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

More documents

Recommendations

Info

PM: main code blocks 25 In the CIC scheme, particle {x p , y p , z p } may contribute to densities in the parent cell (i, j, k) and seven neighboring cells 6 . Let’s define d x = x p − x c ; d y = y p − y c ; d z = z p − z c ; t x = 1 − d x ; t y = 1 − d y ; t z = 1 − d z . Contributions to the eight cells are then linear interpolations in 3D: ρ i,j,k = ρ i,j,k + m p t x t y t z ; ρ i+1,j,k = ρ i+1,j,k + m p d x t y t z ; ρ i,j+1,k = ρ i,j+1,k + m p t x d y t z ; ρ i+1,j+1,k = ρ i+1,j+1,k + m p d x d y t z ; ρ i,j,k+1 = ρ i,j,k+1 + m p t x t y d z ; ρ i+1,j,k+1 = ρ i+1,j,k+1 + m p d x t y d z ; ρ i,j+1,k+1 = ρ i,j+1,k+1 + m p t x d y d z ; ρ i+1,j+1,k+1 = ρ i+1,j+1,k+1 + m p d x d y d z ; , where m p is particle mass. Doing this for all particles will result in the grid of densities ρ i,j,k . 6 Make sure you enforce periodic boundary conditions: i = mod(i, Ng,1 ), etc. for j and k.
PM: main code blocks 26 Solving the Poisson equation With the grid of densities, ρ i,j,k , in hand, the code can proceed to solve the discretized 7 Poisson equation ˜∇ 2 ˜φ ≈ ˜φi−1,j,k + ˜φ i+1,j,k + ˜φ i,j−1,k + ˜φ i,j+1,k + ˜φ i,j,k−1 + ˜φ i,j,k+1 − 6 ˜φ i,j,k = = 3 Ω 0 2 a (˜ρ i,j,k − 1). The discretization thus results in a large system of linear equations relating unknowns, ˜φ i,j,k , to the known right hand side values. This system can be solved using FFT. 7 It is customary in PM codes to discretize the Laplacian operator using the 7-point template.
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: PM: main code blocks 24 Implementin
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 and 44: Setting up cosmological ICs 42 Appl
Page 45 and 46: project summary 44 Project summary
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?