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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Abel, P. Anninos, Y. Zhang, M.L. Norman, New Astron. 2, 181 (1997)
O. Agertz, B. Moore, J. Stadel et al., Mon. Not. R. Astron. Soc. 380, 963 (2007)
E. Athanassoula, A. Bosma, J.-C. Lambert, J. Makino, Mon. Not. R. Astron. Soc. 293, 369 (1998)
J.S. Bagla, J. Astrophys. Astron. 23, 185 (2002)
J.S. Bagla, S. Ray, New Astron. 8, 665 (2003)
D.S. Balsara, J. Comput. Phys. 121, 357 (1995)
J.M. Bardeen, J.R. Bond, N. Kaiser, A.S. Szalay, Astrophys. J. 304, 15 (1986)
J. Barnes, P. Hut, Nature 324, 446 (1986)
E. Bertschinger, COSMICS: Cosmological initial conditions and microwave anisotropy codes. astro-ph/9506070 (1995)
P. Bode, J.P. Ostriker, G. Xu, Astrophys. J. Suppl. Ser. 128, 561 (2000)
A. Bonaldi, G. Tormen, K. Dolag, L. Moscardini, Mon. Not. R. Astron. Soc. 378, 1248 (2007)
S. Borgani, K. Dolag, G. Murante et al., Mon. Not. R. Astron. Soc. 367, 1641 (2006)
S. Borgani, D. Fabjan, L. Tornatore et al., Space Sci. Rev. (2008). doi:10.1007/s11214-008-9322-7
G.L. Bryan, M.L. Norman, J.M. Stone, R. Cen, J.P. Ostriker, Comput. Phys. Commun. 89, 149 (1995)
R. Cen, Astrophys. J. Suppl. Ser. 78, 341 (1992)
S.C. Chapra, R.P. Canale, Numerical Methods for Engineers: With Programming and Software Applications (McGraw–Hill, New York, 1997)
P. Colella, H.M. Glaz, J. Comput. Phys. 59, 264 (1985)
P. Colella, P.R. Woodward, J. Comput. Phys. 54, 174 (1984)
H.M.P. Couchman, Astrophys. J. 368, L23 (1991)
H.M.P. Couchman, P.A. Thomas, F.R. Pearce, Astrophys. J. 452, 797 (1995)
R. Courant, K.O. Friedrichs, Supersonic Flow and Shock Waves (Interscience, New York, 1948)
W. Dehnen, Astrophys. J. 536, L39 (2000)
K. Dolag, M. Jubelgas, V. Springel, S. Borgani, E. Rasia, Astrophys. J. Lett. 606, L97 (2004)
K. Dolag, F. Vazza, G. Brunetti, G. Tormen, Mon. Not. R. Astron. Soc. 364, 753 (2005)
K. Dolag, A.M. Bykov, A. Diaferio, Space Sci. Rev. (2008). doi:10.1007/s11214-008-9319-2
G. Efstathiou, M. Davis, S.D.M. White, C.S. Frenk, Astrophys. J. Suppl. Ser. 57, 241 (1985)
B. Einfeldt, SIAM J. Numer. Anal. 25, 294 (1988)
B. Einfeldt, P.L. Roe, C.D. Munz, B. Sjogreen, J. Comput. Phys. 92, 273 (1991)
S. Ettori, K. Dolag, S. Borgani, G. Murante, Mon. Not. R. Astron. Soc. 365, 1021 (2006)
A.E. Evrard, Mon. Not. R. Astron. Soc. 235, 911 (1988)
A.E. Evrard, T.J. MacFarland, H.M.P. Couchman et al., Astrophys. J. 573, 7 (2002)
L.-L. Feng, C.-W. Shu, M. Zhang, Astrophys. J. 612, 1 (2004)
C.S. Frenk, S.D.M. White, P. Bode et al., Astrophys. J. 525, 554 (1999)
B. Fryxell, K. Olson, P. Ricker et al., Astrophys. J. Suppl. Ser. 131, 273 (2000)
T. Fukushige, T. Ito, J. Makino et al., Publ. Astron. Soc. Jpn. 43, 841 (1991)
D. Galli, F. Palla, Astron. Astrophys. 335, 403 (1998)
