Advertisement

Space Science Reviews

, Volume 134, Issue 1–4, pp 229–268 | Cite as

Simulation Techniques for Cosmological Simulations

  • K. DolagEmail author
  • S. Borgani
  • S. Schindler
  • A. Diaferio
  • A. M. Bykov
Open Access
Article

Abstract

Modern cosmological observations allow us to study in great detail the evolution and history of the large scale structure hierarchy. The fundamental problem of accurate constraints on the cosmological parameters, within a given cosmological model, requires precise modelling of the observed structure. In this paper we briefly review the current most effective techniques of large scale structure simulations, emphasising both their advantages and shortcomings. Starting with basics of the direct N-body simulations appropriate to modelling cold dark matter evolution, we then discuss the direct-sum technique GRAPE, particle-mesh (PM) and hybrid methods, combining the PM and the tree algorithms. Simulations of baryonic matter in the Universe often use hydrodynamic codes based on both particle methods that discretise mass, and grid-based methods. We briefly describe Eulerian grid methods, and also some variants of Lagrangian smoothed particle hydrodynamics (SPH) methods.

Keywords

Cosmology: theory Large-scale structure of universe Hydrodynamics Method: numerical, N-body simulations 

References

  1. T. Abel, P. Anninos, Y. Zhang, M.L. Norman, New Astron. 2, 181 (1997) CrossRefADSGoogle Scholar
  2. O. Agertz, B. Moore, J. Stadel et al., Mon. Not. R. Astron. Soc. 380, 963 (2007) CrossRefADSGoogle Scholar
  3. E. Athanassoula, A. Bosma, J.-C. Lambert, J. Makino, Mon. Not. R. Astron. Soc. 293, 369 (1998) CrossRefADSGoogle Scholar
  4. J.S. Bagla, J. Astrophys. Astron. 23, 185 (2002) CrossRefADSGoogle Scholar
  5. J.S. Bagla, S. Ray, New Astron. 8, 665 (2003) CrossRefADSGoogle Scholar
  6. D.S. Balsara, J. Comput. Phys. 121, 357 (1995) zbMATHCrossRefADSGoogle Scholar
  7. J.M. Bardeen, J.R. Bond, N. Kaiser, A.S. Szalay, Astrophys. J. 304, 15 (1986) CrossRefADSGoogle Scholar
  8. J. Barnes, P. Hut, Nature 324, 446 (1986) CrossRefADSGoogle Scholar
  9. E. Bertschinger, COSMICS: Cosmological initial conditions and microwave anisotropy codes. astro-ph/9506070 (1995) Google Scholar
  10. P. Bode, J.P. Ostriker, G. Xu, Astrophys. J. Suppl. Ser. 128, 561 (2000) CrossRefADSGoogle Scholar
  11. A. Bonaldi, G. Tormen, K. Dolag, L. Moscardini, Mon. Not. R. Astron. Soc. 378, 1248 (2007) CrossRefADSGoogle Scholar
  12. S. Borgani, K. Dolag, G. Murante et al., Mon. Not. R. Astron. Soc. 367, 1641 (2006) CrossRefADSGoogle Scholar
  13. S. Borgani, D. Fabjan, L. Tornatore et al., Space Sci. Rev. (2008). doi: 10.1007/s11214-008-9322-7 Google Scholar
  14. G.L. Bryan, M.L. Norman, J.M. Stone, R. Cen, J.P. Ostriker, Comput. Phys. Commun. 89, 149 (1995) zbMATHCrossRefADSGoogle Scholar
  15. R. Cen, Astrophys. J. Suppl. Ser. 78, 341 (1992) CrossRefADSGoogle Scholar
  16. S.C. Chapra, R.P. Canale, Numerical Methods for Engineers: With Programming and Software Applications (McGraw–Hill, New York, 1997) Google Scholar
  17. P. Colella, H.M. Glaz, J. Comput. Phys. 59, 264 (1985) zbMATHCrossRefADSMathSciNetGoogle Scholar
  18. P. Colella, P.R. Woodward, J. Comput. Phys. 54, 174 (1984) zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. H.M.P. Couchman, Astrophys. J. 368, L23 (1991) CrossRefADSGoogle Scholar
