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2010 | OriginalPaper | Buchkapitel

1. Advances in Discrete-Ordinates Methodology

verfasst von : Edward W. Larsen, Jim E. Morel

Erschienen in: Nuclear Computational Science

Verlag: Springer Netherlands

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Abstract

In 1968, Bengt Carlson and Kaye Lathrop published a comprehensive review on the state of the art in discrete-ordinates (SN) calculations [10]. At that time, SN methodology existed primarily for reactor physics simulations. By today’s standards, those capabilities were limited, due to the less-developed theoretical state of SN methods and the slower and smaller computers that were then available. In this chapter, we review some of the major advances in SN methodology that have occurred since 1968. These advances, combined with the faster speeds and larger memories of today’s computers, enable today’s SN codes to simulate problems of much greater complexity, realism, and physical variety. Since 1968, several books and reviews on general numerical methods for SN simulations have been published [32, 46, 71], but none of these covers the advanced work done during the past 20 years.

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Literatur
1.
Zurück zum Zitat Eddington AS (1922) The internal constitution of the stars. Cambridge University Press, Cambridge Eddington AS (1922) The internal constitution of the stars. Cambridge University Press, Cambridge
2.
Zurück zum Zitat Chandrasekhar S (1960) Radiative transfer. Dover, New York. First published by Oxford University Press, London (1950) Chandrasekhar S (1960) Radiative transfer. Dover, New York. First published by Oxford University Press, London (1950)
3.
Zurück zum Zitat Davison B (1957) Neutron transport theory. Oxford University Press, LondonMATH Davison B (1957) Neutron transport theory. Oxford University Press, LondonMATH
4.
Zurück zum Zitat Carlson BG (1961) Numerical solution of neutron transport problems. In: Proc. of symposia in applied mathematics, Vol. 11, Nuclear reactor theory, American Mathematical Society, Providence, RI, 219 Carlson BG (1961) Numerical solution of neutron transport problems. In: Proc. of symposia in applied mathematics, Vol. 11, Nuclear reactor theory, American Mathematical Society, Providence, RI, 219
5.
Zurück zum Zitat Carlson BG (1963) The numerical theory of neutron transport. In: Methods in Computational Physics, Vol. 1, Academic, New York Carlson BG (1963) The numerical theory of neutron transport. In: Methods in Computational Physics, Vol. 1, Academic, New York
6.
Zurück zum Zitat Kopp HJ (1963) Synthetic method solution of the transport equation. Nucl Sci Eng 17:65 Kopp HJ (1963) Synthetic method solution of the transport equation. Nucl Sci Eng 17:65
7.
Zurück zum Zitat Vladimirov VS (1961) Mathematical problems in the one-velocity theory of particle transport, Transactions of V.A. Steklov Mathematical Institute, USSR Academy of Sciences, 61. English translation published by Atomic Energy of Canada Limited, Tech. Report AECL- 1661 (1963) Vladimirov VS (1961) Mathematical problems in the one-velocity theory of particle transport, Transactions of V.A. Steklov Mathematical Institute, USSR Academy of Sciences, 61. English translation published by Atomic Energy of Canada Limited, Tech. Report AECL- 1661 (1963)
8.
Zurück zum Zitat Gol’din VYa (1964) A quasi-diffusion method for solving the kinetic equation. Zh Vych Mat I Mat Fiz 4:1078 (in Russian) English translation (1967) published in: USSR Comp Math Math Phys 4:136 Gol’din VYa (1964) A quasi-diffusion method for solving the kinetic equation. Zh Vych Mat I Mat Fiz 4:1078 (in Russian) English translation (1967) published in: USSR Comp Math Math Phys 4:136
9.
Zurück zum Zitat Lathrop KD (1965) Anisotropic scattering approximations in the mono-energetic Boltzmann equation. Nucl Sci Eng 21:498 Lathrop KD (1965) Anisotropic scattering approximations in the mono-energetic Boltzmann equation. Nucl Sci Eng 21:498
10.
Zurück zum Zitat Carlson BG, Lathrop KD (1968) Transport theory – the method of discrete ordinates. In: Greenspan H, Kelber CN, Okrent D (eds) Computing methods in reactor physics. Gordon & Breach, New York Carlson BG, Lathrop KD (1968) Transport theory – the method of discrete ordinates. In: Greenspan H, Kelber CN, Okrent D (eds) Computing methods in reactor physics. Gordon & Breach, New York
11.
Zurück zum Zitat Gelbard EM, Hageman LA (1969) The synthetic method as applied to the SN equations. Nucl Sci Eng 37:288 Gelbard EM, Hageman LA (1969) The synthetic method as applied to the SN equations. Nucl Sci Eng 37:288
12.
Zurück zum Zitat Lathrop KD (1969) Spatial differencing of the transport equation: positivity vs accuracy. J Comp Phys 4:475MATH Lathrop KD (1969) Spatial differencing of the transport equation: positivity vs accuracy. J Comp Phys 4:475MATH
13.
Zurück zum Zitat Bell GI, Glasstone S (1970) Nuclear Reactor Theory. Van Nostrand Reinhold, New York Bell GI, Glasstone S (1970) Nuclear Reactor Theory. Van Nostrand Reinhold, New York
14.
Zurück zum Zitat Carlson BG (1970) Transport theory: discrete ordinates quadrature over the unit sphere. Los Alamos Scientific Laboratory report LA-4554 Carlson BG (1970) Transport theory: discrete ordinates quadrature over the unit sphere. Los Alamos Scientific Laboratory report LA-4554
15.
Zurück zum Zitat Carlson BG (1971) Tables of symmetric equal weight quadrature EQ n over the unit sphere. Los Alamos Scientific Laboratory Report LA-4734 Carlson BG (1971) Tables of symmetric equal weight quadrature EQ n over the unit sphere. Los Alamos Scientific Laboratory Report LA-4734
16.
