Consistent spatial approximation of the low-order quasi-diffusion equations on coarse grids

Nuclear Science and Engineering

Volumn 149, Issue 2, 2005, Pages 138-161

  Anistratov, Dmitriy Y ^a  

^a North Carolina State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CALCULATIONS; COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; LINEAR EQUATIONS; MIXED OXIDE FUELS; URANIUM;

COARSE GRIDS; QUASI-DIFFUSION (QD) METHODS; SPATIAL DISCRETIZATION METHODS; SURFACE CURRENTS;

REACTOR CORES;

EID: 14544268612     PISSN: 00295639     EISSN: None     Source Type: Journal    
DOI: 10.13182/NSE05-A2485     Document Type: Article

References (18)

1. K. S. SMITH, "Assembly Homogenization Techniques for Light Water Reactor Analysis," Prog. Nucl. Energy, 17, 303 (1986).
2. D. Y. ANISTRATOV and M. L. ADAMS, "Consistent Coarse-Mesh Discretization of the Low-Order Equations of the Quasi-Diffusion Method," Trans. Am. Nucl. Soc., 83, 250 (2000).
3. K. T. CLARNO and M. L. ADAMS, "Improved Boundary Conditions for Assembly-Level Transport Codes," Proc. Int. Conf. New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing (PHYSOR 2002), Seoul, Korea, October 7-10, 2002, American Nuclear Society (2002).
4. R. NES and T. S. PALMER, "An Advanced Nodal Discretization for the Quasi-Diffusion Low-Order Equations," Proc. Int. Conf. New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing (PHYSOR 2002), Seoul, Korea, October 7-10, 2002, American Nuclear Society (2002).
5. D. Y. ANISTRATOV, "Homogenization Methodology for the Low-Order Equations of the Quasidiffusion Method," Proc. Int. Conf. New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing (PHYSOR 2002), Seoul, Korea, October 7-10, 2002, American Nuclear Society (2002).
6. H. HIKARU, D. Y. ANISTRATOV, and M. L. ADAMS, "Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasidiffusion Equations," Proc. Int. Topl. Mtg. Nuclear Mathematical and Computational Sciences: A Century in Review - A Century Anew, Gatlinburg, Tennessee, April 6-10, 2003, American Nuclear Society (2003).
7. K. T. CLARNO and M. L. ADAMS, "Capturing the Effects of Unlike Neighbors in Single-Assembly Calculations," Proc. Topl. Mtg. Nuclear Mathematical and Computational Sciences: A Century in Review - A Century Anew, Gatlinburg, Tennessee, April 6-10, 2003, American Nuclear Society (2003).
8. V. YA. GOL'DIN, "A Quasidiffusion Method for Solving the Kinetic Equation," USSR Comput. Math. Math. Phys., 4, 136 (1964).
9. N. N. AKSENOV and V. YA. GOL'DIN, "Computation of the Two-Dimensional Stationary Equation of Neutron Transfer by the Quasi-Diffusion Method," USSR Comput. Math. Math. Phys., 19, 263 (1979).
10. V. YA. GOL'DIN, "On Mathematical Modeling of Problems of Non-Equilibrium Transfer in Physical Systems," Modern Problems of Mathematical Physics and Computational Mathematics, pp. 113-127, Nauka, Moscow (1982) (in Russian).
11. D. Y. ANISTRATOV and V. YA. GOL'DIN, "Solving the Multigroup Transport Equation by the Quasidiffusion Method," Preprint of the Keldysh Institute for Applied Mathematics, No. 128, USSR Academy of Sciences (1986) (in Russian).
12. E. N. ARISTOVA, V. YA. GOL'DIN, and A. V. KOLPAKOV, " Multidimensional Calculations of Radiation Transport by Nonlinear Quasi-Diffusion Method," Proc. Int. Conf. Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications, Madrid, Spain, September 27-30, 1999, p. 667 (1999).
13. V. E. TROSHIEV, "Solution of the Kinetic Equation and Quasi-Diffusion Equations by Means of Consistent Schemes," Numerical Methods for Solving Problems of Mathematical Physics, pp. 177-184, Nauka, Moscow (1966) (in Russian).
14. R. E. ALCOUFFE, "Diffusion Synthetic Acceleration Methods for the Diamond-Differenced Discrete-Ordinates Equations," Nucl. Sci. Eng., 64, 344 (1977).
15. P. D. ESSER and K. S. SMITH, "A Semi-Analytic Two-Group Nodal Model for SIMULATE-3," Trans. Am. Nucl. Soc., 68, 220 (1993).
16. R. D. LAWRENCE, "Progress in Nodal Methods for the Solution of the Neutron Diffusion and Transport Equations," Prog. Nucl. Energy, 17, 271 (1986).
17. K. S. SMITH, Personal Communication (2000).
18. D. Y. ANISTRATOV and V. YA. GOL'DIN, "Nonlinear Methods for Solving Particle Transport Problems," Transport Theory Statist. Phys., 22, 42 (1993).