Monday, 07/24: Writing a pm-code - AIP

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Setting up cosmological ICs 43 You will need • Your favorite FFT solver, if you don’t have one see Numerical Recipes (Ch. 12). • A decent random number generator. Be careful here as you will need to generate fairly long sequences of random numbers (I can supply you with a RNG, if needed). The gaussian random pairs can be generated from the uniformly distributed numbers using the Box-Muller method (Numerical Recipes, Ch. 7). • A routine returning P (k) for a specific cosmological model. See Hu & Sugiyama 1996 and Eisenstein & Hu 1999 for useful analytical approximations to P (k).
project summary 44 Project summary • use the blueprint given in this lecture to code up your own code (C or fortran). Use FFT routine given to you by Anatoly Klypin last week or a routine with more transparent packing (e.g., FFT routine from Ch.12 of “Numerical recipes”) • Test the code by simulating a sine-wave and comparing it to the Zeldovich solution • Set up an initial conditions for 64 3 /128 3 or 128 3 /256 3 particles/grid cells and run PM simulations in different cosmologies using the same random seed (which should give you the same phases and the same structures in these cosmologies): ⋆ Ω 0 = 1 CDM universe with σ 8 = 0.8. Evolution of the growth factor in this model is simple: D + (a) = (a/a 0 ). You can check D + by computing the P (k) or two-point correlation function of DM particles at different epochs and comparing it to the expected evolution in linear regime. ⋆ you can then simulate open CDM (Ω 0 = 0.3) and flat ΛCDM (Ω 0 = 0.3, Ω Λ = 0.7) with the same σ 8 (z = 0) = 0.8 as in the SCDM model above.
Page 1 and 2: Writing a PM code Andrey Kravtsov a
Page 3 and 4: equations I 2 Cosmological simulati
Page 5 and 6: N-body approach 4 Cosmological simu
Page 7 and 8: particle initial conditions 6 Cosmo
Page 9 and 10: equations of gasdynamics 8 Cosmolog
Page 11 and 12: equations summary 10 • Baryonic g
Page 13 and 14: dissipationless simulations 12 Part
Page 15 and 16: Model equations 14 Model equations
Page 17 and 18: Model equations 16 The quantities w
Page 19 and 20: Model equations 18 In dimensionless
Page 21 and 22: PM: main code blocks 20 Density Ass
Page 23 and 24: PM: main code blocks 22 In practice
Page 25 and 26: PM: main code blocks 24 Implementin
Page 27 and 28: PM: main code blocks 26 Solving the
Page 29 and 30: PM: main code blocks 28 ⇒ Given a
Page 31 and 32: PM: main code blocks 30 After n tim
Page 33 and 34: Zeldovich approximation (ZA) 32 Zel
Page 35 and 36: A test problem: 1D collapse of a pl
Page 41 and 42: Setting up cosmological ICs 40 The
Page 43: Setting up cosmological ICs 42 Appl
Page 47 and 48: References and links 46 PM in cosmo
Page 49 and 50: References and links 48 • Michael

Monday, 07/24: Writing a pm-code - AIP

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