Zurück zum Zitat Reed WH (1971) The effectiveness of acceleration techniques for iterative methods in transport theory. Nucl Sci Eng 45:245 Reed WH (1971) The effectiveness of acceleration techniques for iterative methods in transport theory. Nucl Sci Eng 45:245
17.
Zurück zum Zitat Pomraning GC (1973) The equations of radiation hydrodynamics. Pergamon Press, Oxford Pomraning GC (1973) The equations of radiation hydrodynamics. Pergamon Press, Oxford
18.
Zurück zum Zitat Reed WH, Hill TR (1973) Triangular mesh methods for the neutron transport equation. Los Alamos Scientific Laboratory Report LA-UR-73–479 Reed WH, Hill TR (1973) Triangular mesh methods for the neutron transport equation. Los Alamos Scientific Laboratory Report LA-UR-73–479
19.
Zurück zum Zitat Dahlquist G, Björck Å (1974) Numerical methods. Prentice Hall, Englewood Cliffs, NJ Dahlquist G, Björck Å (1974) Numerical methods. Prentice Hall, Englewood Cliffs, NJ
20.
Zurück zum Zitat Kellogg RB (July 1974) First derivatives of solutions of the plane neutron transport equation, Technical Note BN-783. Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, MD Kellogg RB (July 1974) First derivatives of solutions of the plane neutron transport equation, Technical Note BN-783. Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, MD
21.
Zurück zum Zitat Briggs LL, Miller WF Jr, Lewis EE (1975) Ray effect mitigation in discrete ordinate-like angular finite-element approximations in neutron transport. Nucl Sci Eng 57:205 Briggs LL, Miller WF Jr, Lewis EE (1975) Ray effect mitigation in discrete ordinate-like angular finite-element approximations in neutron transport. Nucl Sci Eng 57:205
22.
Zurück zum Zitat Hill TR (1975) ONETRAN: a discrete-ordinates finite-element code for the solution of the one-dimensional multigroup transport equation. Los Alamos Scientific Laboratory Report LA-5990-MS Hill TR (1975) ONETRAN: a discrete-ordinates finite-element code for the solution of the one-dimensional multigroup transport equation. Los Alamos Scientific Laboratory Report LA-5990-MS
23.
Zurück zum Zitat Alcouffe RE (1977) Diffusion synthetic acceleration methods for the diamond-differenced discrete-ordinates equations. Nucl Sci Eng 64:344 Alcouffe RE (1977) Diffusion synthetic acceleration methods for the diamond-differenced discrete-ordinates equations. Nucl Sci Eng 64:344
24.
Zurück zum Zitat Miller WF Jr, Reed WH (1977) Ray effect mitigation methods for two-dimensional neutron transport theory. Nucl Sci Eng 62:391 Miller WF Jr, Reed WH (1977) Ray effect mitigation methods for two-dimensional neutron transport theory. Nucl Sci Eng 62:391
25.
Zurück zum Zitat Alcouffe RE, Larsen EW, Miller WF Jr, Wienke BR (1979) Computational efficiency of numerical methods for the multigroup, discrete-ordinates neutron transport equations: the slab geometry case. Nucl Sci Eng 71:111 Alcouffe RE, Larsen EW, Miller WF Jr, Wienke BR (1979) Computational efficiency of numerical methods for the multigroup, discrete-ordinates neutron transport equations: the slab geometry case. Nucl Sci Eng 71:111
26.
Zurück zum Zitat Dudziak DJ, O’Dell RD, Alcouffe RE (July 1979) Transport and reactor theory. Los Alamos National Laboratory Report, LA-7911-PR Dudziak DJ, O’Dell RD, Alcouffe RE (July 1979) Transport and reactor theory. Los Alamos National Laboratory Report, LA-7911-PR
27.
Zurück zum Zitat Morel JE (1979) On the validity of the extended transport cross-section correction for low-energy electron transport. Nucl Sci Eng 71:64 Morel JE (1979) On the validity of the extended transport cross-section correction for low-energy electron transport. Nucl Sci Eng 71:64
28.
Zurück zum Zitat Lawrence RD, Dorning JJ (1980) A discrete nodal integral transport theory method for multidimensional reactor physics and shielding calculations. In: Proc. ANS topical conference. Advances in reactor physics and shielding, 14–19 Sept 1980. Sun Valley, Idaho, 840 Lawrence RD, Dorning JJ (1980) A discrete nodal integral transport theory method for multidimensional reactor physics and shielding calculations. In: Proc. ANS topical conference. Advances in reactor physics and shielding, 14–19 Sept 1980. Sun Valley, Idaho, 840
29.
Zurück zum Zitat Walters WF, O’Dell RD (1980) Nodal methods for discrete-ordinates transport problems in (x-y) geometry. In: Proc. ANS topical conference. Advances in mathematical methods for the solution of nuclear engineering problems, 27–29 April 1980. 1, 115. Munich Walters WF, O’Dell RD (1980) Nodal methods for discrete-ordinates transport problems in (x-y) geometry. In: Proc. ANS topical conference. Advances in mathematical methods for the solution of nuclear engineering problems, 27–29 April 1980. 1, 115. Munich
30.
Zurück zum Zitat Gupta NK (1981) Nodal methods for three-dimensional simulators. Prog Nucl Energy 7:127MATH Gupta NK (1981) Nodal methods for three-dimensional simulators. Prog Nucl Energy 7:127MATH
31.
Zurück zum Zitat Morel JE (1981) Fokker–Planck calculations using standard discrete ordinates codes. Nucl Sci Eng 79:340 Morel JE (1981) Fokker–Planck calculations using standard discrete ordinates codes. Nucl Sci Eng 79:340
32.
Zurück zum Zitat Sanchez R, Mc Cormick NJ (1982) A review of neutron transport approximations. Nucl Sci Eng 80:481 (review) Sanchez R, Mc Cormick NJ (1982) A review of neutron transport approximations. Nucl Sci Eng 80:481 (review)
33.
Zurück zum Zitat Larsen EW (1982) Spatial convergence properties of the diamond difference method in X,Y-geometry. Nucl Sci Eng 80:710 Larsen EW (1982) Spatial convergence properties of the diamond difference method in X,Y-geometry. Nucl Sci Eng 80:710
34.
