131
Views
1
CrossRef citations to date
0
Altmetric
Articles

Benchmarks for Infinite Medium, Time Dependent Transport Problems with Isotropic Scattering

& ORCID Icon

References

  • Alcouffe, R. E., R. D. O’Dell, and F. W. Brinkley. 1990. A first-collision source method that satisfies discrete Sn transport balance. Nucl. Sci. Eng. 105 (2):198–203. doi:10.13182/NSE90-A23749
  • Ganapol, B. D. 2001. Homogeneous Infinite medium time-dependent analytical benchmarks for X-TM transport methods development. Technical Report LA-UR-01-1854. Los Alamos National Laboratory.
  • Garrett, C. K., and C. D. Hauck. 2013. A comparison of moment closures for linear kinetic transport equations: The line source benchmark. Transp. Theory Stat. Phys. 42 (6-7):203–35. doi:10.1080/00411450.2014.910226
  • Harel, R., S. Burov, and S. I. Heizler. 2021. The time-dependent asymptotic PN approximation for the transport equation. Nucl. Sci. Eng. 195 (6):578–97. doi:10.1080/00295639.2020.1829345
  • Hauck, C., and V. Heningburg. 2019. Filtered discrete ordinates equations for radiative transport. J. Sci. Comput. 80 (1):614–48. doi:10.1007/s10915-019-00950-1
  • Hauck, C. D., and R. G. McClarren. 2013. A collision-based hybrid method for time-dependent, linear, kinetic transport equations. Multiscale Model. Simul. 11 (4):1197–227. doi:10.1137/110846610
  • Heizler, S. I. 2010. Asymptotic Telegrapher’s equation (P1) approximation for the transport equation. Nucl. Sci. Eng. 166 (1):17–35. doi:10.13182/NSE09-77
  • Heningburg, V., and C. D. Hauck. 2020. Hybrid solver for the radiative transport equation using finite volume and discontinuous galerkin. arXiv preprint arXiv:2002.02517.
  • McClarren, R. G., and R. B. Lowrie. 2008. Manufactured solutions for the P1 radiation-hydrodynamics equations. J. Quant. Spectrosc. Radiat. Transf. 109 (15):2590–602. doi:10.1016/j.jqsrt.2008.06.003
  • Monin, A. S. 1956. A statistical interpretation of the scattering of microscopic particles. Theory Probab. Appl. 1 (3):298–311. doi:10.1137/1101024
  • Peng, Z., and R. G. McClarren. 2021. A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations. Comput. Phys. 447:110672. doi:10.1016/j.jcp.2021.110672
  • Salari, K., and P. Knupp. 2000. Code verification by the method of manufactured solutions. Technical Report. Sandia National Lab.(SNL-NM), Albuquerque, NM (United States), Sandia.
  • Schlachter, L., and F. Schneider. 2018. A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations. Comput. Phys. 375:80–98. doi:10.1016/j.jcp.2018.07.026
  • Seibold, B., and M. Frank. 2014. “StaRMAP—A second order staggered grid method for spherical harmonics moment equations of radiative transfer. ACM Trans. Math. Softw. 41 (1):1–28. doi:10.1145/2590808
  • Variansyah, I., and R. G. McClarren. 2022. Population Control Techniques for Time-Dependent and Eigenvalue Monte Carlo Neutron Transport Calculations. arXiv preprint arXiv:2202.08631.
  • Walters, W. J., and A. Haghighat. 2017. The adaptive collision source method for discrete ordinates radiation transport. Ann. Nucl. Energy 105:45–58. doi:10.1016/j.anucene.2017.02.013
  • Wright, M. C. M. 2006. Green function or green’s function? Nature Phys. 2 (10):646. doi:10.1038/nphys411

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.