Combining spectral and shock-capturing methods: A new numerical approach for 3D relativistic core collapse simulations

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 71, Issue 6, 2005, Pages 1-30

  Dimmelmeier, Harald ^a   Novak, Jérôme ^b   Font, José A ^c   Ibáñez, José M ^c   Müller, Ewald ^a  

^a MAX PLANCK INSTITUT FÜR ASTROPHYSIK   (Germany)

^b OBSERVATOIRE DE PARIS   (France)

^c UNIVERSITY OF VALENCIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; ARTICLE; COMPARATIVE STUDY; CONFORMATION; GRAVITY; HYDRODYNAMICS; MATHEMATICAL COMPUTING; NEUTRON; ROTATION; SIMULATION; SPECTROSCOPY;

EID: 18444393697     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.71.064023     Document Type: Article

References (76)

1. R. Buras, M. Rampp, H.-T. Janka, and K. Kifonidis, Phys. Rev. Lett. 90, 241101 (2003).
2. E. Müller, in Computational Methods for Astrophysical Fluid Flow, edited by O. Steiner and A. Gautschy (Springer, Berlin, 1998), p. 343.
3. K. New, Living Rev. Relativity 6, 2 (2003), http://www.livingreviews.org/ lrr-2003-2/.
4. E. Müller, Astron. Astrophys. 114, 53 (1982).
5. L. S. Finn and C. R. Evans, Astrophys. J. 351, 588 (1990).
6. R. Mönchmeyer, G. Schäfer, E. Müller, and R. E. Kates, Astron. Astrophys. 246, 417 (1991).
7. S. Yamada and K. Sato, Astrophys. J. 450, 245 (1995).
8. T. Zwerger and E. Müller, Astron. Astrophys. 320, 209 (1997).
9. M. Rampp, E. Müller, and M. Ruffert, Astron. Astrophys. 332, 969 (1998).
10. H. Dimmelmeier, J. A. Font, and E. Müller, Astrophys. J. Lett. 560, L163 (2001).
11. H. Dimmelmeier, J. A. Font, and E. Müller, Astron. Astrophys. 388, 917 (2002).
12. H. Dimmelmeier, J. A. Font, and E. Müller, Astron. Astrophys. 393, 523 (2002).
13. C. L. Fryer, D. E. Holz, and S. A. Hughes, Astrophys. J. 565, 430 (2002).
14. C. L. Fryer, D. E. Holz, S. A. Hughes, and M. S. Warren, astro-ph/0211609.
15. J. N. Imamaura, B. K. Pickett, and R. H. Durisen, Astrophys. J. 587, 341 (2003).
16. K. Kotake, S. Yamada, and K. Sato, Phys. Rev. D 68, 044023 (2003).
17. M. Shibata and Y. I. Sekiguchi, Phys. Rev. D 69, 084024 (2004).
18. C. D. Ott, A. Burrows, E. Livne, and R. Walder, Astrophys. J. 600, 834 (2004).
19. E. Müller and H.-T. Janka, Astron. Astrophys. 317, 140 (1997).
20. E. Müller, M. Rampp, R. Buras, H.-T. Janka, and D. H. Shoemaker, Astrophys. J. 603, 221 (2004).
21. A. Burrows and J. Hayes, Phys. Rev. Lett., 76, 352 (1996).
22. L. Lehner, Classical Quantum Gravity 18, R25 (2001).
23. L. Lindblom and M. A. Scheel, Phys. Rev. D 67, 124005 (2003).
24. J. A. Isenberg, "Waveless Approximation Theories of Gravities", University of Maryland, 1978 (unpublished).
25. J. R. Wilson, G. J. Mathews, and P. Marronetti, Phys. Rev. D 54, 1317 (1996).
26. http://www.mpa-garching.mpg.de/rel_hydro/.
27. T. Pradier, N. Arnaud, M.-A. Bizouard, F. Cavalier, M. Davier, and P. Hello, Phys. Rev. D 63, 042002 (2001).
28. M. Shibata and T. Nakamura, Phys. Rev. D 52, 5428 (1995).
29. T. W. Baumgarte and S. L. Shapiro, Phys. Rev. D 59, 024007 (1999).
30. T. Nakamura, K. Oohara, and Y. Kojima, Prog. Theor. Phys. Suppl. 90, 1 (1987).
31. F. Siebel, J. A. Font, E. Müller, and P. Papadopoulos, Phys. Rev. D 67, 124018 (2003).
32. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (Society of Industrial and Applied Mathematics, Philadelphia, 1977).
33. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer, Berlin, 1988).
34. S. Bonazzola and J. A. Marck, J. Comput. Phys. 87, 201 (1990).
35. http://www.luth.obspm.fr/Groupe1.html.
36. S. Bonazzola, E. Gourgoulhon, and J.-A. Marck, J. Comput. Appl. Math. 109, 433 (1999).
37. L. Villain and S. Bonazzola, Phys. Rev. D 66, 123001 (2002).