Zurück zum Zitat Larsen EW (1982) unconditionally stable diffusion synthetic acceleration methods for the slab geometry discrete-ordinates equations. Part I: theory. Nucl Sci Eng 82:47 Larsen EW (1982) unconditionally stable diffusion synthetic acceleration methods for the slab geometry discrete-ordinates equations. Part I: theory. Nucl Sci Eng 82:47
35.
Zurück zum Zitat McCoy DR, Larsen EW (1982) Unconditionally stable diffusion synthetic acceleration methods for the slab geometry discrete-ordinates equations. Part II: numerical results. Nucl Sci Eng 82:64 McCoy DR, Larsen EW (1982) Unconditionally stable diffusion synthetic acceleration methods for the slab geometry discrete-ordinates equations. Part II: numerical results. Nucl Sci Eng 82:64
36.
Zurück zum Zitat Morel JE (1982) A synthetic acceleration method for discrete ordinates calculations with highly anisotropic scattering. Nucl Sci Eng 82:34 Morel JE (1982) A synthetic acceleration method for discrete ordinates calculations with highly anisotropic scattering. Nucl Sci Eng 82:34
37.
Zurück zum Zitat Caro M, Ligou J (1983) Treatment of scattering anisotropy of neutrons through the Boltzmann–Fokker–Planck equation. Nucl Sci Eng 83:242 Caro M, Ligou J (1983) Treatment of scattering anisotropy of neutrons through the Boltzmann–Fokker–Planck equation. Nucl Sci Eng 83:242
38.
Zurück zum Zitat Morel JE, Montry GR (1984) Analysis and elimination of the discrete ordinates flux dip. Transp Theory Statist Phys 13:615 Morel JE, Montry GR (1984) Analysis and elimination of the discrete ordinates flux dip. Transp Theory Statist Phys 13:615
39.
Zurück zum Zitat Mihalas D, Mihalas BW (1984) Foundations of radiation hydro-dynamics. Oxford University Press, New York Mihalas D, Mihalas BW (1984) Foundations of radiation hydro-dynamics. Oxford University Press, New York
40.
Zurück zum Zitat Morel JE (1985) An improved Fokker–Planck angular differencing scheme. Nucl Sci Eng 89:131–136 Morel JE (1985) An improved Fokker–Planck angular differencing scheme. Nucl Sci Eng 89:131–136
41.
Zurück zum Zitat Morel JE (1985) Diamond-difference multigroup-Legendre coefficients for continuous-slowing down operator. Nucl Sci Eng 91:324 Morel JE (1985) Diamond-difference multigroup-Legendre coefficients for continuous-slowing down operator. Nucl Sci Eng 91:324
42.
Zurück zum Zitat Morel JE, Larsen EW, Matzen MK (1985) A synthetic acceleration scheme for radiative diffusion calculations. J. Quant. Spectro. Radiat Transf 34:243 Morel JE, Larsen EW, Matzen MK (1985) A synthetic acceleration scheme for radiative diffusion calculations. J. Quant. Spectro. Radiat Transf 34:243
43.
Zurück zum Zitat Badruzzaman A (1985) An efficient algorithm for nodal transport solutions in multidimensional geometry Nucl Sci Eng 89:281 Badruzzaman A (1985) An efficient algorithm for nodal transport solutions in multidimensional geometry Nucl Sci Eng 89:281
44.
Zurück zum Zitat Khalil H (1985) A nodal diffusion technique for synthetic acceleration of nodal SN calculations. Nucl Sci Eng 90:263 Khalil H (1985) A nodal diffusion technique for synthetic acceleration of nodal SN calculations. Nucl Sci Eng 90:263
45.
Zurück zum Zitat Lawrence RD (1986) Progress in nodal methods for the solution of the neutron diffusion and transport equations. Prog Nucl Energy 17:271 (review) Lawrence RD (1986) Progress in nodal methods for the solution of the neutron diffusion and transport equations. Prog Nucl Energy 17:271 (review)
46.
Zurück zum Zitat Marchuk GI, Lebedev VI (1986) Numerical methods in the theory of neutron transport. Harwood Academic Publishers, London (originally published in Russian in 1981) Marchuk GI, Lebedev VI (1986) Numerical methods in the theory of neutron transport. Harwood Academic Publishers, London (originally published in Russian in 1981)
47.
Zurück zum Zitat Lazo MS, Morel JE (1986) A linear discontinuous Galerkin approximation for the continuous slowing down operator. Nucl Sci Eng. 92:98 Lazo MS, Morel JE (1986) A linear discontinuous Galerkin approximation for the continuous slowing down operator. Nucl Sci Eng. 92:98
48.
Zurück zum Zitat Ullo JJ (1986) Use of multidimensional transport methodology on nuclear logging problems. Nucl Sci Eng 92:228 Ullo JJ (1986) Use of multidimensional transport methodology on nuclear logging problems. Nucl Sci Eng 92:228
49.
Zurück zum Zitat Larsen EW, Morel JE, Miller WF Jr (1987) Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes. J Comp Phys 69:283MATHMathSciNet Larsen EW, Morel JE, Miller WF Jr (1987) Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes. J Comp Phys 69:283MATHMathSciNet
50.
Zurück zum Zitat Larsen EW (1988) A grey transport acceleration method for thermal radiative transfer problems. J Comp Phys 78:459MATH Larsen EW (1988) A grey transport acceleration method for thermal radiative transfer problems. J Comp Phys 78:459MATH
51.
Zurück zum Zitat Baker RS, Koch KR (1988) An SN algorithm for the massively parallel CM-200 computer. Nucl Sci Eng 128:312 Baker RS, Koch KR (1988) An SN algorithm for the massively parallel CM-200 computer. Nucl Sci Eng 128:312
52.
