Discontinuous Galerkin finite element method applied to the 1-D spherical neutron transport equation

Journal of Computational Physics

Volumn 223, Issue 1, 2007, Pages 67-81

  Machorro, Eric ^a,b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Corner balance method; Diamond difference method; Discontinuous Galerkin methods; Finite elements; Linear hyperbolic equation; Neutron transport; Spherical geometry Sn equations

Indexed keywords

GALERKIN METHODS; NEUTRON FLUX; SPHERES; TRANSPORT PROPERTIES;

BALANCE METHODS; CORNER BALANCE METHOD; DIAMOND DIFFERENCE METHOD; DIFFERENCE METHOD; DISCONTINOUS GALERKIN METHODS; FINITE ELEMENT; LINEAR HYPERBOLIC EQUATION; NEUTRON TRANSPORT; SPHERICAL GEOMETRIES; SPHERICAL GEOMETRY SN EQUATION;

FINITE ELEMENT METHOD;

EID: 33947136356     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.08.020     Document Type: Article

References (18)

1. Ackroyd R.T., and Wilson W.E. Discontinuous finite elements for neutron transport analysis. Progr. Nucl. Energy 18 1-2 (1986) 39-44
2. Adams M.L. A new transport discretization scheme for arbitrary spatial meshes in XY geometry. Proceedings of the International Topl. Mtg. Advances in Mathematics, Computations, and Reactor Physics Pittsburgh, Pennsylvania, April 28-May 2, 1991 vol. III (1991), American Nuclear Society 13.2 2-1
3. Adams M.L. Sub-cell balance methods for radiative transfer on arbitrary grids. Transp. Theory Stat. Phys. 26 (1997) 385-431
4. Asadzadeh M. A finite element method for the neutron transport equation in an infinite cylindrical domain. SIAM J. Numer. Anal. 35 (1998) 1299-1314
5. Carlson B.G., and Lathrop K.D. Transport theory the method of discrete ordinates. In: Greenspan H., Kelber C.N., and Okrent D. (Eds). Computing Methods in Reactor Physics (1968), Gordon and Breach, New York 167-266
6. In: Cockburn B., Karniadakis G.E., and Shu C.-W. (Eds). Discontinuous Galerkin Methods Theory, Computation and Applications (2000), Springer-Verlag, Heidleberg
7. Greenbaum A., and Ferguson J.M. A Petrov-Galerkin finite element for solving the neutron transport equation. J. Comput. Phys. 64 (1986) 97-111
8. Johnson C. Numerical Solution to Partial Differential Equations by the Finite Element Method (1987), University of Cambridge Press, New York
9. n equations. Nucl. Sci. Eng. 134 (2000) 239-264
10. Lesaint P., and Ravaint P.-A. On a finite element method for solving the neutron transport equation. In: de Boor C. (Ed). Mathematical Aspects of Finite Elements in Partial Differential Equations (1974), Academic Press, NY
11. Leveque R.J. Numerical Methods for Conservation Laws (1992), Birkhäuser Verlag, Basel
12. Lewis E.E., and Miller W.F. Computational Methods of Neutron Transport (1984), John Wiley, New York
13. Mathews K.A. On the propagation of rays in discrete ordinates. Nucl. Sci. Eng. 132 (1999) 155-180
14. Morel J.E., and Montry G.R. Analysis and elimination of the discrete-ordinates flux dip. Trans. Theory Stat. Phys. 13 5 (1984) 615-633
15. Palmer T.S., and Adams M.L. Analysis of spherical geometry finite element transport solutions in the thick diffusion limit. Proceedings of the International Topl. Mtg. Advances in Mathematics, Computations, and Reactor Physics Pittsburgh, Pennsylvania, April 28-May 2, 1991 vol. V (1991), American Nuclear Society 21.1 3-1-21.1 3-15
16. T.S. Palmer, M.L. Adams, Curvilinear geometry transport discretization in the "thick" diffusion limit, in: Proceedings of the International Conference Math. Methods & Supercomputing in Nuc. Appl., Karlsrühe, Germany 4/19-4/23, vol. I. Kernforschungszentrum, Karlsrühe, 1993, p. 33.
17. Walters W.F., and Morel J.E. Investigation of linear-discontinuous angular differencing for the 1-D spherical geometry SN equations (U). Proceedings of the International Topl. Mtg. Advances in Mathematics, Computations, and Reactor Physics Pittsburgh, Pennsylvania, April 28-May 2, 1991 vol. III (1991), American Nuclear Society 13.2 3-1
18. Walters W.F., and Wareing T.A. An accurate, strictly-positive, nonlinear characteristic scheme for the discrete-ordinate equations. Trans. Theory Stat. Phys. 25 2 (1996) 197