×

A hybrid transport-diffusion model for radiative transfer in absorbing and scattering media. (English) Zbl 1349.82112

Summary: A new multi-scale hybrid transport-diffusion model for radiative transfer is proposed in order to improve the efficiency of the calculations close to the diffusive regime, in absorbing and strongly scattering media. In this model, the radiative intensity is decomposed into a macroscopic component calculated by the diffusion equation, and a mesoscopic component. The transport equation for the mesoscopic component allows to correct the estimation of the diffusion equation, and then to obtain the solution of the linear radiative transfer equation. In this work, results are presented for stationary and transient radiative transfer cases, in examples which concern solar concentrated and optical tomography applications. The Monte Carlo and the discrete-ordinate methods are used to solve the mesoscopic equation. It is shown that the multi-scale model allows to improve the efficiency of the calculations when the medium is close to the diffusive regime. The proposed model is a good alternative for radiative transfer at the intermediate regime where the macroscopic diffusion equation is not accurate enough and the radiative transfer equation requires too much computational effort.

MSC:

82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
65C05 Monte Carlo methods
82D75 Nuclear reactor theory; neutron transport
85A25 Radiative transfer in astronomy and astrophysics
92C55 Biomedical imaging and signal processing
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Davison, B., Neutron Transport Theory (1958), Clarendon Press: Clarendon Press Oxford · Zbl 0079.43802
[2] Modest, M., Radiative Heat Transfer (2003), McGraw-Hill: McGraw-Hill New York
[3] (Welch, A.; van Gemert, M., Optical-Thermal Response of Laser-Irradiated Tissue (1995), Plenum: Plenum New York)
[4] Goody, R.; Yung, Y., Atmospheric Radiation (1989), Oxford University Press
[5] Howell, J., The Monte Carlo method in radiative heat transfer, J. Heat Transf., 120, 3, 547-560 (1998)
[6] Delatorre, J., Monte Carlo advances and concentrated solar applications, Sol. Energy, 103, 653-681 (2014)
[7] Bal, G.; Davies, A.; Langmore, I., A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport, J. Comput. Phys., 230, 7723-7735 (2011) · Zbl 1231.82059
[8] Roger, M.; Blanco, S.; Hafi, M. E.; Fournier, R., Monte Carlo estimates of domain-deformation sensitivities, Phys. Rev. Lett., 95, 18601, 1-4 (2005)
[9] Avila-Marin, A., Volumetric receivers in solar thermal power plants with central receiver system technology: a review, Sol. Energy, 85, 5, 891-910 (2011)
[10] Wu, Z.; Caliot, C.; Flamant, G.; Wang, Z., Coupled radiation and flow modeling in ceramic foam volumetric solar air receivers, Sol. Energy, 85, 9, 2374-2385 (2011)
[11] Wu, Z.; Wang, Z., Fully coupled transient modeling of ceramic foam volumetric solar air receiver, Sol. Energy, 89, 122-133 (2013)
[12] Kumar, S.; Mitra, K., Microscale aspects of thermal radiation transport and laser application, Adv. Heat Transf., 33, 187-294 (1999)
[13] Wan, S.; Guo, Z.; Kumar, S.; Aber, J.; Garetz, B., Noninvasive detection of inhomogeneities in turbid media with time-resolved log-slope analysis, J. Quant. Spectrosc. Radiat. Transf., 84, 493-500 (2004)
[14] Guo, Z.; Wan, S.; Kim, K.; Kosaraju, C., Comparing diffusion approximation with radiation transfer analysis for light transport in tissues, Opt. Rev., 10, 5, 415-421 (2003)
[15] Lehtikangas, O.; Tarvainen, T., Hybrid forward-peaked-scattering-diffusion approximations for light propagation in turbid media with low-scattering regions, J. Quant. Spectrosc. Radiat. Transf., 116, 132-144 (2013)
[16] Wang, L.; Jacques, S., Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media, J. Opt. Soc. Am. A, 10, 8, 1746-1752 (1993)
[17] Tarvainen, T.; Vauhkonen, M.; Kolehmainen, V.; Arridge, S.; Kaipio, J., Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions, Phys. Med. Biol., 50, 4913-4930 (2005)
[18] Gorpas, D.; Yova, D.; Politopoulos, K., A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging, J. Quant. Spectrosc. Radiat. Transf., 111, 553-568 (2010)
[19] Degond, P.; Jin, S., A smooth transition model between kinetic and diffusion equations, SIAM J. Numer. Anal., 42, 2671-2687 (2005) · Zbl 1086.82005
[20] Roger, M.; Crouseilles, N., A dynamic multi-scale model for transient radiative transfer calculations, J. Quant. Spectrosc. Radiat. Transf., 116, 110-121 (2013)
[21] Crouseilles, N.; Degond, P.; Lemou, M., A hybrid kinetic-fluid model for solving the Vlasov-BGK equation, J. Comput. Phys., 203, 572-601 (2005) · Zbl 1143.82320
[22] Lemou, M.; Mieussens, L., A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit, SIAM J. Sci. Comput., 31, 1, 334-368 (2008) · Zbl 1187.82110
[23] Degond, P.; Dimarco, G.; Mieussens, L., A multiscale kinetic-fluid solver with dynamic localization of kinetic effects, J. Comput. Phys., 229, 4907-4933 (2010) · Zbl 1346.82035
[24] Lemou, M.; Méhats, F., Micro-macro schemes for kinetic equations including boundary layers, SIAM J. Sci. Comput., 34, 6, B734-B760 (2012) · Zbl 1266.82060
[25] Star, W., Diffusion theory of light transport, (Optical-Thermal Response of Laser-Irradiated Tissue (1995), Plenum: Plenum New York), Chapter 6
[26] Coquard, R.; Baillis, D.; Randrianalisoa, J., Homogeneous phase and multi-phase approaches for modeling radiative transfer in foams, Int. J. Therm. Sci., 50, 9, 1648-1663 (2011)
[27] Chai, J., Finite volume method for transient radiative transfer, Numer. Heat Transf., Part B, Fundam., 44, 187-208 (2003)
[28] Ruan, L.; Wang, S.; Qi, H.; Wang, D., Analysis of the characteristics of time-resolved signals for transient radiative transfer in scattering participating media, J. Quant. Spectrosc. Radiat. Transf., 111, 2405-2414 (2010)
[29] Lu, X.; Hsu, P.f., Reverse Monte Carlo simulations of light pulse propagation in nonhomogeneous media, J. Quant. Spectrosc. Radiat. Transf., 93, 349-367 (2005)
[30] Roger, M., Modèles de sensibilité dans le cadre de la méthode de Monte Carlo: illustrations en transfert radiatif (2006), INP: INP Toulouse, France, PhD thesis
[31] Liu, L.; Ruan, L.; Tan, H., On the discrete ordinates method for radiative heat transfer in anisotropically scattering media, Int. J. Heat Mass Transf., 45, 3259-3262 (2002) · Zbl 0994.80501
[32] Hunter, B.; Guo, Z., Conservation of asymmetry factor in phase function discretization for radiative transfer analysis in anisotropic scattering media, Int. J. Heat Mass Transf., 55, 1544-1552 (2012) · Zbl 1262.80021
[33] Hammersley, J.; Handscomb, D., Monte Carlo Methods (1964), Chapman and Hall: Chapman and Hall London · Zbl 0121.35503
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.