Zurück zum Zitat Larsen EW, Morel JE (1989) Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II. J Comp Phys 83:212. See also Corrigendum. J Comp Phys 91:246 (1990)MATHMathSciNet Larsen EW, Morel JE (1989) Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II. J Comp Phys 83:212. See also Corrigendum. J Comp Phys 91:246 (1990)MATHMathSciNet
53.
Zurück zum Zitat Faber V, Manteuffel TA (1989) A look at transport theory from the point of view of linear algebra. In: Nelson P et al. (eds) Lecture notes in pure and applied mathematics, Vol. 115. Marcel Dekker, New York, p 31 Faber V, Manteuffel TA (1989) A look at transport theory from the point of view of linear algebra. In: Nelson P et al. (eds) Lecture notes in pure and applied mathematics, Vol. 115. Marcel Dekker, New York, p 31
54.
Zurück zum Zitat Morel JE (1989) A hybrid collocation-Galerkin-SN method for solving the Boltzmann transport equation. Nucl Sci Eng 101:72 Morel JE (1989) A hybrid collocation-Galerkin-SN method for solving the Boltzmann transport equation. Nucl Sci Eng 101:72
55.
Zurück zum Zitat Landesman M, Morel JE (1989) Angular Fokker–Planck decomposition and representation techniques. Nucl Sci Eng 103:1 Landesman M, Morel JE (1989) Angular Fokker–Planck decomposition and representation techniques. Nucl Sci Eng 103:1
56.
Zurück zum Zitat Cefus GR, Larsen EW (1990) Stability analysis of coarse mesh rebalance. Nucl Sci Eng 105:31 Cefus GR, Larsen EW (1990) Stability analysis of coarse mesh rebalance. Nucl Sci Eng 105:31
57.
Zurück zum Zitat Coppa GGM, Lapenta G, Ravetto P (1990) Angular finite-element techniques in neutron transport. Ann Nucl Energy 17:363 Coppa GGM, Lapenta G, Ravetto P (1990) Angular finite-element techniques in neutron transport. Ann Nucl Energy 17:363
58.
Zurück zum Zitat Lorence LJ Jr, Morel JE,Valdez GD (1990) Results guide to CEPXS/ONELD: a one-dimensional coupled electron-photon discrete ordinates code package. Sandia National Laboratories Report SAND89–211 Lorence LJ Jr, Morel JE,Valdez GD (1990) Results guide to CEPXS/ONELD: a one-dimensional coupled electron-photon discrete ordinates code package. Sandia National Laboratories Report SAND89–211
59.
Zurück zum Zitat Badruzzaman A (1991) Finite moments approaches to the time-dependent Boltzmann equation. Prog Nucl Eng 25:127 Badruzzaman A (1991) Finite moments approaches to the time-dependent Boltzmann equation. Prog Nucl Eng 25:127
60.
Zurück zum Zitat Walters WF, Morel JE (1991) Investigation of linear-discontinuous angular differencing for the 1-D spherical geometry SN equations. In: Proc. ANS M&C topical meeting. Advances in mathematics, computation, and reactor physics, 28 April–May 2 May 1991, Sec. 11.1, Pittsburgh Walters WF, Morel JE (1991) Investigation of linear-discontinuous angular differencing for the 1-D spherical geometry SN equations. In: Proc. ANS M&C topical meeting. Advances in mathematics, computation, and reactor physics, 28 April–May 2 May 1991, Sec. 11.1, Pittsburgh
61.
Zurück zum Zitat Wareing T, Larsen EW, Adams ML (1991) Diffusion accelerated discontinuous finite element schemes for the SN equations in slab and X,Y geometries. In: Proc. ANS topical meeting. Advances in mathematics, computations, and reactor physics, 29 April–2 May 1991, Vol. 3, Sec. 11.1. Pittsburgh, p 2–1 Wareing T, Larsen EW, Adams ML (1991) Diffusion accelerated discontinuous finite element schemes for the SN equations in slab and X,Y geometries. In: Proc. ANS topical meeting. Advances in mathematics, computations, and reactor physics, 29 April–2 May 1991, Vol. 3, Sec. 11.1. Pittsburgh, p 2–1
62.
Zurück zum Zitat Morel JE, Manteuffel TA (1991) An angular multigrid acceleration technique for the SN equations with highly forward-peaked scattering. Nucl Sci Eng 107:330 Morel JE, Manteuffel TA (1991) An angular multigrid acceleration technique for the SN equations with highly forward-peaked scattering. Nucl Sci Eng 107:330
63.
Zurück zum Zitat Ashby SF, Brown PN, Dorr MR, Hindmarsh AC (1991) Preconditioned iterative methods for discretized transport equations. In: Proc. International topical meeting. Advances in mathematics, computations, and reactor physics, 28 April–2 May 1991, Vol. 2. American Nuclear Society, Pittsburgh, PA, p. 6.1 2–1 Ashby SF, Brown PN, Dorr MR, Hindmarsh AC (1991) Preconditioned iterative methods for discretized transport equations. In: Proc. International topical meeting. Advances in mathematics, computations, and reactor physics, 28 April–2 May 1991, Vol. 2. American Nuclear Society, Pittsburgh, PA, p. 6.1 2–1
64.
Zurück zum Zitat Adams ML, Martin WR (1992) Diffusion synthetic acceleration of discontinuous finite element transport iterations. Nucl Sci Eng 111:145 Adams ML, Martin WR (1992) Diffusion synthetic acceleration of discontinuous finite element transport iterations. Nucl Sci Eng 111:145
65.
Zurück zum Zitat Azmy YY (1992) Arbitrarily high order characteristic methods for solving the neutron transport equation. Ann Nucl Energy 19:593 Azmy YY (1992) Arbitrarily high order characteristic methods for solving the neutron transport equation. Ann Nucl Energy 19:593
66.
Zurück zum Zitat Larsen EW (1992) The asymptotic diffusion limit of discretized transport problems. Nucl Sci Eng 112:336 (review) Larsen EW (1992) The asymptotic diffusion limit of discretized transport problems. Nucl Sci Eng 112:336 (review)
67.
