55
Views
0
CrossRef citations to date
0
Altmetric
Radiative Transfer

Iterative space-angle discontinuous Galerkin method for radiative transfer equation

, &
Pages 1388-1404 | Received 17 Dec 2021, Accepted 11 Aug 2022, Published online: 06 Nov 2023

References

  • Siegel R, Howell J. Thermal radiation heat transfer. 4th ed. Taylor and Francis; 2002.
  • Reed WH, Hill T. Triangular mesh methods for the neutron transport equation. N. Mex: Los Alamos Scientific Lab; 1973.
  • Modest MF. Radiative heat transfer. Academic press; 2013.
  • Briggs L, Miller Jr W, Lewis E. Ray-effect mitigation in discrete ordinate-like angular finite element approximations in neutron transport. Nucl Sci Eng. 1975;57(3):205–217.
  • Chai JC, Lee HS, Patankar SV. Ray effect and false scattering in the discrete ordinates method. Numer Heat Transf B Fundam. 1993;24(4):373–389.
  • Rukolaine SA, Vasilyev MG, Yuferev VS, et al. Numerical solution of axisymmetric radiative transfer problems in arbitrary domains using the characteristic method. J Quant Spectrosc Radiat Transf. 2002;73(2-5):205–217. Available from: https://linkinghub.elsevier.com/retrieve/pii/S0022407301002047.
  • Ben Salah M, Askri F, Slimi K, et al. Numerical resolution of the radiative transfer equation in a cylindrical enclosure with the finite-volume method. Int J Heat Mass Transf. 2004;47(10–11):2501–2509.
  • Lewis EE, Miller WF. Computational methods of neutron transport. USA: John Wiley and Sons, Inc; 1984.
  • Wareing TA, McGhee JM, Morel JE, et al. Discontinuous finite element sn methods on three-dimensional unstructured grids. Nucl Sci Eng. 2001;138(3):256–268.
  • Ragusa JC, Guermond JL, Kanschat G. A robust sn-dg-approximation for radiation transport in optically thick and diffusive regimes. J Comput Phys. 2012;231(4):1947–1962.
  • Kópházi J, Lathouwers D. A space–angle dgfem approach for the boltzmann radiation transport equation with local angular refinement. J Comput Phys. 2015;297:637–668.
  • Clarke P, Wang H, Garrard J, et al. Space-angle discontinuous galerkin method for plane-parallel radiative transfer equation. J Quant Spectrosc Radiat Transf. 2019;233:87–98.
  • Yuan D, Cheng J, Shu CW. High order positivity-preserving discontinuous galerkin methods for radiative transfer equations. SIAM J Sci Comput. 2016;38(5):A2987–A3019. DOI:10.1137/16M1061072
  • Crockatt MM, Christlieb AJ, Garrett CK, et al. An arbitrary-order, fully implicit, hybrid kinetic solver for linear radiative transport using integral deferred correction. J Comput Phys. 2017;346:212–241. Available from: http://www.sciencedirect.com/science/article/pii/S002199911730462X.
  • Laboure VM, McClarren RG, Hauck CD. Implicit filtered PN for high-energy density thermal radiation transport using discontinuous galerkin finite elements. J Comput Phys. 2016;321:624–643. Available from: http://www.sciencedirect.com/science/article/pii/S0021999116301917.
  • Sun Y, Li S, Zhou R, et al. Spatial-angular spectral element method with discontinuous galerkin schemes for radiative transfer in 2d irregular enclosures with obstacles based on unstructured spatial elements. J Quant Spectrosc Radiat Transf. 2022;280:Article Id 108082.
  • Wang H, Abedi R, Mudaliar S. Space-angle discontinuous galerkin method for radiative transfer between concentric cylinders. J Quant Spectrosc Radiat Transf. 2020;257. Article Id 107281.
  • Grella K, Schwab C. Sparse tensor spherical harmonics approximation in radiative transfer. J Comput Phys. 2011;230(23):8452–8473.
  • Doktorwurde ED. Parallel and adaptive Galerkin methods for radiative transfer problems [dissertation]. Institut für Angewandte Mathematik, Universität Heidelberg; 1996.
  • Léger L, Chevallier L, Paletou F. Fast 2d non–LTE radiative modelling of prominences-numerical methods and benchmark results. Astronomy & Astrophysics. 2007;470(1):1–9.
  • Kim HK, Charette A. Frequency domain optical tomography using a conjugate gradient method without line search. J Quant Spectrosc Radiat Transf. 2007;104(2):248–256.
  • Dahmen W, Gruber F, Mula O. An adaptive nested source term iteration for radiative transfer equations. Math Comput. 2020;89(324):1605–1646.
  • Le Hardy D, Favennec Y, Rousseau B. Solution of the 2-D steady-state radiative transfer equation in participating media with specular reflections using SUPG and DG finite elements. J Quant Spectrosc Radiat Transf. 2016;179:149–164.
  • Amestoy PR, Duff IS, L'Excellent J-Y, et al. A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J Matrix Anal Appl. 2001;23(1):15–41.
  • Badri MA, Jolivet P, Rousseau B, et al. High performance computation of radiative transfer equation using the finite element method. J Comput Phys. 2018;360:74–92.
  • Abedi R, Chung SH, Erickson J, et al. Spacetime meshing with adaptive refinement and coarsening. In: Twentieth Annual Symposium on Computational Geometry (SCG '04); Brooklyn (NY): 2004.
  • Abedi R, Haber R, Thite S, et al. An h–adaptive spacetime–discontinuous galerkin method for linearized elastodynamics. Revue Européenne De Mécanique Numérique (European Journal of Computational Mechanics). 2006;15(6):619–642.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.