38. P. Grandclément, E. Gourgoulhon, and S. Bonazzola, Phys. Rev. D 65, 044021 (2002).
39. S. Bonazzola, E. Gourgoulhon, P. Grandclément, and J. Novak, Phys. Rev. D 70, 104007 (2004).
40. http://www.lorene.obspm.fr.
41. J. Frauendiener, J. Comput. Appl. Math. 109, 475 (1999).
42. H. P. Pfeiffer, L. E. Kidder, M. A. Scheel, and S. A. Teukolsky, Comput. Phys. Commun. 152, 253 (2003).
43. E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics - A Practical Introduction (Springer, Berlin, 1997).
44. J. A. Font, Living Rev. Relativity 6, 4 (2003), http://www.livingreviews. org/lrr-2003-4/.
45. J. M. Martí and E. Müller, Living Rev. Relativity 6, 7 (2003), http://www.livingreviews.org/lrr-2003-7/.
46. P. Cerdá-Durán, G. Faye, H. Dimmelmeier, J. A. Font, J. M. Ibáñez, E. Müller, and G. Schäfer, to be published.
47. G. Schäfer and A. Gopakumar, Phys. Rev. D 69, 021501 (2004).
48. J. Novak and J. M. Ibáñez, Astrophys. J. 533, 392 (2000).
49. J. A. Font, M. Miller, W.-M. Suen, and M. Tobias, Phys. Rev. D 61, 044011 (2000).
50. J. A. Font, T. Goodale, S. Iyer, M. Miller, L. Rezzolla, E. Seidel, N. Stergioulas, W.-M. Suen, and M. Tobias, Phys. Rev. D 65, 084024 (2002).
51. M. Shibata, Phys. Rev. D 60, 104052 (1999).
52. M. D. Duez, T. W. Baumgarte, S. L. Shapiro, M. Shibata, and K. Uryu, Phys. Rev. D 65, 024016 (2002).
53. L. Baiotti, I. Hawke, P. J. Montero, F. Löffler, L. Rezzolla, N. Stergioulas, J. A. Font, and E. Seidel, Phys. Rev. D 71, 024035 (2005).
54. http://www.aei-potsdam.mpg.de/∼hawke/Whisky.html.
55. F. Banyuls, J. A. Font, J. M. Ibáñez, J. M. Martí, and J. A. Miralles, Astrophys. J. 476, 221 (1997).
56. H.-T. Janka, T. Zwerger, and R. Mönchmeyer, Astron. Astrophys. 268, 360 (1993).
57. R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
58. O. Reula, Living Rev. Relativity 1, 3 (1998), http://www.livingreviews. org/lrr-1998-3/.
59. T. Damour, E. Gourgoulhon, and P. Grandclément, Phys. Rev. D 66, 024007 (2002).
60. C. R. Evans, in Dynamical Spacetimes and Numerical Relativity, edited by J. Centrella, (Cambridge University Press, Cambridge, England, 1986), p. 3.
61. R. F. Stark, in Frontiers in Numerical Relativity, edited by C. R. Evans, L. S. Finn, and D. W. Hobill (Cambridge University Press, Cambridge, England, 1989), p. 281.
62. J. P. Boyd, Chebyshev and Fourier Spectral Methods (Dover, New York, 2001), 2nd edition.
63. R. Donat, J. A. Font, J. M. Ibáñez, and A. Marquina, J. Comput. Phys. 146, 58 (1998).
64. M. Shibata, Phys. Rev. D 67, 024033 (2003).
65. D. Potter, Computational Physics (Wiley, Chichester, U. K., 1973).
66. P. Grandclément, S. Bonazzola, E. Gourgoulhon, and J. A. Marck, J. Comput. Phys. 170, 231 (2001).
67. L. S. Finn, in Frontiers in Numerical Relativity, edited by C. R. Evans, S. L. Finn, and D. W. Hobbill, (Cambridge University Press, Cambridge, England, 1989), p. 126.
68. L. Blanchet, T. Damour, and G. Schäfer, Mon. Not. R. Astron. Soc. 242, 289 (1990).
69. M. Shibata and Y. I. Sekiguchi, Phys. Rev. D 68, 104020 (2003).
70. H. Komatsu, Y. Eriguchi, and I. Hachisu, Mon. Not. R. Astron. Soc. 237, 335 (1989).
71. J. A. Font, N. Stergioulas, and K. D. Kokkotas, Mon. Not. R. Astron. Soc. 313, 678 (2000).
72. M. Alcubierre, S. Brandt, B. Brügmann, D. Holz, E. Seidel, R. Takahashi, and J. Thornburg, Int. J. Mod. Phys. D 10, 273 (2001).
73. K. D. Kokkotas and B. G. Schmidt, Living Rev. Relativity 2, 2 (1999), http://www.livingreviews.org/lrr-1999-2/.
74. J. A. Font, H. Dimmelmeier, A. Gupta, and N. Stergioulas, Mon. Not. R. Astron. Soc. 325, 1463 (2001).
75. N. Stergioulas, T. A. Apostolatos, and J. A. Font, Mon. Not. R. Astron. Soc. 352, 1089 (2004).
76. H. Dimmelmeier, N. Stergioulas, and J. A. Font, to be published.