## One-dimensional transient radiative transfer by lattice Boltzmann method |

Optics Express, Vol. 21, Issue 21, pp. 24532-24549 (2013)

http://dx.doi.org/10.1364/OE.21.024532

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### Abstract

The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing scattering media subjected to a collimated short laser irradiation. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. The accuracy and computational efficiency of this algorithm are examined firstly. Afterwards, effects of the medium properties such as the extinction coefficient, the scattering albedo and the anisotropy factor, and the shapes of laser pulse on time-resolved signals of transmittance and reflectance are investigated. Results of the present method are found to compare very well with the data from the literature. For an oblique incidence, the LBM results in this paper are compared with those by Monte Carlo method generated by ourselves. In addition, transient radiative transfer in a two-Layer inhomogeneous media subjected to a short square pulse irradiation is investigated. At last, the LBM is further extended to study the transient radiative transfer in homogeneous medium with a refractive index discontinuity irradiated by the short pulse laser. Several trends on the time-resolved signals different from those for refractive index of 1 (i.e. refractive-index-matched boundary) are observed and analysed.

© 2013 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(140.7090) Lasers and laser optics : Ultrafast lasers

(290.7050) Scattering : Turbid media

(010.5620) Atmospheric and oceanic optics : Radiative transfer

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: July 26, 2013

Revised Manuscript: September 15, 2013

Manuscript Accepted: September 30, 2013

Published: October 7, 2013

**Citation**

Yong Zhang, Hongliang Yi, and Heping Tan, "One-dimensional transient radiative transfer by lattice Boltzmann method," Opt. Express **21**, 24532-24549 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-24532

