Volume 44, Number 6, November-December 2010
|Page(s)||1193 - 1224|
|Published online||15 April 2010|
- G. Bell and S. Glasstone, Nuclear Reactor Theory. Van Nostrand, Princeton (1970).
- C. Berthon, P. Charrier and B. Dubroca, An HLLC scheme to solve the M1 model of radiative transfer in two space dimensions. J. Sci. Comp. 31 (2007) 347–389. [CrossRef]
- T.A. Brunner, Riemann solvers for time-dependent transport based on the maximum entropy and spherical harmonics closures. Ph.D. Thesis, University of Michigan (2000).
- C. Buet and B. Despres, Asymptotic preserving and positive schemes for radiation hydrodynamics. J. Comput. Phys. 215 (2006) 717–740. [CrossRef] [MathSciNet]
- C. Buet and S. Cordier, Asymptotic preserving scheme and numerical methods for radiative hydrodynamic models. C. R. Acad. Sci., Sér. 1 Math. 338 (2004) 951–956.
- K.M. Case and P.F. Zweifel, Linear Transport Theory. Addison-Wesley Publishing Co., Inc. Reading (1967).
- S. Chandrasekhar, Radiative transfer. Dover, New York (1960).
- R. Dautray and J.L. Lions, Analyse mathématique et calcul numérique. Chap. 21, Masson, Paris (1988).
- J.J. Duderstadt and W.R. Martin, Transport theory. Wiley-Interscience, New York (1979).
- E.M. Gelbard, Simplified spherical harmonics equations and their use in shielding problems. Technical report WAPD-T-1182, Bettis Atomic Power Laboratory, USA (1961).
- L. Gosse and G. Toscani, An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations. C. R. Acad. Sci., Sér. 1 Math. 334 (2002) 337–342.
- L. Gosse and G. Toscani, Space localization and well-balanced schemes for discrete kinetic models in diffusive regimes. SIAM J. Numer. Anal. 41 (2003) 641–658. [CrossRef] [MathSciNet]
- J.M. Greenberg and A.Y. Leroux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1–16. [CrossRef] [EDP Sciences] [MathSciNet]
- H.B. Keller, Approximate solutions of transport problems. II. Convergence and applications of the discrete-ordinate method. J. Soc. Indust. Appl. Math. 8 (1960) 43–73. [CrossRef] [MathSciNet]
- E.W. Larsen, On numerical solutions of transport problems in the diffusion limit. Nucl. Sci. Eng. 83 (1983) 90.
- E.W. Larsen and J.B. Keller, Asymptotic solution of neutron transport problems for small mean free paths. J. Math. Phys. 15 (1974) 75. [CrossRef]
- E.W. Larsen, G.C. Pomraning and V.C. Badham, Asymptotic analysis of radiative transfer problems. J. Quant. Spectrosc. Radiat. Transfer 29 (1983) 285. [CrossRef]
- K.D. Lathrop, Ray effects in discrete ordinates equations. Nucl. Sci. Eng. 32 (1968) 357.
- C.D. Levermore, Relating Eddington factors to flux limiters. J. Quant. Spec. Rad. Transfer. 31 (1984) 149–160. [NASA ADS] [CrossRef]
- R. McClarren, J.P. Holloway, T.A. Brunner and T. Melhorn, An implicit Riemann solver for the time-dependent Pn equations, in International Topical Meeting on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, American Nuclear Society, Avignon, France (2005).
- R. McClarren, J.P. Holloway and T.A. Brunner, Establishing an asymptotic diffusion limit for Riemann solvers on the time-dependent Pn equations, in International Topical Meeting on Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, American Nuclear Society, Avignon, France (2005).
- R. McClarren, J.P. Holloway and T.A. Brunner, On solutions to the Pn equations for thermal radiative transfer. J. Comput. Phys. 227 (2008) 2864–2885. [CrossRef] [MathSciNet]
- G.C. Pomraning, Diffusive limits for linear transport equations. Nucl. Sci. Eng. 112 (1992) 239–255.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.