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Multiscale Radiative Transfer in Cylindrical Coordinates

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Abstract

The radiative transfer equations in cylindrical coordinates are important in the application of inertial confinement fusion. In comparison with the equations in Cartesian coordinates, an additional angular derivative term appears in the cylindrical case. This term adds great difficulty for a numerical scheme to keep the conservation of total energy. In this paper, based on weighting factors, the angular derivative term is properly discretized, and the interface fluxes in the radial r-direction depend on such a discretization as well. A unified gas kinetic scheme (UGKS) with asymptotic preserving property for the gray radiative transfer equations is constructed in cylindrical coordinates. The current UGKS can naturally capture the radiation diffusion solution in the optically thick regime with the cell size being much larger than photon’s mean free path. At the same time, the current UGKS can present accurate solutions in the optically thin regime as well. Moreover, it is a finite volume method with total energy conservation. Due to the scale-dependent time evolution solution for the interface flux evaluation, the scheme can cover multiscale transport mechanism seamlessly. The cylindrical hohlraum tests in inertial confinement fusion are used to validate the current approach, and the solutions are compared with implicit Monte Carlo result.

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Acknowledgements

The authors wish to thank all referees for their useful suggestions to improve the current paper. The research of Sun is supported by NSFC (Grant nos. 11671048, 91630310) and CAEP Project (2015B0202041, 2015B0202040); Jiang is supported by the National Basic Research Program under Grant 2014CB745002 and NSFC (Grant no. 11631008); and Xu is supported by Hong Kong research Grant council (16206617,16207715) and NSFC (Grant nos. 11772281,91530319).

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, China

    Wenjun Sun & Song Jiang

  2. Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Kun Xu

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  1. Wenjun Sun
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  2. Song Jiang
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  3. Kun Xu
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Correspondence to Song Jiang.

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Sun, W., Jiang, S. & Xu, K. Multiscale Radiative Transfer in Cylindrical Coordinates. Commun. Appl. Math. Comput. 1, 117–139 (2019). https://doi.org/10.1007/s42967-019-0007-x

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  • DOI: https://doi.org/10.1007/s42967-019-0007-x

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