A. Gardini, E. Rasia, P. Mazzotta et al., Mon. Not. R. Astron. Soc. 351, 505 (2004)
R.A. Gingold, J.J. Monaghan, Mon. Not. R. Astron. Soc. 181, 375 (1977)
F. Haardt, P. Madau, Astrophys. J. 461, 20 (1996)
A. Harten, J. Comput. Phys. 49, 357 (1983)
A. Harten, P.D. Lax, B. van Leer, SIAM Rev. 25, 35 (1983)
A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, J. Comput. Phys. 71, 231 (1987)
K. Heitmann, Z. Lukic, P. Fasel et al., astro-ph/0706.1270 (2007). Report LA-UR-07-1953
L. Hernquist, Astrophys. J. 404, 717 (1993)
L. Hernquist, N. Katz, Astrophys. J. Suppl. Ser. 70, 419 (1989)
R.W. Hockney, J.W. Eastwood, Computer Simulation Using Particles (Hilger, Bristol, 1988)
P. Hut, J. Makino, S. McMillan, Astrophys. J. 443, L93 (1995)
I.T. Iliev, B. Ciardi, M.A. Alvarez et al., Mon. Not. R. Astron. Soc. 371, 1057 (2006)
T. Ito, J. Makino, T. Fukushige et al., Publ. Astron. Soc. Jpn. 45, 339 (1993)
G.-S. Jiang, C.-W. Shu, J. Comput. Phys. 126, 202 (1996)
M. Jubelgas, V. Springel, K. Dolag, Mon. Not. R. Astron. Soc. 351, 423 (2004)
J.S. Kaastra, F.B.S. Paerels, F. Durret, S. Schindler, P. Richter, Space Sci. Rev. (2008). doi:10.1007/s11214-008-9310
H. Kang, J.P. Ostriker, R. Cen et al., Astrophys. J. 430, 83 (1994)
W. Kapferer, T. Kronberger, J. Weratschnig, S. Schindler, Astron. Astrophys. 472, 757 (2007)
N. Katz, D.H. Weinberg, L. Hernquist, Astrophys. J. Suppl. Ser. 105, 19 (1996)
A. Kawai, T. Fukushige, J. Makino, M. Taiji, Publ. Astron. Soc. Jpn. 52, 659 (2000)
A. Kravtsov, in APS Meeting Abstracts (2002). http://flux.aps.org/meetings/YR02/APR02/baps/abs/S820004.html
A.V. Kravtsov, A.A. Klypin, A.M. Khokhlov, Astrophys. J. Suppl. Ser. 111, 73 (1997)
A.V. Kravtsov, D. Nagai, A.A. Vikhlinin, Astrophys. J. 625, 588 (2005)
R. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics (Cambridge University Press, Cambridge, 2002)
D. Levy, G. Puppo, G. Russo, Berkeley CPAM 762 (1999). arXiv:math/9911089
S. Li, J. Comput. Phys. 203, 344 (2005)
S. Li, H. Li, R. Cen, Astrophys. J. Suppl. Ser. 174, 1–12 (2008). astro-ph/0611863
L.B. Lucy, Astron. J. 82, 1013 (1977)
U. Maio, K. Dolag, B. Ciardi, L. Tornatore, Mon. Not. R. Astron. Soc. 379, 963 (2007)
J. Makino, Publ. Astron. Soc. Jpn. 43, 621 (1991)
B.F. Mathiesen, A.E. Evrard, Astrophys. J. 546, 100 (2001)
P. Mazzotta, E. Rasia, L. Moscardini, G. Tormen, Mon. Not. R. Astron. Soc. 354, 10 (2004)
M. Meneghetti, P. Melchior, A. Grazian et al., Astron. Astrophys. (2008, in press). astro-ph/0711.3418
J.J. Monaghan, Annu. Rev. Astron. Astrophys. 30, 543 (1992)
J.J. Monaghan, J. Comput. Phys. 136, 298 (1997)
J.J. Monaghan, R.A. Gingold, J. Comput. Phys. 52, 374 (1983)
J.P. Morris, J.J. Monaghan, J. Comput. Phys. 136, 41 (1997)
J.F. Navarro, S.D.M. White, Mon. Not. R. Astron. Soc. 265, 271 (1993)
