A nonlinear corner-balance spatial discretization for transport on arbitrary grids

Nuclear Science and Engineering

Volumn 128, Issue 3, 1998, Pages 278-296

  Castrianni, Chris L ^a   Adams, Marvin L ^a  

^a Texas AandM University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001437017     PISSN: 00295639     EISSN: None     Source Type: Journal    
DOI: 10.13182/NSE98-A1956     Document Type: Article

References (20)

1. K. MATHEWS and B. M. MINOR, "Adaptive Characteristic Spatial Quadratures for Discrete Ordinates Neutral Particle Transport - The Rectangular Case," Transp. Theory Stat. Phys., 22, 5, 655 (1993).
2. K. MATHEWS, G. SJODEN, and B. M. MINOR, "Exponential Characteristic Spatial Quadrature for Discrete Ordinales Radiation Transport in Slab Geometry," Nucl. Sci. Eng., 118, 24 (1994).
3. W. F. WALTERS and T. A. WAREING, "An Accurate, Strictly-Positive, Nonlinear Characteristic Scheme for the Discrete-Ordinate Equations," Transp. Theory Stat. Phys., 25, 2, 197 (1996).
4. W. F. WALTERS, T. A. WAREING, and D. R. MARR, "The Nonlinear Characteristic Scheme for X-Y Geometry Transport Problems," Proc. Int. Conf. Mathematics and Computations, Reactor Physics, and Environmental Analyses, Portland, Oregon, April 30-May 4, 1995, Vol. 1, p. 340, American Nuclear Society (1995).
5. C. L. CASTRIANNI and M. L. ADAMS, "A Nonlinear Corner-Balance Method for Spatially Discretizing the Transport Equation," Trans. Am. Nucl. Soc., 71, 265 (1994).
6. M. L. ADAMS, "A New Transport Discretization Scheme for Arbitrary Spatial Meshes in XY Geometry," Proc. Int. Conf. Advances in Mathematics, Computations, and Reactor Physics, Pittsburgh, Pennsylvania, April 28-May 2, 1991. Vol. 3, p. 13.2 2-1, American Nuclear Society (1991).
7. R. E. ALCOUFFE, "An Adaptive Weighted Diamond-Differencing Method for Three-Dimensional XYZ Geometry," Trans. Am. Nucl Soc., 68. 206 (1993).
8. N Differencing Scheme," Trans. Am. Nucl. Soc., 73, 195 (1995).
9. N Methods: The One-Dimensional Case," Nucl. Sci. Eng., 63, 179 (1977).
10. C. L. CASTRIANNI and M. L. ADAMS, "A Nonlinear Corner-Balance Spatial Discretization for Transport on Arbitrary Grids," Proc. Int. Conf. Mathematics and Computations, Reactor Physics, and Environmental Analyses, Portland, Oregon, April 30-May 4, 1995, Vol. 2, p. 916, American Nuclear Society (1995).
11. E. W. LARSEN and J. B. KELLER, "Asymptotic Solution of Neutron Transport Problems for Small Mean Free Paths," J. Math. Phys., 15, 75 (1974).
12. F. MALGAVI and G. C. POMRANING, "Initial and Boundary Conditions for Diffusive Linear Transport Problems," J. Math. Phys., 32, 805 (1990).
13. S. CHANDRASEKHAR, Radiative Transfer, Dover Publications, New York (1960).
14. E. W. LARSEN and W. F. MILLER, Jr., "Convergence Rates of Spatial Difference Equations for the Discrete-Ordinates Neutron Transport Equations in Slab Geometry," Nucl. Sci. Eng., 73, 76 (1980).
15. T. L. EATON and M. L. ADAMS, "A New Corner-Balance/ Linear-Discontinuous Method for Transport in Slab Geometry," Trans. Am. Nucl. Soc., 70, 158 (1994).
16. E. E. LEWIS and W. F. MILLER, Computational Methods of Neutron Transport, American Nuclear Society, La Grange Park, Illinois (1993).
17. T. A. WAREING, W. F. WALTERS, and J. E. MOREL, "A Diffusion Accelerated Solution Method for the Nonlinear Characteristic Scheme," Proc. Int. Conf. Mathematics and Computations, Reactor Physics and Environmental Analyses, Portland, Oregon, April 30-May 4, 1995, Vol. 2, p. 1335, American Nuclear Society (1995).
18. G. L. RAMONE, M. L. ADAMS, and P. F. NOWAK, "A Transport Synthetic Acceleration Method for Transport Iterations," Nucl. Sci. Eng., 125, 257 (1997).
19. W. HACKBUSCH, Iterative Solutions of Large Sparse Systems of Equations, Springer-Verlag, New York (1994).
20. M. L. ADAMS, W. F. WALTERS, and T. A. WAREING, "Characteristics Methods in Thick Diffusive Problems," Proc. Int. Conf. Mathematics and Computations, Reactor Physics, and Environmental Analyses, Portland, Oregon, April 30-May 4, 1995, Vol. 1, p. 349, American Nuclear Society (1995).