Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions

Gao Cong-Zhang; Cai Ying; Huang Cheng-Wu; Zhao Yang; Yin Jian-Wei; Fan Zheng-Feng; Yang Jia-Min; Wang Pei; Zhu Shao-Ping

doi:10.1063/5.0208236

Volume 9 Issue 6

Nov. 2024

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Gao Cong-Zhang, Cai Ying, Huang Cheng-Wu, Zhao Yang, Yin Jian-Wei, Fan Zheng-Feng, Yang Jia-Min, Wang Pei, Zhu Shao-Ping. Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions[J]. Matter and Radiation at Extremes, 2024, 9(6): 067802. doi: 10.1063/5.0208236

Citation:

Gao Cong-Zhang, Cai Ying, Huang Cheng-Wu, Zhao Yang, Yin Jian-Wei, Fan Zheng-Feng, Yang Jia-Min, Wang Pei, Zhu Shao-Ping. Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions[J]. Matter and Radiation at Extremes, 2024, 9(6): 067802. doi: 10.1063/5.0208236

Citation:

Gao Cong-Zhang, Cai Ying, Huang Cheng-Wu, Zhao Yang, Yin Jian-Wei, Fan Zheng-Feng, Yang Jia-Min, Wang Pei, Zhu Shao-Ping. Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions[J]. Matter and Radiation at Extremes, 2024, 9(6): 067802. doi: 10.1063/5.0208236

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Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions

doi: 10.1063/5.0208236

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, People’s Republic of China
2.
Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang, Sichuan 621900, People’s Republic of China

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Author Bio:
cwhuang@mail.ustc.edu.cn

yin_jianwei@iapcm.ac.cn

fan_zhengfeng@iapcm.ac.cn

wangpei@iapcm.ac.cn
Received Date: 2024-03-14
Accepted Date: 2024-08-03

Available Online: 2024-11-01

Publish Date: 2024-11-01

Abstract

Abstract

We study radiative transfer in participating binary stochastic mixtures in two dimensions (2D) by developing an accurate and efficient simulation tool. For two different sets of physical parameters, 2D benchmark results are presented, and it is found that the influence of the stochastic mixture on radiative transfer is clearly parameter-dependent. Our results confirm that previous multidimensional results obtained in different studies are basically consistent, which is interpreted in terms of the relationship between the photon mean free path l_p and the system size L. Nonlinear effects, including those due to scattering and radiation–material coupling, are also discussed. To further understand the particle size effect, we employ a dimensionless parameter l_p/L, from which a critical particle size can be derived. On the basis of further 2D simulations, we find that an inhomogeneous mix is obtained for l_p/L > 0.1. Furthermore, 2D material temperature distributions reveal that self-shielding and particle–particle shielding of radiation occur, and are enhanced when l_p/L is increased. Our work is expected to provide benchmark results to verify proposed homogenized models and/or other codes for stochastic radiative transfer in realistic physical scenarios.

Conflict of Interest
The authors have no conflicts to disclose.
C.-Z.G. and Y.C. contributed equally to this work.
Author Contributions
Cong-Zhang Gao: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Software (equal); Writing – original draft (equal). Ying Cai: Data curation (equal); Software (equal); Visualization (equal). Cheng-Wu Huang: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). Yang Zhao: Formal analysis (equal); Project administration (equal). Jian-Wei Yin: Formal analysis (equal); Methodology (equal); Resources (equal); Supervision (equal); Validation (equal). Zheng-Feng Fan: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Resources (equal). Jia-Min Yang: Investigation (equal); Supervision (equal). Pei Wang: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal). Shao-Ping Zhu: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Supervision (equal).
The data that supports the findings of this study are available within the article and additional data are available from the corresponding author upon reasonable request.