Zurück zum Zitat Wareing T (November, 1992) Asymptotic diffusion accelerated discontinuous finite element methods for transport problems. Los Alamos National Laboratory Report LA-12425-T Wareing T (November, 1992) Asymptotic diffusion accelerated discontinuous finite element methods for transport problems. Los Alamos National Laboratory Report LA-12425-T
68.
Zurück zum Zitat Adams ML, Wareing TA (1993) Diffusion-synthetic acceleration given anisotropic scattering, general quadratures, and multi-dimensions. Trans Am Nucl Soc 68:203 Adams ML, Wareing TA (1993) Diffusion-synthetic acceleration given anisotropic scattering, general quadratures, and multi-dimensions. Trans Am Nucl Soc 68:203
69.
Zurück zum Zitat Adams BT, Morel JE (1993) A two-grid acceleration scheme for the multigroup SN equations with neutron upscattering. Nucl Sci Eng 115:253 Adams BT, Morel JE (1993) A two-grid acceleration scheme for the multigroup SN equations with neutron upscattering. Nucl Sci Eng 115:253
70.
Zurück zum Zitat Morel JE, Dendy JE Jr, Wareing TA (1993) Diffusion accelerated solution of the 2-D SN equations with bilinear-discontinuous differencing. Nucl Sci Eng 115:304 Morel JE, Dendy JE Jr, Wareing TA (1993) Diffusion accelerated solution of the 2-D SN equations with bilinear-discontinuous differencing. Nucl Sci Eng 115:304
71.
Zurück zum Zitat Lewis EE, Miller WF Jr (1984) Computational methods of neutron transport. Wiley-Interscience, New York [reprinted: American Nuclear Society, La Grange Park, IL (1993)] Lewis EE, Miller WF Jr (1984) Computational methods of neutron transport. Wiley-Interscience, New York [reprinted: American Nuclear Society, La Grange Park, IL (1993)]
72.
Zurück zum Zitat Briesmeister JF (ed) (1993) MCNP – A General Monte Carlo N-Particle Transport Code, Version 4A. Los Alamos National Laboratory Report, LA-12625 Briesmeister JF (ed) (1993) MCNP – A General Monte Carlo N-Particle Transport Code, Version 4A. Los Alamos National Laboratory Report, LA-12625
73.
Zurück zum Zitat Morel JE, McGhee JM (1994) A fission-source acceleration technique for time-dependent even-parity SN calculations. Nucl Sci Eng 116:73–85 Morel JE, McGhee JM (1994) A fission-source acceleration technique for time-dependent even-parity SN calculations. Nucl Sci Eng 116:73–85
74.
Zurück zum Zitat Brown PN (1995) A linear algebraic development of diffusion synthetic acceleration for three-dimensional transport equations. SIAM J. Numer Anal 32:179MATHMathSciNet Brown PN (1995) A linear algebraic development of diffusion synthetic acceleration for three-dimensional transport equations. SIAM J. Numer Anal 32:179MATHMathSciNet
75.
Zurück zum Zitat Kelly CT (1995) Multilevel source iteration accelerators for the linear transport equation in slab geometry. Transp Theory Stat Phys 24:697 Kelly CT (1995) Multilevel source iteration accelerators for the linear transport equation in slab geometry. Transp Theory Stat Phys 24:697
76.
Zurück zum Zitat Castrianni CL, Adams ML (1995) A nonlinear corner-balance spatial discretization for transport on arbitrary grids. In: Proc. ANS M&C international conference on mathematics and computations, reactor physics, and environmental analyses, 30 April–4 May 1995, Vol. 2. Portland, p 916 Castrianni CL, Adams ML (1995) A nonlinear corner-balance spatial discretization for transport on arbitrary grids. In: Proc. ANS M&C international conference on mathematics and computations, reactor physics, and environmental analyses, 30 April–4 May 1995, Vol. 2. Portland, p 916
77.
Zurück zum Zitat Morel JE, Wareing TA, Smith K (1996) A linear-discontinuous spatial differencing scheme for SN radiative transfer calculations. J Comp Phys 128:445MATHMathSciNet Morel JE, Wareing TA, Smith K (1996) A linear-discontinuous spatial differencing scheme for SN radiative transfer calculations. J Comp Phys 128:445MATHMathSciNet
78.
Zurück zum Zitat Wareing TA, McGhee JM, Morel JE (1996) ATTILA: a three-dimensional unstructured tetrahedral mesh discrete ordinates transport code. Trans Am Nucl Soc 17:146 Wareing TA, McGhee JM, Morel JE (1996) ATTILA: a three-dimensional unstructured tetrahedral mesh discrete ordinates transport code. Trans Am Nucl Soc 17:146
79.
Zurück zum Zitat Patton BW, Holloway JP (1996) Application of Krylov subspace iterative methods to the slab geometry transport equation. In: Proc. 1996 ANS topical meeting. Advances and applications in radiation protection and shielding, 21–25 April 1996, Vol. 1. N. Falmouth, MA, p 384 Patton BW, Holloway JP (1996) Application of Krylov subspace iterative methods to the slab geometry transport equation. In: Proc. 1996 ANS topical meeting. Advances and applications in radiation protection and shielding, 21–25 April 1996, Vol. 1. N. Falmouth, MA, p 384
80.
Zurück zum Zitat Kelly CT, Xue ZQ (1996) GMRES and integral operators. SIAM J Sci Comp 17:217 Kelly CT, Xue ZQ (1996) GMRES and integral operators. SIAM J Sci Comp 17:217
81.
Zurück zum Zitat Saad Y (1996) Iterative methods for sparse linear systems. PWS Publishing Company, Boston, MAMATH Saad Y (1996) Iterative methods for sparse linear systems. PWS Publishing Company, Boston, MAMATH
82.
Zurück zum Zitat Ramone GL, Adams ML, Nowak PF (1997) A transport synthetic acceleration method for transport iterations. Nucl Sci Eng 125:257 Ramone GL, Adams ML, Nowak PF (1997) A transport synthetic acceleration method for transport iterations. Nucl Sci Eng 125:257
83.
