A Unified Gas-Kinetic Particle Method for Frequency-Dependent Radiative Transfer Equations with Isotropic Scattering Process on Unstructured Mesh

Hu, Yuan; Chang, Liu

doi:10.2139/ssrn.4360158

Cited by 3 publications

(5 citation statements)

References 41 publications

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“…The asymptotic preserving (AP) property is important for the construction of a multiscale scheme. For the free transport and single-temperature diffusive regimes, the asymptotic preserving analysis is similar to that in our previous work [37]. For brevity, we omit the repetition of those details here.…”

Section: Asymptotic Analysismentioning

confidence: 91%

“…Based on the definition of S and Equation ( 20 ), the discretized scattering source

equals:

With Equation ( 25 ), the components of moments

have the form:

where

is the l th-order moments of S , and

is the

component of

. The even-order moments have the following relationship for all flow regimes [ 41 ]:

In the diffusion limit, we have [ 37 , 41 ]:

Thus, the components of moments

can be written as:

Therefore, Equation ( 29 ) can be proved:

where a reverse derivation of Equation ( 20 ) is used. Based on Equation ( 35 ), the angular distribution of scattering source

can be equivalent to one single scattering process with ( 27 ), saving the computational costs.…”

Section: Methodsmentioning

confidence: 99%

“…The length of the edge k is

. The two vertexes of edge k are

and

, and the unit normal and tangential vector are

and

, respectively [ 37 ].…”

Section: Figurementioning

confidence: 99%

“…The integral solution of the transport equation bridges the macroscopic and microscopic equations, which covers the physics from the free transport to the diffusion limit and makes the UGKS method asymptotic preserving (AP). Based on the framework of UGKS, different numerical schemes have been constructed, including the discrete unified gas kinetic scheme (DUGKS) method [ 29 , 30 , 31 ], the implicit unified gas kinetic scheme (IUGKS) method [ 32 , 33 , 34 , 35 ], the unified gas-kinetic particle (UGKP) method [ 36 , 37 ], and the unified gas-kinetic wave-particle (UGKWP) method [ 38 , 39 , 40 ]. These methods share a similar framework with the UGKS method, making them asymptotic preserving as well.…”

Section: Introductionmentioning

confidence: 99%

“…In our prior work, we extended the UGKP method for the frequency-dependent radiative system, considering both absorption–emission and isotropic scattering processes under a general unstructured mesh [ 37 ]. However, practical applications usually involve media with anisotropic scattering properties.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Unified Gas-Kinetic Particle Method for Radiation Transport in an Anisotropic Scattering Medium

Hu,

Liu,

Shen

et al. 2024

Entropy

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In this paper, a unified gas kinetic particle (UGKP) method is developed for radiative transfer in both absorbing and anisotropic scattering media. This numerical method is constructed based on our theoretical work on the model reduction for an anisotropic scattering system. The macroscopic solver of this method directly solves the macroscopic anisotropic diffusion equations, eliminating the need to solve higher-order moment equations. The reconstruction of macroscopic scattering source in the microscopic solver, based on the multiscale equivalent phase function we proposed in this work, has also been simplified as one single scattering process, significantly reducing the computational costs. The proposed method has also the property of asymptotic preserving. In the optically thick regime, the proposed method solves the diffusion limit equations for an anisotropic system. In the optically thin regime, the kinetic processes of photon transport are simulated. The consistency and efficiency of the proposed method have been validated by numerical tests in a wide range of flow regimes. The novel equivalent scattering source reconstruction can be used for various transport processes, and the proposed numerical scheme is widely applicable in high-energy density engineering applications.

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Section: Asymptotic Analysismentioning

confidence: 91%

“…Based on the definition of S and Equation ( 20 ), the discretized scattering source

equals:

With Equation ( 25 ), the components of moments

have the form:

where

is the l th-order moments of S , and

is the

component of

. The even-order moments have the following relationship for all flow regimes [ 41 ]:

In the diffusion limit, we have [ 37 , 41 ]:

Thus, the components of moments

can be written as:

Therefore, Equation ( 29 ) can be proved:

where a reverse derivation of Equation ( 20 ) is used. Based on Equation ( 35 ), the angular distribution of scattering source

can be equivalent to one single scattering process with ( 27 ), saving the computational costs.…”

Section: Methodsmentioning

confidence: 99%

“…The length of the edge k is

. The two vertexes of edge k are

and

, and the unit normal and tangential vector are

and

, respectively [ 37 ].…”

Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Unified Gas-Kinetic Particle Method for Radiation Transport in an Anisotropic Scattering Medium

Hu,

Liu,

Shen

et al. 2024

Entropy

Self Cite

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show abstract

Unified gas-kinetic wave-particle method for frequency-dependent radiation transport equation

Yang,

Zhu,

Liu

et al. 2025

Journal of Computational Physics

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An implicit unified gas-kinetic wave–particle method for radiative transport process

Liu,

Li,

Wang

et al. 2023

Physics of Fluids

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The unified gas-kinetic wave–particle method (UGKWP) has been developed for the multiscale gas, plasma, and multiphase flow transport processes for the past years. In this work, we propose an implicit UGKWP (IUGKWP) method to remove the Courant–Friedrichs–Lewy time step constraint. Based on the local integral solution of the radiative transfer equation (RTE), the particle transport processes are categorized into the long-λ streaming process and the short-λ streaming process compared to a local physical characteristic time tp. In the construction of the IUGKWP method, the long-λ streaming process is tracked by the implicit Monte Carlo method; the short-λ streaming process is evolved by solving the implicit moment equations; and the photon distribution is closed by a local integral solution of RTE. In the IUGKWP method, the multiscale flux of radiation energy and the multiscale closure of photon distribution are constructed based on the local integral solution. The IUGKWP method preserves the second-order asymptotic expansion of RTE in the optically thick regime and adapts its computational complexity to the flow regime. The numerical dissipation is well controlled, and the teleportation error is significantly reduced in the optically thick regime. The computational complexity of the IUGKWP method decreases exponentially as the Knudsen number approaches zero, and the computational efficiency is remarkably improved in the optically thick regime. The IUGKWP is formulated on a generalized unstructured mesh, and multidimensional 2D and 3D algorithms are developed. Numerical tests are presented to validate the capability of IUGKWP in capturing the multiscale photon transport process. The algorithm and code will apply in the engineering applications of inertial confinement fusion.

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A Unified Gas-Kinetic Particle Method for Frequency-Dependent Radiative Transfer Equations with Isotropic Scattering Process on Unstructured Mesh

Cited by 3 publications

References 41 publications

A Unified Gas-Kinetic Particle Method for Radiation Transport in an Anisotropic Scattering Medium

A Unified Gas-Kinetic Particle Method for Radiation Transport in an Anisotropic Scattering Medium

Unified gas-kinetic wave-particle method for frequency-dependent radiation transport equation

An implicit unified gas-kinetic wave–particle method for radiative transport process

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