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References(53)

References

[1]	J. Nuckolls, L. Wood, A. Thiessen, and G. Zimmerman, “Laser compression of matter to super-high densities: Thermonuclear (CTR) applications,” Nature 239, 139–142 (1972).10.1038/239139a0
[2]	R. Betti and O. A. Hurricane, “Inertial-confinement fusion with lasers,” Nat. Phys. 12, 435–448 (2016).10.1038/nphys3736
[3]	H. Abu-Shawareb, R. Acree, P. Adams, J. Adams, B. Addis, R. Aden, P. Adrian, B. Afeyan, M. Aggleton, L. Aghaian et al., “Achievement of target gain larger than unity in an inertial fusion experiment,” Phys. Rev. Lett. 132, 065102 (2024).10.1103/physrevlett.132.065102
[4]	O. Hurricane, D. Callahan, D. Casey, A. Christopherson, A. Kritcher, O. Landen, S. Maclaren, R. Nora, P. Patel, J. Ralph et al., “Energy principles of scientific breakeven in an inertial fusion experiment,” Phys. Rev. Lett. 132, 065103 (2024).10.1103/physrevlett.132.065103
[5]	O. Landen, R. Benedetti, D. Bleuel, T. Boehly, D. Bradley, J. Caggiano, D. Callahan, P. Celliers, C. Cerjan, D. Clark et al., “Progress in the indirect-drive national ignition campaign,” Plasma Phys. Controlled Fusion 54, 124026 (2012).10.1088/0741-3335/54/12/124026
[6]	T. R. Dittrich, B. A. Hammel, C. J. Keane, R. McEachern, R. E. Turner, S. W. Haan, and L. J. Suter, “Diagnosis of pusher-fuel mix in indirectly driven nova implosions,” Phys. Rev. Lett. 73, 2324 (1994).10.1103/physrevlett.73.2324
[7]	L. Rayleigh, “Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density,” Proc. London Math. Soc. s1-14, 170–177 (1882).10.1112/plms/s1-14.1.170
[8]	G. I. Taylor, “The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I,” Proc. R. Soc. London, Ser. A 201, 192–196 (1950).10.1098/rspa.1950.0052
[9]	R. D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids,” Commun. Pure Appl. Math. 13, 297–319 (1960).10.1002/cpa.3160130207
[10]	E. E. Meshkov, “Instability of the interface of two gases accelerated by a shock wave,” Fluid Dyn. 4, 101–104 (1972).10.1007/bf01015969
[11]	V. Smalyuk, C. Weber, O. Landen, S. Ali, B. Bachmann, P. Celliers, E. Dewald, A. Fernandez, B. Hammel, G. Hall et al., “Review of hydrodynamic instability experiments in inertially confined fusion implosions on National Ignition Facility,” Plasma Phys. Controlled Fusion 62, 014007 (2019).10.1088/1361-6587/ab49f4
[12]	G. C. Pomraning, “Radiative transfer in Rayleigh–Taylor unstable ICF pellets,” Laser Part. Beams 8, 741–751 (1990).10.1017/s0263034600009137
[13]	S. P. Regan, R. Epstein, B. A. Hammel, L. J. Suter, H. A. Scott, M. A. Barrios, D. K. Bradley, D. A. Callahan, C. Cerjan, G. W. Collins et al., “Hot-spot mix in ignition-scale inertial confinement fusion targets,” Phys. Rev. Lett. 111, 045001 (2013).10.1103/physrevlett.111.045001
[14]	B. Bachmann, J. E. Ralph, A. B. Zylstra, S. A. MacLaren, T. Döppner, D. O. Gericke, G. W. Collins, O. A. Hurricane, T. Ma, J. R. Rygg et al., “Localized mix-induced radiative cooling in a capsule implosion at the National Ignition Facility,” Phys. Rev. E 101, 033205 (2020).10.1103/physreve.101.033205
[15]	D. S. Miller, F. Graziani, and G. Rodrigue, “Benchmarks and models for time-dependent grey radiation transport with material temperature in binary stochastic media,” J. Quant. Spectrosc. Radiat. Transfer 70, 115–128 (2001).10.1016/s0022-4073(00)00128-x