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### References

- A. Majumdar, “Microscale heat conduction in dielectric thin films,” J. Heat Transfer115(1), 7–16 (1993). [CrossRef]
- J. Y. Murthy and S. R. Mathur, “Computation of sub-micron thermal transport using an unstructured finite volume method,” J. Heat Transfer124(6), 1176–1181 (2002). [CrossRef]
- T. Q. Qiu and C. L. Tien, “Short-pulse laser heating on metals,” Int. J. Heat Mass Transfer35(3), 719–726 (1992). [CrossRef]
- F. Liu, K. M. Yoo, and R. R. Alfano, “Ultrafast Laser-Pulse Transmission and Imaging Through Biological Tissues,” Appl. Opt.32(4), 554–558 (1993). [CrossRef] [PubMed]
- M. C. van Gemert and A. J. Welch, “Clinical Use of Laser-Tissue Interactions,” IEEE Eng. Med. Biol. Mag.8(4), 10–13 (1989). [CrossRef] [PubMed]
- K. J. Grant, J. A. Piper, D. J. Ramsay, and K. L. Williams, “Pulsed lasers in particle detection and sizing,” Appl. Opt.32(4), 416–417 (1993). [CrossRef] [PubMed]
- S. Kumar and K. Mitra, “Microscale Aspects of Thermal Radiation and Laser Applications,” Adv. Heat Transfer33, 187–294 (1999). [CrossRef]
- H. Schweiger, A. Oliva, M. Costa, and C. D. P. Segarra, “A Monte Carlo method for the simulation of transient radiation heat transfer: application to compound honeycomb transparent insulation,” Numer. Heat Transf. B35, 113–136 (2001).
- Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transf.73(2-5), 159–168 (2002). [CrossRef]
- X. D. Lu and P. F. Hsu, “Reverse Monte Carlo method for transient radiative transfer in participating media,” J. Heat Transfer126(4), 621–627 (2004). [CrossRef]
- X. D. Lu and P. F. Hsu, “Reverse Monte Carlo simulations of light pulse propagation in nonhomogeneous media,” J. Quant. Spectrosc. Radiat. Transf.93(1-3), 349–367 (2005). [CrossRef]
- M. Martinelli, A. Gardner, D. Cuccia, C. Hayakawa, J. Spanier, and V. Venugopalan, “Analysis of single Monte Carlo methods for prediction of reflectance from turbid media,” Opt. Express19(20), 19627–19642 (2011). [CrossRef] [PubMed]
- Z. X. Guo and S. Kumar, “Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media,” Appl. Opt.40(19), 3156–3163 (2001). [CrossRef] [PubMed]
- M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light-pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transf.73(2-5), 169–179 (2002). [CrossRef]
- Z. X. Guo and S. Kumar, “Three-dimensional discrete ordinates method in transient radiative transfer,” J. Thermophys, Heat Transfer16, 289–296 (2002).
- J. M. Wang and C. Y. Wu, “Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate,” Int. J. Heat Mass Transfer53(19-20), 3799–3806 (2010). [CrossRef]
- Z. M. Tan and P. F. Hsu, “An integral formulation of transient radiative transfer,” J. Heat Transfer123(3), 466–475 (2001). [CrossRef]
- C. Y. Wu, “Propagation of scattered radiation in a participating planar medium with pulse irradiation,” J. Quant. Spectrosc. Radiat. Transf.64(5), 537–548 (2000). [CrossRef]
- P. F. Hsu, “Effects of multiple scattering and reflective boundary on the transient radiative transfer process,” Int. J. Therm. Sci.40(6), 539–549 (2001). [CrossRef]
- J. C. Chai, “One-dimensional transient radiation heat transfer modeling using a finite-volume method,” Numer. Heat Transf. B44(2), 187–208 (2003). [CrossRef]
- M. Y. Kim, S. Menon, and S. W. Baek, “On the transient radiative transfer in a one-dimensional planar medium subjected to radiative equilibrium,” Int. J. Heat Mass Transfer53(25-26), 5682–5691 (2010). [CrossRef]
- L. M. Ruan, S. G. Wang, H. Qi, and D. L. Wang, “Analysis of the characteristics of time-resolved signals for transient radiative transfer in scattering participating media,” J. Quant. Spectrosc. Radiat. Transf.111(16), 2405–2414 (2010). [CrossRef]
- S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer49(11-12), 1820–1832 (2006). [CrossRef]
- L. H. Liu and L. J. Liu, “Discontinuous finite element approach for transient radiative transfer equation,” J. Heat Transfer129(8), 1069–1074 (2007). [CrossRef]
- L. H. Liu and P. F. Hsu, “Time shift and superposition method for solving transient radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transf.109(7), 1297–1308 (2008). [CrossRef]
- X. He, S. Chen, and R. A. Zhang, “Lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability,” J. Comput. Phys.152(2), 642–663 (1999). [CrossRef]
- S. Succi, The Lattice Boltzmann Method for Fluid Dynamics and Beyond (Oxford University, 2001).
- W. S. Jiaung, J. R. Ho, and C. P. Kuo, “Lattice Boltzmann method for heat conduction problem with phase change,” Numer. Heat Transfer, Part B39, 167–187 (2001).
- S. C. Mishra and A. Lankadasu, “Analysis of transient conduction and radiation heat transfer using the lattice Boltzmann method and the discrete transfer method,” Numer. Heat Transfer, Part A47, 935–954 (2005).
- S. C. Mishra and H. K. Roy, “Solving transient conduction-radiation problems using the lattice Boltzmann method and the finite volume method,” J. Comput. Phys.223(1), 89–107 (2007). [CrossRef]
- S. C. Mishra, T. B. Pavan Kumar, and B. Mondal, “Lattice Boltzmann method applied to the solution of energy equation of a radiation and non-Fourier heat conduction problem,” Numer. Heat Transfer, Part A54, 798–818 (2008).
- B. Mondal and S. C. Mishra, “Simulation of natural convection in the presence of volumetric radiation using the lattice Boltzmann method,” Numer. Heat Transfer, Part A55, 18–41 (2009).
- P. Asinari, S. C. Mishra, and R. Borchiellini, “A lattice Boltzmann formulation to the analysis of radiative heat transfer problems in a participating medium,” Numer. Heat Transfer, Part B57, 126–146 (2010).
- A. F. D. Rienzo, P. Asinari, R. Borchiellini, and S. C. Mishra, “Improved angular discretization and error analysis of the lattice Boltzmann method for solving radiative heat transfer in a participating medium,” Int. J. Numer. Methods Heat Fluid Flow21(5), 640–662 (2011). [CrossRef]
- Y. Ma, S. K. Dong, and H. P. Tan, “Lattice Boltzmann method for one-dimensional radiation transfer,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.84(1), 016704 (2011). [CrossRef] [PubMed]
- H. Bindra and D. V. Patil, “Radiative or neutron transport modeling using a lattice Boltzmann equation framework,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.86(1), 016706 (2012). [CrossRef] [PubMed]
- S. C. Mishra and R. R. Vernekar, “Analysis of transport of collimated radiation in a participating media using the lattice Boltzmann method,” J. Quant. Spectrosc. Radiat. Transf.113(16), 2088–2099 (2012). [CrossRef]
- R. Siegel, “Variable Refractive Index Effects on Radiation in Semitransparent Scattering Multilayered Regions,” J. Thermophys. Heat Transfer7, 624–630 (1993).

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