  20. H.M.P. Couchman, P.A. Thomas, F.R. Pearce, Astrophys. J. 452, 797 (1995) CrossRefADSGoogle Scholar
  21. R. Courant, K.O. Friedrichs, Supersonic Flow and Shock Waves (Interscience, New York, 1948) zbMATHGoogle Scholar
  22. W. Dehnen, Astrophys. J. 536, L39 (2000) CrossRefADSGoogle Scholar
  23. K. Dolag, M. Jubelgas, V. Springel, S. Borgani, E. Rasia, Astrophys. J. Lett. 606, L97 (2004) CrossRefADSGoogle Scholar
  24. K. Dolag, F. Vazza, G. Brunetti, G. Tormen, Mon. Not. R. Astron. Soc. 364, 753 (2005) CrossRefADSGoogle Scholar
  25. K. Dolag, A.M. Bykov, A. Diaferio, Space Sci. Rev. (2008). doi: 10.1007/s11214-008-9319-2 Google Scholar
  26. G. Efstathiou, M. Davis, S.D.M. White, C.S. Frenk, Astrophys. J. Suppl. Ser. 57, 241 (1985) CrossRefADSGoogle Scholar
  27. B. Einfeldt, SIAM J. Numer. Anal. 25, 294 (1988) zbMATHCrossRefMathSciNetGoogle Scholar
  28. B. Einfeldt, P.L. Roe, C.D. Munz, B. Sjogreen, J. Comput. Phys. 92, 273 (1991) zbMATHCrossRefADSMathSciNetGoogle Scholar
  29. S. Ettori, K. Dolag, S. Borgani, G. Murante, Mon. Not. R. Astron. Soc. 365, 1021 (2006) CrossRefADSGoogle Scholar
  30. A.E. Evrard, Mon. Not. R. Astron. Soc. 235, 911 (1988) zbMATHADSGoogle Scholar
  31. A.E. Evrard, T.J. MacFarland, H.M.P. Couchman et al., Astrophys. J. 573, 7 (2002) CrossRefADSGoogle Scholar
  32. L.-L. Feng, C.-W. Shu, M. Zhang, Astrophys. J. 612, 1 (2004) CrossRefADSGoogle Scholar
  33. C.S. Frenk, S.D.M. White, P. Bode et al., Astrophys. J. 525, 554 (1999) CrossRefADSGoogle Scholar
  34. B. Fryxell, K. Olson, P. Ricker et al., Astrophys. J. Suppl. Ser. 131, 273 (2000) CrossRefADSGoogle Scholar
  35. T. Fukushige, T. Ito, J. Makino et al., Publ. Astron. Soc. Jpn. 43, 841 (1991) ADSGoogle Scholar
  36. D. Galli, F. Palla, Astron. Astrophys. 335, 403 (1998) ADSGoogle Scholar
  37. A. Gardini, E. Rasia, P. Mazzotta et al., Mon. Not. R. Astron. Soc. 351, 505 (2004) CrossRefADSGoogle Scholar
  38. R.A. Gingold, J.J. Monaghan, Mon. Not. R. Astron. Soc. 181, 375 (1977) zbMATHADSGoogle Scholar
  39. F. Haardt, P. Madau, Astrophys. J. 461, 20 (1996) CrossRefADSGoogle Scholar
  40. A. Harten, J. Comput. Phys. 49, 357 (1983) zbMATHCrossRefADSMathSciNetGoogle Scholar
  41. A. Harten, P.D. Lax, B. van Leer, SIAM Rev. 25, 35 (1983) zbMATHCrossRefMathSciNetGoogle Scholar
  42. A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, J. Comput. Phys. 71, 231 (1987) zbMATHCrossRefADSMathSciNetGoogle Scholar
  43. K. Heitmann, Z. Lukic, P. Fasel et al., astro-ph/0706.1270 (2007). Report LA-UR-07-1953 Google Scholar
  44. L. Hernquist, Astrophys. J. 404, 717 (1993) CrossRefADSGoogle Scholar
  45. L. Hernquist, N. Katz, Astrophys. J. Suppl. Ser. 70, 419 (1989) CrossRefADSGoogle Scholar
  46. R.W. Hockney, J.W. Eastwood, Computer Simulation Using Particles (Hilger, Bristol, 1988) zbMATHGoogle Scholar
  47. P. Hut, J. Makino, S. McMillan, Astrophys. J. 443, L93 (1995) CrossRefADSGoogle Scholar
  48. I.T. Iliev, B. Ciardi, M.A. Alvarez et al., Mon. Not. R. Astron. Soc. 371, 1057 (2006) CrossRefADSGoogle Scholar
  49. T. Ito, J. Makino, T. Fukushige et al., Publ. Astron. Soc. Jpn. 45, 339 (1993) ADSGoogle Scholar
  50. G.-S. Jiang, C.-W. Shu, J. Comput. Phys. 126, 202 (1996) zbMATHCrossRefMathSciNetGoogle Scholar
  51. M. Jubelgas, V. Springel, K. Dolag, Mon. Not. R. Astron. Soc. 351, 423 (2004) CrossRefADSGoogle Scholar