[16]	C. D. Levermore, G. C. Pomraning, D. L. Sanzo, and J. Wong, “Linear transport theory in a random medium,” J. Math. Phys. 27, 2526–2536 (1986).10.1063/1.527320
[17]	M. L. Adams, E. W. Larsen, and G. C. Pomraning, “Benchmark results for particle transport in a binary Markov statistical medium,” J. Quant. Spectrosc. Radiat. Transfer 42, 253–266 (1989).10.1016/0022-4073(89)90072-1
[18]	G. C. Pomraning, Linear Kinetic Theory and Particle Transport in Stochastic Mixtures (World Scientific, 1991), Vol. 7.
[19]	B. Su and G. C. Pomraning, “Limiting correlation lenght solutions in stochastic radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 51, 893–912 (1994).10.1016/0022-4073(94)90019-1
[20]	G. L. Olson, “Gray radiation transport in multi-dimensional stochastic binary media with material temperature coupling,” J. Quant. Spectrosc. Radiat. Transfer 104, 86–98 (2007).10.1016/j.jqsrt.2006.08.013
[21]	G. L. Olson, “Grey and multigroup radiation transport models for two-dimensional stochastic media with material temperature coupling,” J. Quant. Spectrosc. Radiat. Transfer 113, 325–334 (2012).10.1016/j.jqsrt.2011.12.009
[22]	G. L. Olson, “Gray and multigroup radiation transport models for two-dimensional binary stochastic media using effective opacities,” J. Quant. Spectrosc. Radiat. Transfer 168, 57–65 (2016).10.1016/j.jqsrt.2015.09.005
[23]	G. L. Olson, “Gray and multigroup radiation transport through 3D binary stochastic media with different sphere radii distributions,” J. Quant. Spectrosc. Radiat. Transfer 189, 243–248 (2017).10.1016/j.jqsrt.2016.12.003
[24]
[25]
[26]	P. S. Brantley, “Benchmark investigation of a 3D Monte Carlo Levermore–Pomraning algorithm for binary stochastic media,” Trans. Am. Nucl. Soc. 111, 655–658 (2014).
[27]
[28]
[29]	P. A. Rosen, J. M. Foster, M. J. Taylor, P. A. Keiter, C. C. Smith, J. R. Finke, M. Gunderson, and T. S. Perry, “Experiments to study radiation transport in clumpy media,” Astrophys. Space Sci. 307, 213–217 (2007).10.1007/s10509-006-9235-4
[30]	P. Keiter, M. Gunderson, J. Foster, P. Rosen, A. Comley, M. Taylor, and T. Perry, “Radiation transport in inhomogeneous media,” Phys. Plasmas 15, 056901 (2008).10.1063/1.2927529
[31]	G. Meng, J. She, T. Song, J. Yang, and M. Wang, “Theoretical investigations on x-ray transport in radiation transport experiments on the Shenguang-III prototype laser facility,” Matter Radiat. Extremes 7, 025901 (2022).10.1063/5.0043745
[32]	P. S. Brantley, “A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures,” J. Quant. Spectrosc. Radiat. Transfer 112, 599–618 (2011).10.1016/j.jqsrt.2010.06.007
[33]	C.-Z. Gao, Y. Cai, C.-B. Zhang, Z.-Y. Hong, Z.-F. Fan, P. Wang, and J.-G. Wang, “Stochastic radiative transfer in random media. II. Coupling of radiation to material,” Phys. Rev. E 105, 014131 (2022).10.1103/physreve.105.014131
[34]
[35]	G. L. Olson, L. H. Auer, and M. L. Hall, “Diffusion, P1, and other approximate forms of radiation transport,” J. Quant. Spectrosc. Radiat. Transfer 64, 619–634 (2000).10.1016/s0022-4073(99)00150-8
