The convergence of numerical transfer schemes in diffusive regimes I: Discrete-ordinate method

SIAM Journal on Numerical Analysis

Volumn 36, Issue 5, 1999, Pages 1333-1369

  Golse, François ^a,b   Jin, Shi ^c   Levermore, C David ^d  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITÉ PARIS DESCARTES   (France)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^d University of Arizona   (United States)

Author keywords

Boundary layer; Boundary value problem; Convergence; Diffusion approximation; Discrete ordinate method; Matched asymptotics; Transfer equation

Indexed keywords

EID: 0000804338     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997315986     Document Type: Article

References (25)

1. P.M. ANSELONE, Convergence of Chandrasekhar's method for inhomogeneous transfer problems, J. Math. Mech., 10 (1961), pp. 537-546.
2. C. BARDOS, R. SANTOS, AND R. SENTIS, Diffusion approximation and computation of the critical size, Trans. Amer. Math. Soc., 284 (1984), pp. 617-649.
3. A. BENSOUSSAN, J.L. LIONS, AND G.C. PAPANICOLAOU, Boundary layers and homogenization of transport process, J. Publ. RIMS Kyoto Univ., 15 (1979), pp. 53-157.
4. G. BLANKENSHIP AND G.C. PAPANICOLAOU, Stability and control of stochastic systems with wide-band noise disturbance. I, SIAM J. Appl. Math., 34 (1978), pp. 437-476.
5. K.M. CASE AND P.F. ZWEIFEL, Linear Transport Theory, Addison-Wesley, Reading, MA, 1967.
6. S. CHANDRASEKHAR, Radiative Transfer, Dover, New York, 1960.
7. F. GOLSE, Knudsen layers from a computational viewpoint, Transport Theory Statist. Phys., 21 (1992), pp. 211-236.
8. F. GOLSE, S. JIN, AND C.D. LEVERMORE, The Convergence of Numerical Transfer Schemes in Diffusive Regimes II: The Cell-Edge Even-Parity Scheme, in preparation.
9. G.J. HABETLER AND B.J. MATKOWSKY, Uniform asymptotic expansion in transport theory with small mean free paths, and the diffusion approximation, J. Math. Phys., 16 (1975), pp. 846-854.
10. S. JIN AND D. LEVERMORE, The discrete-ordinate method in diffusive regimes, Transport Theory Statist. Phys., 20 (1991), pp. 413-439.
11. S. JIN AND C.D. LEVERMORE, Fully-discrete numerical transfer in diffusive regimes, Transport Theory Statist. Phys., 22 (1993), pp. 739-791.
12. H.B. KELLER, Approximate solutions of transport problems. II. Convergence and applications of the discrete ordinate method, J. Soc. Indust. Appl. Math., 8 (1960), pp. 43-73.
13. H.B. KELLER, On the pointwise convergence of the discrete-ordinate method, J. Soc. Indust. Appl. Math., 8 (1960), pp. 560-567.
14. H.B. KELLER, Convergence of the discrete-ordinate method for the anisotropic scattering transport equation, in Symposium on the Numerical Treatment of Ordinary Differential Equations, Integral and Integro-differential Equations, Birkhäuser Verlag, Basel, 1960, pp. 292-299.
15. E.W. LARSEN, The asymptotic diffusion limit of discretized transport problems, Nuclear Sci. Engrg., 112 (1992), pp. 336-346.
16. E.W. LARSEN AND J.B. KELLER, Asymptotic solutions of neutron transport problem, J. Math. Phys., 15 (1974), pp. 75-81.
17. E.W. LARSEN AND W.F. MILLER JR., Convergence rates of spatial difference equations for the discrete-ordinates neutron transport equations in slab geometry, Nuclear Sci. Engrg., 73 (1980), pp. 76-83.
18. E.W. LARSEN, J.E. MOREL, AND W.F. MILLER JR., Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes, J. Comput. Phys., 69 (1987), pp 283-324.
19. F. MALVAGI AND G.C. POMRANING, Initial and boundary conditions for diffusive linear transport problems, J. Math. Phys., 32 (1991), pp. 805-820.
20. P. NELSON, JR., Convergence of the discrete-ordinates method for anisotropically scattering multiplying particles in a subcritical slab, SIAM J. Numer. Anal., 10 (1973), pp. 175-181.
21. M.K. NESTELL, The Convergence of the Discrete-Ordinates Method for Integral Equations of Anisotropic Radiative Transfer, Tech. Rep. 23, Math. Dept., Oregon State University, Corvallis, OR, 1965.
22. G.C. PAPANICOLAOU, Asymptotic analysis of transport processes, Bull. Amer. Math. Soc., 81 (1975), pp. 330-392.
23. J. PITKÄRANTA AND L.R. SCOTT, Error estimates for the combined spatial and angular approximations of the transport equation for slab geometry, SIAM J. Numer. Anal., 20 (1983), pp. 922-950.
24. B. WENDROFF, On the convergence of the discrete ordinate method, J. Soc. Indust. Appl. Math., 8 (1960), pp. 508-513.
25. H. WEYL, The Classical Groups, Princeton University Press, Princeton, NJ, 1946, p. 202.