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

Li, Weiming; Liu, Chang; Zhu, Yajun; Zhang, Jiwei; Xu, Kun

doi:10.1016/j.jcp.2020.109280

Cited by 43 publications

(39 citation statements)

References 70 publications

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“…In this work, we extend the unified gas-kinetic wave-particle method to the field of multi-species gas mixture and multiscale plasma transport. The construction of numerical scheme for multiscale transport is based on the direct modeling methodology [20], where the flow physics is UGKWP method has great potential to solve multiscale transport problems in rarefied flow [24,25], radiative transfer [26,43], and plasma physics.…”

Section: Resultsmentioning

confidence: 99%

“…The UGKS has been proved to be a second order unified preserving scheme that can accurately capture the NS solution with cell size and time step being much larger than the mean free path and mean collision time [24], the same as traditional NS solvers in discretizing the macroscopic equations directly. To improve the efficiency of UGKS in the simulation of high speed flow, the unified gas-kinetic wave-particle (UGKWP) method has been proposed and applied in the simulation of multiscale gas dynamics and photon transport [24][25][26]. The construction of UGKWP method follows the direct modeling methodology of UGKS: the evolution of microscopic simulation particle is coupled with the evolution macroscopic variables, and the multiscale particle evolution equation is derived from the integral solution of the kinetic equation.…”

Section: Introductionmentioning

confidence: 99%

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Unified Gas-Kinetic Wave-Particle Method IV: Multi-Species Gas Mixture and Plasma Transport

Liu¹,

Xu²

2020

Preprint

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In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method 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 cell's Knudsen number the scheme can capture the non-equilibrium flow physics in the rarefied flow regime, and preserve the asymptotic Euler, Navier-Stokes, and magnetohydrodynamics limit in the continuum regime. The asymptotic complexity diminishing property means that the total degree of freedom of the scheme automatically decreases as cell's Knudsen number decreases. In the continuum regime, the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver. In 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 are modeled from the time accumulating solution up to a time step scale from the kinetic model equation. For plasma transport, current scheme provides a smooth transition from particle in cell (PIC) method in the rarefied regime to the magnetohydrodynamic (MHD) solver in the continuum regime. In the continuum limit, the cell size and time step of the UGKWP method is not restricted to be less than the 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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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unified Gas-Kinetic Wave-Particle Method IV: Multi-Species Gas Mixture and Plasma Transport

Liu¹,

Xu²

2020

Preprint

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“…For example, for a space vehicle computation at hypersonic speed in the near space flight, the local Knudsen number around the flying vehicle can be changed greatly over a fifth-order magnitude and the UGKS can present accurate solution with a large variation of the ratio between the local cell size and local particle mean free path [35]. The UGKS has also been successfully extended to radiative transfer [36][37][38][39], plasma transport [40], and multiphase flow [41].…”

Section: Introductionmentioning

confidence: 99%

Unified gas-kinetic wave-particle methods I: Continuum and rarefied gas flow

Liu

Zhu

2020

Journal of Computational Physics

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The unified gas-kinetic scheme (UGKS) provides a framework for simulating multiscale transport with the updates of both gas distribution function and macroscopic flow variables on the cell size and time step scales. The multiscale dynamics in UGKS is achieved through the coupled particle transport and collision in the particle evolution process within a time step. In this paper, under the UGKS framework, we propose an efficient multiscale unified gas-kinetic wave-particle (UGKWP) method. The gas dynamics in UGKWP method is described by the individual particle movement coupled with the evolution of the probability density function (PDF). During a time step, the trajectories of simulation particles are tracked until collision happens, and the post-collision particles are evolved collectively through the evolution of the corresponding distribution function. The evolution of simulation particles and distribution function is guided by evolution of macroscopic variables. The two descriptions on a gas particle, i.e. wave and particle, switch dynamically with time. A new concept of multiscale multi-efficiency preserving (MMP) method is introduced, and the UGKWP method is shown to be an MMP scheme. Multiscale preserving means UGKWP method preserves the flow regime from collisionless regime to hydrodynamic regime without requiring the cell size and time step to be less than the mean free path and collision time. Multi-efficiency preserving means the computational cost of UGKWP method including the computational time and memory cost is on the same level as the particle methods in the rarefied regime, and becomes comparable to the hydrodynamic solvers in continuum regime. The UGKWP method is specially efficient for hypersonic flow simulation in all regimes in comparison with the wave-type discrete ordinate 1 arXiv:1811.07141v1 [math.NA] 17 Nov 2018 methods, and presents a much lower stochastic noise in the continuum flow regime in comparison with the particle-based Monte Carlo methods. Numerical tests for flows over a wide range of Mach and Knudsen numbers are presented. The examples include mainly the hypersonic flow passing a circular cylinder at Mach numbers 20 and 30 and Knudsen numbers 1 and 10 −4 , low speed lid-driven cavity flow, and laminar boundary layer. These results validate the accuracy, efficiency, and multiscale property of UGKWP method.

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“…For unsteady problems, some AP schemes have also been proposed [27,28]. Recently, an AP method, the unified gas kinetic scheme (UGKS) was successfully developed for radiative transfer problems [29][30][31]. Another asymptotic preserving multiscale method, the discrete unified gas kinetic scheme, which was initially designed for gas flows [32,33], was also extended to solve the radiative heat transfer problems in isotropic scattering media [1].…”

Section: Introductionmentioning

confidence: 99%

Discrete unified gas kinetic scheme for multiscale anisotropic radiative heat transfer

et al. 2020

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In this work, a discrete unified gas kinetic scheme (DUGKS) is developed for radiative transfer in anisotropic scattering media. The method is an extension of a previous one for isotropic radiation problems [1]. The present scheme is a finite-volume discretization of the anisotropic gray radiation equation, where the anisotropic scattering phase function is approximated by the Legendre polynomial expansion. With the coupling of free transport and scattering processes in the reconstruction of the flux at cell interfaces, the present DUGKS has the nice unified preserving properties such that the cell size is not limited by the photon mean free path even in the optical thick regime. Several one-and two-dimensional numerical tests are conducted to validate the performance of the present DUGKS, and the numerical results demonstrate that the scheme is a reliable method for anisotropic radiative heat transfer problems.

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

Cited by 43 publications

References 70 publications

Unified Gas-Kinetic Wave-Particle Method IV: Multi-Species Gas Mixture and Plasma Transport

Unified Gas-Kinetic Wave-Particle Method IV: Multi-Species Gas Mixture and Plasma Transport

Unified gas-kinetic wave-particle methods I: Continuum and rarefied gas flow

Discrete unified gas kinetic scheme for multiscale anisotropic radiative heat transfer

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