[36]	G. L. Olson, D. S. Miller, E. W. Larsen, and J. E. Morel, “Chord length distributions in binary stochastic media in two and three dimensions,” J. Quant. Spectrosc. Radiat. Transfer 101, 269–283 (2006).10.1016/j.jqsrt.2005.11.070
[37]	G. C. Pomraning, The Equations of Radiation Hydrodynamics (Pergamon, Oxford, 1973).
[38]	C.-Z. Gao, C.-B. Zhang, C.-X. Yu, X.-F. Xu, S.-C. Wang, C. Yang, Z.-Y. Hong, Z.-F. Fan, and P. Wang, “Stochastic radiative transfer in random media: Pure absorbing cases,” Phys. Rev. E 102, 022111 (2020).10.1103/physreve.102.022111
[39]	C. D. Levermore, J. Wong, and G. C. Pomraning, “Renewal theory for transport processes in binary statistical mixtures,” J. Math. Phys. 29, 995–1004 (1988).10.1063/1.527997
[40]	B. Su and G. C. Pomraning, “Benchmark results for particle transport in binary non-Markovian mixtures,” J. Quant. Spectrosc. Radiat. Transfer 50, 211–226 (1993).10.1016/0022-4073(93)90119-3
[41]	O. Zuchuat, R. Sanchez, I. Zmijarevic, and F. Malvagi, “Transport in renewal statistical media: Benchmarking and comparison with models,” J. Quant. Spectrosc. Radiat. Transfer 51, 689–722 (1994).10.1016/0022-4073(94)90125-2
[42]	A. K. Prinja and G. L. Olson, “Grey radiative transfer in binary statistical media with material temperature coupling: Asymptotic limits,” J. Quant. Spectrosc. Radiat. Transfer 90, 131–159 (2005).10.1016/j.jqsrt.2004.03.010
[43]	G. L. Olson, “Gray radiation transport models for two-dimensional binary stochastic media with material temperature coupling using spherical harmonics,” J. Quant. Spectrosc. Radiat. Transfer 148, 127–133 (2014).10.1016/j.jqsrt.2014.07.002
[44]	C. Larmier, F.-X. Hugot, F. Malvagi, A. Mazzolo, and A. Zoia, “Benchmark solutions for transport in d-dimensional Markov binary mixtures,” J. Quant. Spectrosc. Radiat. Transfer 189, 133–148 (2017).10.1016/j.jqsrt.2016.11.015
[45]	B. Widom, “Random sequential addition of hard spheres to a volume,” J. Chem. Phys. 44, 3888–3894 (1966).10.1063/1.1726548
[46]	W. Ji, J. L. Conlin, W. R. Martin, J. C. Lee, and F. B. Brown, “Explicit modeling of particle fuel for the very-high temperature gas-cooled reactor,” Trans. Am. Nucl. Soc. 92, 236–238 (2005).
[47]	H. Liu, H. Song, Q. Zhang, G. Zhang, and Y. Zhao, “Validation for equation of state in wide regime: Copper as prototype,” Matter Radiat. Extremes 1, 123 (2016).10.1016/j.mre.2016.03.002
[48]	N. Hirao, Y. Akahama, and Y. Ohishi, “Equations of state of iron and nickel to the pressure at the center of the Earth,” Matter Radiat. Extremes 7, 038403 (2022).10.1063/5.0074340
[49]	J. Colgan, D. P. Kilcrease, N. Magee, M. E. Sherrill, J. Abdallah Jr, P. Hakel, C. J. Fontes, J. A. Guzik, and K. Mussack, “A new generation of Los Alamos opacity tables,” Astrophys. J. 817, 116 (2016).10.3847/0004-637x/817/2/116
[50]	N. Y. Orlov, M. A. Kadatskiy, O. B. Denisov, and K. V. Khishchenko, “Application of quantum-statistical methods to studies of thermodynamic and radiative processes in hot dense plasmas,” Matter Radiat. Extremes 4, 054403 (2019).10.1063/1.5096439
[51]	E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport (John Wiley and Sons, Inc., New York, 1984).
[52]	M. Zeyao and F. Lianxiang, “Parallel flux sweep algorithm for neutron transport on unstructured grid,” J. Supercomput. 30, 5–17 (2004).10.1023/b:supe.0000032778.36178.d8
[53]