On Consistent Time-Integration Methods for Radiation Hydrodynamics in the Equilibrium Diffusion Limit: Low-Energy-Density Regime

Journal of Computational Physics

Volumn 167, Issue 1, 2001, Pages 99-130

  Bates, J W ^a   Knoll, D A ^b   Rider, W J ^c   Lowrie, R B ^c   Mousseau, V A ^b  

^a NAVAL RESEARCH LABORATORY   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Finite volume methods; Newton Krylov; Nonlinear iterative schemes; Radiation hydrodynamics

Indexed keywords

CONTROL NONLINEARITIES; DIFFUSION; HEAT TRANSFER; HYDRODYNAMICS; ITERATIVE METHODS; LINEARIZATION; NONLINEAR EQUATIONS; RADIATION EFFECTS;

DENSITY REGIME; DIFFUSION LIMITS; ENERGY DENSITY; FINITE-VOLUME METHOD; ITERATIVE SCHEMES; LOWER ENERGIES; NEWTON-KRYLOV; NONLINEAR ITERATIVE SCHEME; PRESSURE DENSITY; RADIATION HYDRODYNAMICS;

FINITE VOLUME METHOD;

EID: 0013124510     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6661     Document Type: Article

References (44)

1. R. L. Bowers and J. R. Wilson, Numerical Modeling in Applied Physics and Astrophysics (Jones & Bartlett, Boston, 1991).
2. D. Milhalas and B. W. Milhalas, Foundations of Radiation Hydrodynamics (Oxford Univ. Press, New York, 1984).
3. Y. B. Zel'dovich and Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Vols. I and II (Academic Press, New York, 1966, 1967).
4. C. Hirsch, Numerical Computation of Internal and External Flows (Wiley, Chichester, 1990).
5. R. J. LeVeque, Numerical Methods for Conservation Laws (Birkhäuser, Basel, 1992).
6. C. A. Fletcher, Computational Techniques for Fluid Dynamics (Springer-Verlag, Berlin/New York, 1997).
7. E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics (Springer- Verlag, Berlin/New York, 1997).
8. W. Dai and P. R. Woodward, Numerical simulations for radiation hydrodynamics. I. Diffusion limit, J. Comput. Phys. 142, 182 (1998).
9. W. Dai and P. R. Woodward, Numerical simulations for radiation hydrodynamics. II. Transport limit, J. Comput. Phys. 157, 199 (2000).
10. R. B. Lowrie, J. E. Morel, and J. A. Hittinger, The coupling of radiation and hydrodynamics, Astrophys. J. 521, 432 (1999).
11. D. S. Balsara, An analysis of the hyperbolic nature of the equations of radiation hydrodynamics, J. Quant. Spectrosc. Radiat. Transfer 61, 617 (1999).
12. D. S. Balsara, Linearized formulation of the Riemann problem for radiation hydrodynamics, J. Quant. Spectrosc. Radiat. Transfer 61, 629 (1999).
13. P. J. Roache, Computational Fluid Dynamics (Hermosa, Albuquerque, NM 1998).
14. J. H. Ferziger and M. Perić, Computational Methods for Fluid Dynamics (Springer-Verlag, Berlin/New York, 1996).
15. W H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge Univ. Press, Cambridge, UK 1992).
16. D. A. Knoll, W. J. Rider, and G. L. Olsen, An efficient nonlinear solution method for non-equilibrium radiation diffusion, J. Quant. Spectrosc. Radiat. Transfer 63, 15 (1999).
17. Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving non-symmetric linear systems, SIAM J. Sci. Stat. Comput. 7, 856 (1986).
18. P. N. Brown and Y. Saad, Hybrid Krylov methods for nonlinear systems of equations, SIAM J. Sci. Stat. Comput. 11, 450 (1990).
19. S. K. Godunov, Difference methods for the numerical calculation of the equations of fluid dynamics, Math. Sb. 47, 271 (1959).
20. G. C. Pomraning, The Equations of Radiation Hydrodynamics (Pergamon, Oxford, 1973).
21. W. Hackbush, Muti-grid Methods and Applications (Springer-Verlag, Berlin/New York, 1985).
22. C. Baldwin, P. N. Brown, R. Falgout, F. Graziani, and J. Jones, Iterative linear solvers in a 2D radiation-hydrodynamics code: methods and performance, J. Comput. Phys. 154, 1 (1999).
23. A. I. Shestakov, Time-dependent simulations of point explosions with heat conduction, Phys. Fluids 11, 1091 (1999).
24. P. Reinicke and J. Meyer-ter-Vehn, The point explosion with heat conduction, Phys. Fluids A 3, 1807 (1991).
25. R. E. Marshak, Effect of radiation on shock wave behavior, Phys. Fluids 1, 24 (1958).
26. P. Colella, A direct Eulerian MUSCL scheme for gas dynamics, SIAM J. Sci. Stat. Comput. 6, 104 (1985).
27. P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43, 357 (1981).
28. C. T. Kelly, Iterative Methods for Linear and Nonlinear Equations (Soc. for Indus. & Appl. Math., Philadelphia, 1995).
29. Y. Saad, Iterative Methods for Sparse Linear Systems (PWS-Kent, Boston, 1996).
30. V. A. Mousseau, D. A. Knoll, and W. J. Rider, Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion, J. Comput. Phys. 160, 743 (2000).
31. D. A. Knoll and W. J. Rider, A multigrid preconditioned Newton-Krylov method, SIAM J. Sci. Comput. 21, 691 (1999).
32. W. J. Rider, D. A. Knoll, and G. L. Olson, A multigrid Newton-Krylov method for multimaterial equilibrium radiation diffusion, J. Comput. Phys. 152, 164 (1999).
33. H. T. Huynh, Accurate upwind methods for the Euler equations, SIAM. J. Numer. Anal. 32, 1565 (1995).
34. J. Crank and P. Nicolson, A practical method for numerical evaluation of solution of partial differential equations of the heat conduction type, Proc. Camb. Philos. Soc. 43, 50 (1947).
35. W. J. Rider and D. A. Knoll, Time step size selection for radiation diffusion calculations, J. Comput. Phys. 152, 790 (1999).
36. G. I. Barenblatt, Similarity, Self-Similarity and Intermediate Asymptotics (Consultants Bureau, New York, 1979).
37. L. I. Sedov, Similarity and Dimensional Methods in Mechanics (Academic Press, New York, 1959).
38. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987).
39. A. I. Shestakov, M. K. Prasad, J. L. Milovich, N. A. Gentile, J. F. Painter, and G. Furnish, The Radiation Hydrodynamic ICF3D Code, Report No. UCRL-JC-124448, Lawrence Livermore National Laboratory, 1997.
40. W. J. Rider, An adaptive Riemann solver using a two-shock approximation, Comput. Fluids 28, 741 (1999).
41. L. Spitzer, Physics of Fully Ionized Gases (Interscience, New York, 1962).
42. B. Van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, J. Comput. Phys. 32, 101 (1979).
43. E. S. Oran and J. P. Boris, Numerical Simulation of Reactive Flow (Elsevier, Amsterdam/New York, 1987).
44. A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49, 357 (1983).