AREPO: a moving-mesh code for cosmological hydrodynamical simulations

Transcription

1 AREPO: a moving-mesh code for cosmological hydrodynamical simulations E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh Springel, 2010 arxiv: Rubens Machado Seminário de Extragaláctica - IAG 27/10/2011

2 and some of its recent results Moving mesh cosmology: numerical techniques and global statistics (Vogelsberger et al, 2011) arxiv: Moving mesh cosmology: the hydrodynamics of galaxy formation (Sijacki et al, 2011) arxiv: Moving mesh cosmology: characteristics of galaxies and haloes (Keres et al, 2011) arxiv:

3 collisionless simulations (only dark matter) N-body problem is well understood there is little doubt about what is required to achieve high accuracy hydrodynamical simulations variety of fundamentally different numerical methods in use most prominent: - Lagrangian (particles) - Eulerian (mesh) both have problems that make them innacurate in certain regimes

4 slide from Springel, 2006

5 slide from Springel, 2006

6 mesh SPH self-gravity needs to be done on a mesh SPH smooths out sharp shocks and contact discontinuities

7 discrete distribution of particles

8 discrete distribution of particles What is the density at any given location? +

9 Smoothed Particle Hydrodynamics (SPH) + kernel interpolation to build continuous fluid quantities from discrete tracer particles

10 Smoothed Particle Hydrodynamics (SPH) + kernel interpolation to build continuous fluid quantities from discrete tracer particles

11 Adaptive Mesh Refinement (AMR)

12 Adaptive Mesh Refinement (AMR) RAMSES, Teyssier 2010 large dynamical range of cosmological simulations: dense regions require high resolution; low resolution for empty regions

13 AREPO: based on a moving unstructured mesh mesh defined by Voronoi tesselation of a set of discrete points grid-generating points move with the flow inherits main advantages - from SPH: resolution follows density automatically and continuously - from Eulerian codes: finite volume discretization gives accurate treatment of instabilities avoids main problems - from SPH: noise and diffusiveness - from Eulerian: lack of Galilean-invariance

14 Tesselation the careful juxtaposition of shapes in a mosaic pattern no overlaps, no gaps

15 Tesselation the careful juxtaposition of shapes in a mosaic pattern no overlaps, no gaps

16 Delaunay Tesselation triangulation of the plane grid-generating points: vertices of triangles maximizes smallest angle within each circumference: no other points

17 Delaunay Tesselation connecting the centers: centers of circumferences Voronoi Tesselation The centers of the circumcircles around each Delaunay triangle define the vertices of the Voronoi cells.

18 Voronoi Tesselation Voronoi mesh-generating points Delaunay both

19 at each timestep: - calculate a new Voronoi tesselation, based on current coordinates of mesh-generating points - calculate (density, velocity, pressure) in each cell - assign velocities to the mesh-generating points - compute flux across each Voronoi cell - update quantities for this timestep - move mesh-generating points

20 Mesh regularization for computational efficiency, regions of similar gas properties should be represented by cells of comparable size desirable to have cells where center-of-mass is close to its mesh-generating point

21 Mesh regularization Adaptive mesh refinement no longer necessary: The resolution automatically stays where it is needed

22 Self-gravity in cosmological simulations, dark matter structures grow from very small seed perturbations in AMR codes, grid refinement may be placed too late

23 Some test problems: Kevin-Helmholtz instability

24 Some test problems: Kevin-Helmholtz instability AREPO moving AREPO fixed ATHENA (in the non-linear regime, KH instability seems to develop faster with AREPO moving mesh)

25 Some test problems: Kevin-Helmholtz instability AREPO fixed = ATHENA Frame of reference velocity: v =1 AREPO fixed = ATHENA AREPO fixed = ATHENA V = 10 with AREPO moving, result is independent of frame-of-reference v = 100

26 Some test problems: isolated disk galaxy

27 Some test problems: galaxy collision initial conditions

28 Some test problems: galaxy collision AMR not well suited for this problem (high resolution regions moving; no Galilean invariance)

29 Some test problems: galaxy collision stars gas AREPO GADGET2

30 Paralelization of the tesselation: Point set is decomposed into disjoint spacial domains, each mapped to a different compute core with its own physical memory... Speed: 2x slower than SPH at same resolution 3-4x slower than Eulerian fixed mesh (polyhedra with more than 6 faces) once self-gravity is included: performance difference less important AREPO reaches good accuracy in test problems at lower resolution than SPH and fixed mesh

31 - first hydrodynamical simulations of galaxy formation using AREPO - comparison with GADGET (same gravity solver, same star formation treatment) - overall distribution of gas temperature and density broadly in agreement - SFR at high z in good agreement global baryon statistics with AREPO: - lower mean temperatures - reduced amount of hot gas - more gas cooling at low z - higher star formation rates in late times

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33 Gas density

34 Code performance AREPO GADGET

35 - variety of numerical experiments to establish link between simple problems with analytic solutions and systematic effects in cosmological simulations of galaxy formation - With AREPO, gas from infalling substructures is readily depleted and incorporated into the host halo atmosphere, facilitating the formation of an extended central disk. - With GADGET, gaseous subclumps are more coherent, transforming the central disk as they impact it.

36 gas density 1014 Mo isolated halo + 10 orbiting subhalos

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38 AREPO: Moving Mesh Cosmology:

39 "Sator Arepo Tenet Opera Rotas"