Zurück zum Zitat Adams ML (1997) A subcell balance method for radiative transfer on arbitrary spatial grids. Transp Theory Stat Phys 26(4 & 5):385MATH Adams ML (1997) A subcell balance method for radiative transfer on arbitrary spatial grids. Transp Theory Stat Phys 26(4 & 5):385MATH
84.
Zurück zum Zitat Adams BT, Morel JE (1997) An acceleration scheme for the multigroup SN equations with fission and thermal upscatter. In: Proc. ANS M&C topical meeting. Joint international conference on mathematical methods and supercomputing for nuclear applications, 5–10 Oct 1997, Vol. 1. Saratoga Springs, New York, p. 343 Adams BT, Morel JE (1997) An acceleration scheme for the multigroup SN equations with fission and thermal upscatter. In: Proc. ANS M&C topical meeting. Joint international conference on mathematical methods and supercomputing for nuclear applications, 5–10 Oct 1997, Vol. 1. Saratoga Springs, New York, p. 343
85.
Zurück zum Zitat Aussourd C (1997) An adapted DSN scheme for solving the two-dimensional neutron transport equation on a structured AMR grid. In: Proc international conference on mathematical methods and supercomputing for nuclear applications, October 5–9, 1997, Vol. 1. American Nuclear Society, Saratoga Springs, New York, p. 41 Aussourd C (1997) An adapted DSN scheme for solving the two-dimensional neutron transport equation on a structured AMR grid. In: Proc international conference on mathematical methods and supercomputing for nuclear applications, October 5–9, 1997, Vol. 1. American Nuclear Society, Saratoga Springs, New York, p. 41
86.
Zurück zum Zitat Adams ML, Nowak PF (1998) Asymptotic analysis of a computational method for time- and frequency-dependent radiative transfer. J Comp Phys 146:366MATH Adams ML, Nowak PF (1998) Asymptotic analysis of a computational method for time- and frequency-dependent radiative transfer. J Comp Phys 146:366MATH
87.
Zurück zum Zitat Azmy YY (2002) Unconditionally stable and robust adjacent-cell diffusive preconditioning of weighted-difference particle transport methods is impossible. J Comp Phys 182:213MATHMathSciNet Azmy YY (2002) Unconditionally stable and robust adjacent-cell diffusive preconditioning of weighted-difference particle transport methods is impossible. J Comp Phys 182:213MATHMathSciNet
88.
Zurück zum Zitat Adams ML, Wareing TA, Walters WF (1988) Characteristic methods in thick diffusive problems. Nucl Sci Eng 130:18 Adams ML, Wareing TA, Walters WF (1988) Characteristic methods in thick diffusive problems. Nucl Sci Eng 130:18
89.
Zurück zum Zitat Wareing TA, Morel JE (1998) ACTI Task 1 Summary. Los Alamos National Laboratory Report LA-UR-98–4749 Wareing TA, Morel JE (1998) ACTI Task 1 Summary. Los Alamos National Laboratory Report LA-UR-98–4749
90.
Zurück zum Zitat Castrianni CL, Adams ML (1998) A nonlinear corner-balance spatial discretization for transport on arbitrary grids. Nucl Sci Eng 128:278 Castrianni CL, Adams ML (1998) A nonlinear corner-balance spatial discretization for transport on arbitrary grids. Nucl Sci Eng 128:278
91.
Zurück zum Zitat Warsa JS, Prinja AK (1998) Bilinear-discontinuous numerical solution of the time dependent transport equation in slab geometry. Ann Nucl Energy 26:195 Warsa JS, Prinja AK (1998) Bilinear-discontinuous numerical solution of the time dependent transport equation in slab geometry. Ann Nucl Energy 26:195
92.
Zurück zum Zitat Jesse JP, Fiveland WA, Howell LH, Colella P, Pember RB (1998) An adaptive mesh refinement algorithm for the radiative transport equation. J Comp Phys 139:380 Jesse JP, Fiveland WA, Howell LH, Colella P, Pember RB (1998) An adaptive mesh refinement algorithm for the radiative transport equation. J Comp Phys 139:380
93.
Zurück zum Zitat Pautz SD, Morel JE, Adams ML (1999) An angular multigrid acceleration method for SN equations with highly forward-peaked scattering. In: Proc international conference on mathematics and computation, reactor physics and environmental analyses in nuclear applications, 27–30 Sept 1999, Vol. 1. Madrid, Spain, pp 647–656 Pautz SD, Morel JE, Adams ML (1999) An angular multigrid acceleration method for SN equations with highly forward-peaked scattering. In: Proc international conference on mathematics and computation, reactor physics and environmental analyses in nuclear applications, 27–30 Sept 1999, Vol. 1. Madrid, Spain, pp 647–656
94.
Zurück zum Zitat Azmy YY (1999) Iterative convergence acceleration of neutral particle transport methods via adjacent-cell preconditioners. J Comp Phys 152:359MATH Azmy YY (1999) Iterative convergence acceleration of neutral particle transport methods via adjacent-cell preconditioners. J Comp Phys 152:359MATH
95.
Zurück zum Zitat Guthrie B, Holloway JP, Patton BW (1999) GMRES as a multi-step transport sweep accelerator. Transp Theory Statist Phys 28:83MATH Guthrie B, Holloway JP, Patton BW (1999) GMRES as a multi-step transport sweep accelerator. Transp Theory Statist Phys 28:83MATH
96.
Zurück zum Zitat Thompson KG, Adams ML (1999) A spatial discretization for solving the transport equation on unstructured grids of polyhedra. In: Proc. ANS M&C international topical conference. Mathematics and computation, reactor physics and environmental analysis, 27–30 Sept 1999, Vol. 2. Madrid, p 1196 Thompson KG, Adams ML (1999) A spatial discretization for solving the transport equation on unstructured grids of polyhedra. In: Proc. ANS M&C international topical conference. Mathematics and computation, reactor physics and environmental analysis, 27–30 Sept 1999, Vol. 2. Madrid, p 1196
97.
