111
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Two-Level Transport Methods with Independent Discretization

&
Pages 424-450 | Received 16 Mar 2018, Accepted 04 Jul 2018, Published online: 19 Nov 2018

References

  • Adams, M. L. 2001. Discontinuous finite element transport solutions in thick diffusive problems. Nucl. Sci. Eng. 137: 298–333. doi:10.13182/NSE00-41.
  • Adams, M. L., and E. W. Larsen. 2002. Fast iterative methods for discrete-ordinates particle transport calculations. Prog. Nucl. Energy 40: 3–159. doi:10.1016/S0149-1970(01)00023-3.
  • Alcouffe, R. E., E. W. Larsen, W. F. Miller Jr., and B. R. Wienke. 1979. Computational efficiency of numerical methods for the multigroup, discrete-ordinates neutron transport equations: the slab geometry case. Nucl. Sci. Eng. 71 (2): 111–127. doi:10.13182/NSE71-111.
  • Anistratov, D. Y., and J. S. Warsa. 2017. DFEM discretization of quasidiffusion moment equations in 1D slab geometry. Proceedings of M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Jeju, Korea, April 16–20.
  • Anistratov, D. Y., and J. S. Warsa. 2018. Discontinuous finite element quasidiffusion methods. Nucl. Sci. Eng. 191: 105–120. doi:10.1080/00295639.2018.1450013.
  • Anistratov, D. Y., and V. Ya. Gol’din. 1986. Comparison of difference schemes for the quasi-diffusion method for solving the transport equation. Probl. Atomic Sci. Eng. 2: 17–23 [in Russian].
  • Anistratov, D. Y., and V. Ya. Gol’din. 1986. Solution of the multigroup transport equation by the quasi-diffusion method, Preprint of the Keldysh Institute for Applied Mathematics. USSR Acad. Sci. 128: 19 [in Russian].
  • Anistratov, D. Y., and V. Ya. Gol’din. 1993. Nonlinear methods for solving particle transport problems. Trans. Theory Stat. Phys. 22: 42–77. doi:10.1080/00411459308203810.
  • Anistratov, D. Y., and V. Ya. Gol’din. 2011. Multilevel quasidiffusion methods for solving multigroup transport k-eigenvalue problems in one-dimensional slab geometry. Nucl. Sci. Eng. 169: 111–132. doi:10.13182/NSE10-64.
  • Aristova, E. N., and V. Ya. Gol’din. 2000. Computation of anisotropy scattering of solar radiation in atmosphere (monoenergetic case). J. Quant. Spectrosc. Radiat. Transfer 67: 139–157. doi:10.1016/S0022-4073(99)00201-0.
  • Aristova, E. N., V. Ya. Gol’din, and A. V. Kolpakov. 1999. Multidimensional calculations of radiation transport by nonlinear quasi-diffusion method. Proc. of Int. Conf. on Math. and Comp., M&C 1999, Madrid, Spain, 667–676.
  • Calef, M. T., E. D. Fichtl, J. S. Warsa, M. Berndt, and N. N. Carlson. 2013 Nonlinear Krylov acceleration applied to a discrete ordinates formulation of the k-eigenvalue problem. J. Comput. Phys. 238: 188–209. doi:10.1016/j.jcp.2012.12.024.
  • Cornejo, L. R., and D. Y. Anistratov. 2017. The multilevel quasidiffusion method with multigrid in energy for eigenvalue transport problem. Prog. Nucl. Energy 101: 401–408. doi:10.1016/j.pnucene.2017.05.014.
  • Gol’din, V. Ya. 1964. A quasi-diffusion method of solving the kinetic equation. USSR Comp. Math. Math. Phys. 4: 136–149. doi:10.1016/0041-5553(64)90085-0.
  • Gol’din, V. Ya., and B. N. Chetverushkin. 1972. Methods of solving one-dimensional problems of radiation gas dynamics. USSR Comp. Math. Math. Phys. 12: 177–189. doi:10.1016/0041-5553(72)90122-X.
  • Haut, T. S., R. B. Lowrie, H. Park, R. M. Rauenzahn, and A. B. Wollaber. 2015. A linear stability analysis of the multigroup high-order low-order (HOLO) method. Proc. of M&C 2015, Joint Int. Conf. on Math. and Comp. (M&C), Supercomp. in Nucl. Appl. (SNA) and the Monte Carlo (MC) Method, Nashville, TN, 13.
  • Larsen, E. W. 1986. Projected discrete ordinates methods for numerical transport problems. Nucl. Sci. Eng. 92: 179–185. doi:10.13182/NSE86-A18163.
  • Larsen, E. W. 1991. Transport acceleration methods as two-level multigrid algorithms. In: Modern mathematical methods in transport theory, eds., W. Greenberg and J. Polewczak Vol. 51, 34–47. Birkhauser.
  • Larsen, E. W., and J. E. Morel. 1989. Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes, II. J. Comput. Phys. 83: 212–236. doi:10.1016/0021-9991(89)90229-5.
  • Larsen, E. W., and J. Yang. 2008. A functional Monte Carlo method for k-eigenvalue problems. Nucl. Sci. Eng. 159: 107–126. doi:10.13182/NSE07-92.
  • Miften, M. M., and E. W. Larsen. 1993. The quasi-diffusion method for solving transport problems in planar and spherical geometries. Trans. Theory Stat. Phys. 22: 165–186. doi:10.1080/00411459308203811.
  • Mihalas, D. 1978. Stellar atmospheres. San Francisco: W.H. Freeman & Co.
  • Morel, J. E., T. A. Wareing, and K. Smith. 1996. A linear-discontinuous spatial differencing scheme for SN radiative transfer calculations. J. Comput. Phys. 128 (2): 445–462. doi:10.1006/jcph.1996.0223.
  • Olivier, S. S., and J. E. Morel. 2017. Variable Eddington factor method for the SN equations with lumped discontinuous Galerkin spatial discretization coupled to a drift-diffusion acceleration equation with mixed finite-element discretization. J. Comput. Theoret. Trans. 46 (6–7): 480–496. doi:10.1080/23324309.2017.1418378.
  • Tamang, A., and D. Y. Anistratov. 2014. A multilevel quasidiffusion method for solving space-time multigroup neutron kinetics equations coupled with the heat transfer equation. Nucl. Sci. Eng. 177: 1–19. doi:10.13182/NSE13-42.
  • Vallette, N. D. 2002. Discretisation and solution of quasi-diffusion equations. Master’s thesis, Texas A&M University, Nuclear Engineering, Advisor: M. L. Adams.
  • Wareing, T. A., E. W. Larsen, and M. L. Adams. 1991. Diffusion accelerated discontinuous finite element schemes for the SN equations in slab and x-y geometries. Proceedings of Int. Topl. Mtg on Advances in Mathematics, Computations and Reactor Physics, Pittsburg, PA., USA, April 29–May 2.
  • Wieselquist, W. A., D. Y. Anistratov, and J. E. Morel. 2014. A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes. J. Comput. Phys. 273: 343–357. doi:10.1016/j.jcp.2014.05.011.
  • Wieselquist, W. A. 2010. A low-order quasidiffusion discretization via linear-continuous finite-elements on unstructured triangular meshes. Proceedings of Int. conf. PHYSOR 2010 - Advances in Reactor Physics to Power the Nuclear Renaissance, Pittsburg, PA., USA, May 9–14.

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.