied to the field of radiative transfer [23,24,25,26,27,28], plasma transport [32], and disperse multi-phase flow [33]. Since it is a discrete ordinate based numerical scheme, it has no statistical noise, but unavoidably suffers from the ray effect.…”

Section: Introductionmentioning

confidence: 99%

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Unified gas-kinetic wave-particle methods III: Multiscale photon transport

Liu

Zhu

et al. 2020

Journal of Computational Physics

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In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method to the multiscale photon transport. In this method, the photon free streaming and scattering processes are treated in an un-splitting way. The duality descriptions, namely the simulation particle and distribution function, are utilized to describe the photon. By accurately recovering the governing equations of the unified gas-kinetic scheme (UGKS), the UGKWP preserves the multiscale dynamics of photon transport from optically thin to optically thick regime. In the optically thin regime, the UGKWP becomes a Monte Carlo type particle tracking method, while in the optically thick regime, the UGKWP becomes a diffusion equation solver. The local photon dynamics of the UGKWP, as well as the proportion of wave-described and particle-described photons are automatically adapted according to the numerical resolution and transport regime. Compared to the S n -type UGKS, the UGKWP requires less memory cost and does not suffer ray effect. Compared to the implicit Monte Carlo (IMC) method, the statistical noise of UGKWP is greatly reduced and computational efficiency is significantly improved in the optically thick regime. Several numerical examples covering all transport regimes from the optically thin to optically thick are computed to validate the accuracy and efficiency of the UGKWP method. In comparison to the S n -type UGKS and IMC method, the UGKWP method may have several-order-of-magnitude reduction in computational cost and memory requirement in solving some multsicale transport problems.

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Section: Review Of the Ugks For The Linear Transport Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Unified gas-kinetic wave-particle methods III: Multiscale photon transport

Liu

Zhu

et al. 2020

Journal of Computational Physics

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“…The time derivatives of Maxwellian satisfy the compatibility condition (44) from which the moments < a st > can be obtained, and hence a st can be calculated in a similar manner to the spatial derivative functions [50,52]. Substituting Eq.…”

Section: Multiscale Fluxmentioning

confidence: 99%

“…Originally proposed for the neutral gas flow simulation, the UGKS has been successfully developed for many other multiscale transport problems in the subsequent studies. For neutral gas transport, the UGKS can capture gas dynamic physics from the highly non-equilibrium regime to continuum regime [48,49,22,47]; for radiative transport, the UGKS can present solutions from optically thin regime to optically thick regime [41,44,42,43]; for plasma transport, the UGKS can capture solution from collisionless Vlasov regime to highly collisional magnetized hydrodynamic regime [21]. The UGKS has distinguishable advantages compared with many other numerical methods.…”

Section: Introductionmentioning

confidence: 99%

A unified gas-kinetic scheme for continuum and rarefied flows VI: Dilute disperse gas-particle multiphase system

Liu

Wang

2019

Journal of Computational Physics

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In this paper, a unified gas kinetic scheme (UGKS) for multiphase dilute gas-particle system is proposed. The UGKS multiphase (UGKS-M) is a finite volume method, which captures flow physics in the regimes from collisionless multispecies transport to the two-fluid hydrodynamic Navier-Stokes (NS) solution with the variation of Knudsen number, and from granular flow regime to dusty gas dynamics with the variation of Stokes number. The reason for preserving the multiscale nature in UGKS-M is mainly coming from the direct modeling of the flow physics in the scales of discrete cell size and time step, where the ratio of the time step over the particle collision time determines flow behavior in different regimes. For the particle phase, the integral solution of the kinetic equation is used in the construction of numerical flux, which takes into account the particle transport, collision, and acceleration. The gas phase, which is assumed to be in the continuum flow regime, evolves numerically by the gas kinetic scheme (GKS), which is a subset of the UGKS for the Navier-Stokes solutions. The interaction between the gas and particle phase is calculated based on a velocity space mapping method, which solves accurately the kinetic acceleration process. The stability of UGKS-M is determined by the CFL condition only. With the inclusion of the material temperature evolution equation of solid particles, once the total energy loss in inelastic collision transfers into particle material thermal energy, the UGKS-M conserves the total mass, momentum, and energy for the whole multiphase system.In the numerical tests, the UGKS-M shows good multiscale property in capturing the particle trajectory crossing (PTC), particle wall reflecting phenomena, and vortex-induced segregation of inertial particles under different Stokes numbers. The scheme is also applied to simulate shock induced fluidization problem and the simulation results agree well with experimental 1 arXiv:1802.04961v2 [physics.comp-ph] 11 Sep 2018 measurement.

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Multiscale Simulation for the System of Radiation Hydrodynamics

Sun

Jiang

et al. 2020

J Sci Comput

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An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations

Cited by 60 publications

References 21 publications

Unified gas-kinetic wave-particle methods III: Multiscale photon transport

Unified gas-kinetic wave-particle methods III: Multiscale photon transport

A unified gas-kinetic scheme for continuum and rarefied flows VI: Dilute disperse gas-particle multiphase system

Multiscale Simulation for the System of Radiation Hydrodynamics

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