Zurück zum Zitat Wareing TA, McGhee JM, Morel JE, Pautz SD (1999) Discontinuous finite element SN methods on 3-D unstructured grids. In: Proc. ANS M&C international topical conference. Mathematics and computation, reactor physics and environmental analysis, 27–30 Sept 1999, Vol. 2. Madrid, p 1185 Wareing TA, McGhee JM, Morel JE, Pautz SD (1999) Discontinuous finite element SN methods on 3-D unstructured grids. In: Proc. ANS M&C international topical conference. Mathematics and computation, reactor physics and environmental analysis, 27–30 Sept 1999, Vol. 2. Madrid, p 1185
98.
Zurück zum Zitat Wareing TA, Morel JE, McGhee JM (1999) A diffusion synthetic acceleration method for the SN equations with discontinuous finite element space and time differencing, In: Proc. ANS M&C international topical conference. Mathematics and computation, reactor physics and environmental analysis, 27–30 Sept 1999. Vol. 1. Madrid, p 45 Wareing TA, Morel JE, McGhee JM (1999) A diffusion synthetic acceleration method for the SN equations with discontinuous finite element space and time differencing, In: Proc. ANS M&C international topical conference. Mathematics and computation, reactor physics and environmental analysis, 27–30 Sept 1999. Vol. 1. Madrid, p 45
99.
Zurück zum Zitat Azmy YY (2000) Acceleration of multidimensional discrete ordinates methods via adjacent-cell preconditioners. Nucl Sci Eng 136:202 Azmy YY (2000) Acceleration of multidimensional discrete ordinates methods via adjacent-cell preconditioners. Nucl Sci Eng 136:202
100.
Zurück zum Zitat Lathrop KD (2000) A comparison of angular difference schemes for one-dimensional spherical geometry SN equations. Nucl Sci Eng 134:239 Lathrop KD (2000) A comparison of angular difference schemes for one-dimensional spherical geometry SN equations. Nucl Sci Eng 134:239
101.
Zurück zum Zitat Wareing TA, Morel JE, McGhee JM (2000) Coupled electron–photon transport methods on 3-D unstructured grids. Trans Am Nucl Soc 83:240–242 Wareing TA, Morel JE, McGhee JM (2000) Coupled electron–photon transport methods on 3-D unstructured grids. Trans Am Nucl Soc 83:240–242
102.
Zurück zum Zitat Mathews KA, Miller RL, Brennan CR (2000) Split-cell linear characteristic transport method for unstructured tetrahedral meshes. Nucl Sci Eng 136:178 Mathews KA, Miller RL, Brennan CR (2000) Split-cell linear characteristic transport method for unstructured tetrahedral meshes. Nucl Sci Eng 136:178
103.
Zurück zum Zitat Zika MR, Adams ML (2000) Transport synthetic acceleration with opposing reflecting boundary conditions. Nucl Sci Eng 134:159 Zika MR, Adams ML (2000) Transport synthetic acceleration with opposing reflecting boundary conditions. Nucl Sci Eng 134:159
104.
Zurück zum Zitat Plimpton S, Hendrickson B, Burns S, McLendon W III (2000) Parallel algorithms for radiation transport on unstructured grids. In: Proc. SuperComputing 2000, 4–10 Nov 2000. Dallas, TX Plimpton S, Hendrickson B, Burns S, McLendon W III (2000) Parallel algorithms for radiation transport on unstructured grids. In: Proc. SuperComputing 2000, 4–10 Nov 2000. Dallas, TX
105.
Zurück zum Zitat Adams ML (2001) Discontinuous finite element transport solutions in thick diffusive problems. Nucl Sci Eng 137:298 Adams ML (2001) Discontinuous finite element transport solutions in thick diffusive problems. Nucl Sci Eng 137:298
106.
Zurück zum Zitat Brennan CR, Miller RL, Mathews KA (2001) Split-cell exponential characteristic transport method for unstructured tetrahedral meshes. Nucl Sci Eng 138:26 Brennan CR, Miller RL, Mathews KA (2001) Split-cell exponential characteristic transport method for unstructured tetrahedral meshes. Nucl Sci Eng 138:26
107.
Zurück zum Zitat Sanchez R, Santandrea S (2001) Symmetrization of the transport operator and Lanczos’ iterations. In: Proc. international meeting on mathematical methods for nuclear applications, 9–13 Sept 2001. American Nuclear Society, Salt Lake City, Utah Sanchez R, Santandrea S (2001) Symmetrization of the transport operator and Lanczos’ iterations. In: Proc. international meeting on mathematical methods for nuclear applications, 9–13 Sept 2001. American Nuclear Society, Salt Lake City, Utah
108.
Zurück zum Zitat Sanchez R, Chetaine A (2001) A synthetic acceleration for a two-dimensional characteristic method in unstructured meshes. Nucl Sci Eng 136:122 Sanchez R, Chetaine A (2001) A synthetic acceleration for a two-dimensional characteristic method in unstructured meshes. Nucl Sci Eng 136:122
109.
Zurück zum Zitat Wareing TA, McGhee JM, Morel JE, Pautz SD (2001) Discontinuous finite element SN methods on three-dimensional unstructured grids. Nucl Sci Eng 138:256 Wareing TA, McGhee JM, Morel JE, Pautz SD (2001) Discontinuous finite element SN methods on three-dimensional unstructured grids. Nucl Sci Eng 138:256
110.
Zurück zum Zitat Adams ML, Larsen EW (2002) Fast iterative methods for discrete-ordinates particle transport calculations. Prog Nucl Energy 40:3 (review) Adams ML, Larsen EW (2002) Fast iterative methods for discrete-ordinates particle transport calculations. Prog Nucl Energy 40:3 (review)
111.
Zurück zum Zitat Baker RS (2002) A block adaptive mesh refinement algorithm for the neutral particle transport equation. Nucl Sci Eng 141:1 Baker RS (2002) A block adaptive mesh refinement algorithm for the neutral particle transport equation. Nucl Sci Eng 141:1
112.
