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

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dissipationless simulations 11 Cosmological simulations: dissipationless case • For many problems it is warranted to ignore the baryonic effects and solve only evolution of dissipationless component (dark matter, stars). • In this case, only equations of particle motion and the Poisson equation are solved. • Very generally, each evolution time step of a dissipationless simulation consists of the following two main parts: — gravity solver: solve the Poisson equation and calculate particle accelerations. — time integrator: update particle positions and velocities. • different <strong>code</strong>s differ in how these two parts are implemented. • Today we will consider the Particle-Mesh (PM) technique for solving the Poisson equation and integrating particle trajectories.
dissipationless simulations 12 Particle-Mesh (PM) technique: a brief history • PM was invented in the 1950’s at LANL for simulations of compressible fluid flows • However, the first wide-spread application was for collisionless plasma simulations (for which PM was reinvented in the 1960’s and popularized by Hockney and collaborators) • In the late 70’s PM was first applied for 3D cosmological simulations. The method and its descendants (such as P 3 M, AP 3 M, and ART) have been used in most cosmological simulations ever since 3 . 3 In the 1990’s Tree <strong>code</strong>s have also enjoyed increasing popularity
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: equations summary 10 • Baryonic g
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 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

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