  52. J.S. Kaastra, F.B.S. Paerels, F. Durret, S. Schindler, P. Richter, Space Sci. Rev. (2008). doi: 10.1007/s11214-008-9310 Google Scholar
  53. H. Kang, J.P. Ostriker, R. Cen et al., Astrophys. J. 430, 83 (1994) CrossRefADSGoogle Scholar
  54. W. Kapferer, T. Kronberger, J. Weratschnig, S. Schindler, Astron. Astrophys. 472, 757 (2007) CrossRefADSGoogle Scholar
  55. N. Katz, D.H. Weinberg, L. Hernquist, Astrophys. J. Suppl. Ser. 105, 19 (1996) CrossRefADSGoogle Scholar
  56. A. Kawai, T. Fukushige, J. Makino, M. Taiji, Publ. Astron. Soc. Jpn. 52, 659 (2000) ADSGoogle Scholar
  57. A. Kravtsov, in APS Meeting Abstracts (2002). http://flux.aps.org/meetings/YR02/APR02/baps/abs/S820004.html
  58. A.V. Kravtsov, A.A. Klypin, A.M. Khokhlov, Astrophys. J. Suppl. Ser. 111, 73 (1997) CrossRefADSGoogle Scholar
  59. A.V. Kravtsov, D. Nagai, A.A. Vikhlinin, Astrophys. J. 625, 588 (2005) CrossRefADSGoogle Scholar
  60. R. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics (Cambridge University Press, Cambridge, 2002) zbMATHGoogle Scholar
  61. D. Levy, G. Puppo, G. Russo, Berkeley CPAM 762 (1999). arXiv:math/9911089 Google Scholar
  62. S. Li, J. Comput. Phys. 203, 344 (2005) zbMATHCrossRefADSMathSciNetGoogle Scholar
  63. S. Li, H. Li, R. Cen, Astrophys. J. Suppl. Ser. 174, 1–12 (2008). astro-ph/0611863 CrossRefADSGoogle Scholar
  64. L.B. Lucy, Astron. J. 82, 1013 (1977) CrossRefADSGoogle Scholar
  65. U. Maio, K. Dolag, B. Ciardi, L. Tornatore, Mon. Not. R. Astron. Soc. 379, 963 (2007) CrossRefADSGoogle Scholar
  66. J. Makino, Publ. Astron. Soc. Jpn. 43, 621 (1991) ADSGoogle Scholar
  67. B.F. Mathiesen, A.E. Evrard, Astrophys. J. 546, 100 (2001) CrossRefADSGoogle Scholar
  68. P. Mazzotta, E. Rasia, L. Moscardini, G. Tormen, Mon. Not. R. Astron. Soc. 354, 10 (2004) CrossRefADSGoogle Scholar
  69. M. Meneghetti, P. Melchior, A. Grazian et al., Astron. Astrophys. (2008, in press). astro-ph/0711.3418 Google Scholar
  70. J.J. Monaghan, Annu. Rev. Astron. Astrophys. 30, 543 (1992) CrossRefADSGoogle Scholar
  71. J.J. Monaghan, J. Comput. Phys. 136, 298 (1997) zbMATHCrossRefADSMathSciNetGoogle Scholar
  72. J.J. Monaghan, R.A. Gingold, J. Comput. Phys. 52, 374 (1983) zbMATHCrossRefADSGoogle Scholar
  73. J.P. Morris, J.J. Monaghan, J. Comput. Phys. 136, 41 (1997) zbMATHCrossRefMathSciNetGoogle Scholar
  74. J.F. Navarro, S.D.M. White, Mon. Not. R. Astron. Soc. 265, 271 (1993) ADSGoogle Scholar
  75. B.W. O’Shea, K. Nagamine, V. Springel, L. Hernquist, M.L. Norman, Astrophys. J. Suppl. Ser. 160, 1 (2005) CrossRefADSGoogle Scholar
  76. J.M. Owen, J.V. Villumsen, P.R. Shapiro, H. Martel, Astrophys. J. Suppl. Ser. 116, 155 (1998) CrossRefADSGoogle Scholar
  77. P.J.E. Peebles, The Large-Scale Structure of the Universe (Princeton University Press, Princeton, 1980) Google Scholar
  78. U.-L. Pen, Astrophys. J. Suppl. Ser. 115, 19 (1998) CrossRefADSGoogle Scholar
  79. K.G. Powell, P.L. Roe, T.J. Linde, T.I. Gombosi, D.L. de Zeeuw, J. Comput. Phys. 154, 284 (1999) zbMATHCrossRefADSMathSciNetGoogle Scholar
  80. C. Power, J.F. Navarro, A. Jenkins et al., Mon. Not. R. Astron. Soc. 338, 14 (2003) CrossRefADSGoogle Scholar
  81. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in FORTRAN. The Art of Scientific Computing, 2nd edn. (Cambridge University Press, Cambridge, 1992) zbMATHGoogle Scholar
