Vol. 29, issue 09, article # 3

Budak V. P., Zheltov V. S., Lubenchenko A. V., Freidlin K. S., Shagalov O. V. Fast and accurate algorithm for the numerical simulation of radiative transfer in turbid media. // Optika Atmosfery i Okeana. 2016. V. 29. No. 09. P. 739–746. DOI: 10.15372/AOO20160903 [in Russian].
Copy the reference to clipboard
Abstract:

It is shown that the regular part of the solution (RPS) remained after the separation of the anisotropic part of the solution (APS) in the small-angle modification of the spherical harmonics method (MSH) is a smooth quasi-isotropic function with some peaks in the angular distribution. The smooth part of the RPS without peaks can be determined in two-streaming or diffuse approximation. The first iteration of the resulting radiance angular distribution significantly refines the solution and allows restoring the specified angular peaks. Quasi-diffusion approach – the separation of APS by MSH, the definition of RPS in the diffuse approximation and refinement of solutions based on the first iteration, – is independent of the problem symmetry, and therefore can be generalized to the case of arbitrary medium geometry.

Keywords:

discrete radiative transfer equation, quasi-diffusion approximation, synthetic iteration

References:

  1. Yokota T., Oguma H., Morino I., Inoue G. A nadir looking SWIR FTS to monitor CO2 column density for Japanese GOSAT project // Proc. XXIV Int. Sym. Space Technol. Sci. Miyazaki, Japan, May–June 2004. P. 887.
  2. Budak V.P., Klyuykov D.A., Korkin S.V. Convergence acceleration of radiative transfer equation solution at strongly anisotropic scattering // Light Scattering Reviews 5. Single Light Scattering and Radiative Transfer / Ed. A.A. Kokhanovsky. Springer Praxis Books, 2010. P. 147–204.
  3. Budak V.P., Shagalov O.V., Zheltov V.S. Numerical radiative transfer modeling in turbid medium slab // 20th Int. Symp. on Atmospheric and Ocean Optics: Atmospheric Physics. Proc. SPIE. 9292. 2014. P. 92920Y.
  4. Krylov V.I. Priblizhennoe vychislenie integralov. M.: Nauka, 1967. 500 p.
  5. Apresjan L.A., Kravcov Ju.A. Teorija perenosa izluchenija: Statisticheskie i volnovye aspekty. M.: Nauka, Gl. red. fiz.-mat. literatury, 1983. 320 p.
  6. Budak V.P., Veklenko B.A. Boson peak, flickering noise, backscattering processes and radiative transfer in random media // J. Quant. Spectrosc. Radiat. Transfer. 2011. V. 112, N 5. P. 864–875.
  7. Budak V.P., Kozel'skij A.V., Savickij E.N. Uluchshenie shodimosti metoda sfericheskih garmonik pri sil'no anizotropnom rassejanii // Optika atmosf. i okeana. 2004. V. 17, N 1. P. 36–41.
  8. Budak V.P., Korkin S.V. On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering // J. Quant. Spectrosc. Radiat. Transfer. 2008. V. 109, N 2. P. 220–234.
  9. Budak V.P., Klyuykov D.A., Korkin S.V. Complete matrix solution of radiative transfer equation for pile of horizontally homogeneous slabs // J. Quant. Spectrosc. Radiat. Transfer. 2011. V. 112, N 7. P. 1141–1148.
  10. Kokhanovsky A.A., Budak V.P., Cornet C., Duan M., Emde C., Katsev I.L., Klyukov D.A., Korkin S.V., C-Labonnote L., Mayer B., Min Q., Nakajima T., Ota Y., Prikhach A.S., Rozanov V.V., Yokota T., Zege E.P. Benchmark results in vector atmospheric radiative transfer // J. Quant. Spectrosc. Radiat. Transfer. 2010. V. 111, N 12–13. P. 1931–1946.
  11. Sokoletsky L.G., Budak V.P., Shen F., Kokhanovsky A.A. Comparative analysis of radiative transfer approaches for calculation of plane transmittance and diffuse attenuation coefficient of plane-parallel light scattering layers // Appl. Opt. 2014. V. 53, N 3. P. 459–468.
  12. Budak V.P., Kozel'skij A.V. O tochnosti i granicah primenimosti malouglovogo priblizhenija // Optika atmosf. i okeana. 2005. V. 18, N 1–2. P. 38–44.
  13. Budak V.P., Sapmin S.Je. Reshenie uravnenija perenosa izluchenija metodom sfericheskih garmonik v malouglovoj modifikacii // Optika atmosfery. 1990. V. 3, N 9. P. 981–987.
  14. Budak V.P., Kljujkov D.A., Korkin S.V. CIAO – programma modelirovanija poljarizacionnyh signalov spektral'nyh priborov distancionnogo zondirovanija v sisteme «okean–atmosfera» // Izv. vuzov. Fiz. 2010. V. 53, N 9/3. P. 58–69.
  15. Budak V.P., Efremenko D.S., Shagalov O.V. Efficiency of algorithm for solution of vector radiative transfer equation in turbid medium slab // J. Phys.: Conference Series. 2012. V. 369. 012021 (10 p.).
  16. Budak V.P., Kaloshin G.A., Shagalov O.V., Zheltov V.S. Numerical modeling of the radiative transfer in a turbid medium using the synthetic iteration // Opt. Express. 2015. V. 23, N 15. P. A829.
  17. Adams M.L., Larsen E.W. Fast iterative methods for discrete-ordinates particle transport calculations // Progr. Nuclear Energy. 2002. V. 40, N 1. P. 3–159.
  18. Li H.-S., Flamant G., Lu J.-D. An alternative discrete ordinate scheme for collimated irradiation problems // Int. Comm. Heat Mass Transfer. 2003. V. 30, N 1. P. 61–70.
  19. Efremenko D., Doicu A., Loyola D., Trautmann T. Acceleration techniques for the discrete ordinate method // J. Quant. Spectrosc. Radiat. Transfer. 2013. V. 114. P. 73–81.
  20. Thomas G.E., Stamnes K. Radiative Transfer in the Atmosphere and Ocean. N.Y.; Cambridge: Cambridge University Press, 2006. 540 p.
  21. Gol'din V.Ja. Kvazidiffuzionnyj metod reshenija kineticheskogo uravnenija // Zh. vychisl. mat. i mat. fiz. 1964. V. 4, N 6. P. 1078–1087.
  22. Aristova E.N., Gol'din V.Ja. Raschet anizotropnogo rassejanija solnechnogo izluchenija v atmosfere (monojenergeticheskij sluchaj) // Mat. modelir. 1998. V. 10, N 9. P. 14–34.
  23. Djevidson B. Teorija perenosa nejtronov. M.: Atomizdat, 1960. 438 p.

Back