B.W. O’Shea, K. Nagamine, V. Springel, L. Hernquist, M.L. Norman, Astrophys. J. Suppl. Ser. 160, 1 (2005)
J.M. Owen, J.V. Villumsen, P.R. Shapiro, H. Martel, Astrophys. J. Suppl. Ser. 116, 155 (1998)
P.J.E. Peebles, The Large-Scale Structure of the Universe (Princeton University Press, Princeton, 1980)
U.-L. Pen, Astrophys. J. Suppl. Ser. 115, 19 (1998)
K.G. Powell, P.L. Roe, T.J. Linde, T.I. Gombosi, D.L. de Zeeuw, J. Comput. Phys. 154, 284 (1999)
C. Power, J.F. Navarro, A. Jenkins et al., Mon. Not. R. Astron. Soc. 338, 14 (2003)
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)
T. Quinn, N. Katz, J. Stadel, G. Lake, Astrophys. J. (1997). Submitted but not published, astro-ph/9710043
E. Rasia, P. Mazzotta, S. Borgani et al., Astrophys. J. 618, L1 (2005)
E. Rasia, S. Ettori, L. Moscardini et al., Mon. Not. R. Astron. Soc. 369, 2013 (2006)
E. Rasia, P. Mazzotta, H. Bourdin et al., Astrophys. J. (2007, in press). astro-ph/0707.2614
P.M. Ricker, S. Dodelson, D.Q. Lamb, Astrophys. J. 536, 122 (2000)
D. Ryu, J.P. Ostriker, H. Kang, R. Cen, Astrophys. J. 414, 1 (1993)
H.-Y. Schive, C.-H. Chien, S.-K. Wong, Y.-C. Tsai, T. Chiueh, New Astron. (2007, in press). astro-ph/0707.2991
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
D. Sijacki, V. Springel, T. di Matteo, L. Hernquist, Mon. Not. R. Astron. Soc. 380, 877 (2007)
B.W. Silverman, Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability (Chapman & Hall, London, 1986)
V. Springel, Mon. Not. R. Astron. Soc. 364, 1105 (2005)
V. Springel, L. Hernquist, Mon. Not. R. Astron. Soc. 333, 649 (2002)
V. Springel, L. Hernquist, Mon. Not. R. Astron. Soc. 339, 289 (2003)
V. Springel, M. White, L. Hernquist, Astrophys. J. 549, 681 (2001a)
V. Springel, N. Yoshida, S.D.M. White, New Astron. 6, 79 (2001b)
M. Steinmetz, Mon. Not. R. Astron. Soc. 278, 1005 (1996a)
M. Steinmetz, in IAU Symp. 171: New Light on Galaxy Evolution (1996b), p. 259
F. Stoehr, S.D.M. White, V. Springel, G. Tormen, N. Yoshida, Mon. Not. R. Astron. Soc. 345, 1313 (2003)
J.M. Stone, M.L. Norman, Astrophys. J. Suppl. Ser. 80, 753 (1992)
R.S. Sutherland, M.A. Dopita, Astrophys. J. Suppl. Ser. 88, 253 (1993)
G. Tormen, F.R. Bouchet, S.D.M. White, Mon. Not. R. Astron. Soc. 286, 865 (1997)
S.D.M. White, in Cosmology and Large Scale Structure, ed. by R. Schaeffer, J. Silk, M. Spiro, J. Zinn-Justin (1996) p. 349
G. Xu, Astrophys. J. Suppl. Ser. 98, 355 (1995)
Y.B. Zel’dovich, Astron. Astrophys. 5, 84 (1970)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Dolag, K., Borgani, S., Schindler, S. et al. Simulation Techniques for Cosmological Simulations. Space Sci Rev 134, 229–268 (2008). https://doi.org/10.1007/s11214-008-9316-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11214-008-9316-5