  82. T. Quinn, N. Katz, J. Stadel, G. Lake, Astrophys. J. (1997). Submitted but not published, astro-ph/9710043 Google Scholar
  83. E. Rasia, P. Mazzotta, S. Borgani et al., Astrophys. J. 618, L1 (2005) CrossRefADSGoogle Scholar
  84. E. Rasia, S. Ettori, L. Moscardini et al., Mon. Not. R. Astron. Soc. 369, 2013 (2006) CrossRefADSGoogle Scholar
  85. E. Rasia, P. Mazzotta, H. Bourdin et al., Astrophys. J. (2007, in press). astro-ph/0707.2614 Google Scholar
  86. P.M. Ricker, S. Dodelson, D.Q. Lamb, Astrophys. J. 536, 122 (2000) CrossRefADSGoogle Scholar
  87. D. Ryu, J.P. Ostriker, H. Kang, R. Cen, Astrophys. J. 414, 1 (1993) CrossRefADSGoogle Scholar
  88. H.-Y. Schive, C.-H. Chien, S.-K. Wong, Y.-C. Tsai, T. Chiueh, New Astron. (2007, in press). astro-ph/0707.2991 Google Scholar
  89. C.-W. Shu, in Advanced Numerical Approximate of Nonlinear Hyperbolic Equations, ed. by A. Quarteroni. Lecture Notes in Mathematics, vol. 1697 (Springer, Berlin, 1998), p. 285 CrossRefGoogle Scholar
  90. D. Sijacki, V. Springel, T. di Matteo, L. Hernquist, Mon. Not. R. Astron. Soc. 380, 877 (2007) CrossRefADSGoogle Scholar
  91. B.W. Silverman, Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability (Chapman & Hall, London, 1986) zbMATHGoogle Scholar
  92. V. Springel, Mon. Not. R. Astron. Soc. 364, 1105 (2005) CrossRefADSGoogle Scholar
  93. V. Springel, L. Hernquist, Mon. Not. R. Astron. Soc. 333, 649 (2002) CrossRefADSGoogle Scholar
  94. V. Springel, L. Hernquist, Mon. Not. R. Astron. Soc. 339, 289 (2003) CrossRefADSGoogle Scholar
  95. V. Springel, M. White, L. Hernquist, Astrophys. J. 549, 681 (2001a) CrossRefADSGoogle Scholar
  96. V. Springel, N. Yoshida, S.D.M. White, New Astron. 6, 79 (2001b) CrossRefADSGoogle Scholar
  97. M. Steinmetz, Mon. Not. R. Astron. Soc. 278, 1005 (1996a) ADSGoogle Scholar
  98. M. Steinmetz, in IAU Symp. 171: New Light on Galaxy Evolution (1996b), p. 259 Google Scholar
  99. F. Stoehr, S.D.M. White, V. Springel, G. Tormen, N. Yoshida, Mon. Not. R. Astron. Soc. 345, 1313 (2003) CrossRefADSGoogle Scholar
  100. J.M. Stone, M.L. Norman, Astrophys. J. Suppl. Ser. 80, 753 (1992) CrossRefADSGoogle Scholar
  101. R.S. Sutherland, M.A. Dopita, Astrophys. J. Suppl. Ser. 88, 253 (1993) CrossRefADSGoogle Scholar
  102. G. Tormen, F.R. Bouchet, S.D.M. White, Mon. Not. R. Astron. Soc. 286, 865 (1997) ADSGoogle Scholar
  103. S.D.M. White, in Cosmology and Large Scale Structure, ed. by R. Schaeffer, J. Silk, M. Spiro, J. Zinn-Justin (1996) p. 349 Google Scholar
  104. G. Xu, Astrophys. J. Suppl. Ser. 98, 355 (1995) CrossRefADSGoogle Scholar
  105. Y.B. Zel’dovich, Astron. Astrophys. 5, 84 (1970) ADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • K. Dolag
    • 1
    Email author
  • S. Borgani
    • 2
  • S. Schindler
    • 3
  • A. Diaferio
    • 4
    • 5
  • A. M. Bykov
    • 6
  1. 1.Max-Planck-Institut für AstrophysikGarchingGermany
  2. 2.Department of AstronomyUniversity of TriesteTriesteItaly
  3. 3.Institut für Astro- und TeilchenphysikUniversität InnsbruckInnsbruckAustria
  4. 4.Dipartimento di Fisica Generale “Amedeo Avogadro”Università degli Studi di TorinoTurinItaly
  5. 5.Istituto Nazionale di Fisica Nucleare (INFN), Sezione di TorinoTurinItaly
  6. 6.A.F. Ioffe Institute of Physics and TechnologySt. PetersburgRussia

Personalised recommendations