Zurück zum Zitat Liscum-Powell JL, Prinja AB, Morel JE, Lorence LJ Jr (2002) Finite element solution of the self-adjoint angular flux equation for coupled electron–photon transport. Nucl Sci Eng 142:270 Liscum-Powell JL, Prinja AB, Morel JE, Lorence LJ Jr (2002) Finite element solution of the self-adjoint angular flux equation for coupled electron–photon transport. Nucl Sci Eng 142:270
113.
Zurück zum Zitat Pautz SD, Adams ML (2002) An asymptotic study of discretized transport equations in the Fokker–Planck limit. Nucl Sci Eng 140:51 Pautz SD, Adams ML (2002) An asymptotic study of discretized transport equations in the Fokker–Planck limit. Nucl Sci Eng 140:51
114.
Zurück zum Zitat Pautz SD (2002) An algorithm for parallel SN sweeps on unstructured meshes. Nucl Sci Eng 140:111 Pautz SD (2002) An algorithm for parallel SN sweeps on unstructured meshes. Nucl Sci Eng 140:111
115.
Zurück zum Zitat Patton BW, Holloway JP (2002) Application of preconditioned GMRES to the numerical solution of the neutron transport equation. Ann Nucl Energy 29:109 Patton BW, Holloway JP (2002) Application of preconditioned GMRES to the numerical solution of the neutron transport equation. Ann Nucl Energy 29:109
116.
Zurück zum Zitat Warsa JS, Wareing TA, Morel JE (2002) Fully consistent diffusion synthetic acceleration of linear discontinuous SN transport discretizations on unstructured tetrahedral meshes. Nucl Sci Eng 141:236 Warsa JS, Wareing TA, Morel JE (2002) Fully consistent diffusion synthetic acceleration of linear discontinuous SN transport discretizations on unstructured tetrahedral meshes. Nucl Sci Eng 141:236
117.
Zurück zum Zitat Aussourd C (2003) Styx: a multidimensional AMR SN scheme. Nucl Sci Eng 143:281 Aussourd C (2003) Styx: a multidimensional AMR SN scheme. Nucl Sci Eng 143:281
118.
Zurück zum Zitat Haghighat A, Wagner JC (2003) Monte Carlo variance reduction with deterministic importance functions. Prog Nucl Energy 42:25 (review) Haghighat A, Wagner JC (2003) Monte Carlo variance reduction with deterministic importance functions. Prog Nucl Energy 42:25 (review)
119.
Zurück zum Zitat Morel JE, Wareing TA, Lowrie RB, Parsons DK (2003) Analysis of ray-effect mitigation techniques. Nucl Sci Eng 144:1 Morel JE, Wareing TA, Lowrie RB, Parsons DK (2003) Analysis of ray-effect mitigation techniques. Nucl Sci Eng 144:1
120.
Zurück zum Zitat Morel JE, Prinja AK, McGhee JM, Wareing TA, Franke BC (2003) A discretization scheme for the 3-D continuous-scattering operator. Trans Am Nucl Soc 89:360 Morel JE, Prinja AK, McGhee JM, Wareing TA, Franke BC (2003) A discretization scheme for the 3-D continuous-scattering operator. Trans Am Nucl Soc 89:360
121.
Zurück zum Zitat Hanshaw HL, Larsen EW (2003) The explicit slope SN discretization method. In: Proc. topical meeting on mathematics and computations in nuclear applications, 6–10 April 2003. American Nuclear Society, Gatlinburg, Tennessee Hanshaw HL, Larsen EW (2003) The explicit slope SN discretization method. In: Proc. topical meeting on mathematics and computations in nuclear applications, 6–10 April 2003. American Nuclear Society, Gatlinburg, Tennessee
122.
Zurück zum Zitat Hanshaw HL, Nowak PF, Larsen EW (2003) Stretched and filtered transport-synthetic acceleration of SN problems: part 1, homogeneous media. Trans Am Nucl Soc 89:354 Hanshaw HL, Nowak PF, Larsen EW (2003) Stretched and filtered transport-synthetic acceleration of SN problems: part 1, homogeneous media. Trans Am Nucl Soc 89:354
123.
Zurück zum Zitat Shashkov M, Wendroff B (2004) The repair paradigm and application to conservation laws. J Comp Phys 198:265MATHMathSciNet Shashkov M, Wendroff B (2004) The repair paradigm and application to conservation laws. J Comp Phys 198:265MATHMathSciNet
124.
Zurück zum Zitat Warsa JS, Wareing TA, Morel JE (2004) Krylov iterative methods and the degraded effectiveness of diffusion synthetic acceleration for multidimensional SN calculations in problems with material discontin-uities. Nucl Sci Eng 147:218 Warsa JS, Wareing TA, Morel JE (2004) Krylov iterative methods and the degraded effectiveness of diffusion synthetic acceleration for multidimensional SN calculations in problems with material discontin-uities. Nucl Sci Eng 147:218
125.
Zurück zum Zitat Sanchez R, McCormick NJ (2004) Discrete ordinates solutions for highly forward peaked scattering. Nucl Sci Eng 147:249 Sanchez R, McCormick NJ (2004) Discrete ordinates solutions for highly forward peaked scattering. Nucl Sci Eng 147:249
126.
Zurück zum Zitat Warsa JS, Wareing TA, Morel JE, McGhee JM, Lehoucq RB (2004) Krylov subspace iterations for deterministic k-eigenvalue calculations. Nucl Sci Eng 147:26 Warsa JS, Wareing TA, Morel JE, McGhee JM, Lehoucq RB (2004) Krylov subspace iterations for deterministic k-eigenvalue calculations. Nucl Sci Eng 147:26
Metadaten
Titel
Advances in Discrete-Ordinates Methodology
verfasst von
Edward W. Larsen
Jim E. Morel
Copyright-Jahr
2010
Verlag
Springer Netherlands
DOI
https://doi.org/10.1007/978-90-481-3411-3_1