Why
simulate structure formation ?
 to understand the
effects of nonlinear processes
 to connect the early
universe to statistical surveys at low redshifts
 to validate upcoming
instruments via mocks
 to advance the field of
High Performane Computing/ computationnal geometry
Purposes
 AB INITIO MODELING
 understand what matters: can we explain what
we (think) we see?
Numerical
simulations
seek to contrain the nature of the dark matter and designs experiments
for its direct detection. Numerical simulations also seek to explore
the
formation of galaxies
including our own Galaxy. The fundamental equations governing the
forces between particles and fields in this lowenergy regime are
fairly well known. They aim to explain cosmic objects we see around us,
like galaxies and compact objects (e.g. supermassives black holes).
Structure formation involves a complicated blend of gravity,
hydrodynamics, nuclear and atomic physics, as well as
magnetohydrodynamics and radiation physics. One challenge is to
separate the important from the unimportant, and to find some answers
to the many questions that astrophysicists face in contemporary
extragalactic astronomy.
For LSS:
 expanding background:
not everything collapses, but when it does
gravity almost always win
 expanding background:
voids repel
 t_{dyn}~1/√ρ
 Gaussian ICs:
anisotropic collapse: formation of cosmic web
 STATISTICS
Concordant model intrinsically statistical: it
can only be disproved
statistically.

make (large) virtual
data sets/ surveys
 validate inverse methods
 build realistic estimators/ model biases
 estimate error bars/covariance matrices
 validate perturbation theory
 "bias theory (light does not trace DM)
 "semianalytic models;properly account for scale coupling/anisotropy
 allow for visualisation of the effect of complex processes
 PROSPECTIVE FOR ASTROPHYSICS
 design new instrument: assume everything holds; how well can we measure things from a given incomplete survey?
LSS as probes of cosmology:
Carrying out highresolution cosmological simulations of different dark
energy cosmologies, including also nonstandard theories of gravity (e.g. MG) and coupled
dark matterdark energy cosmologies, and to comparing them to the standard ŒõCDM model allows us to
explore the viability of these theories
LSS as environment for galaxies :
The basis of (dark matter) nbody simulation. Basic concepts of numerical simulations, continuous and discrete
simulations.Discretization of ordinary differential equations, integration schemes
of different order. Nbody problems.
 dynamics in a expanding universe
 symplectic integrators
 multiscale dynamics
 Multigrid Poisson solver
 Cosmological initial conditions
 Zoom simulations
Accounting for baryons :
 Multiscale hydrodynamics
 Optimal discretization of partial differential equations
 Finite element and finite volume methods
 Subgrid physics: effective laws
 Inverse cascade
 Feedback or not feedback?
 ISM, ray tracing, dust, magnetic fields, cosmic rays,anisotropic
diffusion etc.

SIMULATION AS A BRANCH OF COMPUTATIONAL SCIENCE
Simulation
techniques are used to study cosmic structure formation.In order to
allow use of the full power of modern supercomputers, the community
develops massive parallel simulation algorithms, and new methods for
discretizing the Euler and
NavierStokes equations,for example on a refining/moving mesh,and
subgrid techniques that allow multiphysics.

Lattice methods
 Adaptive mesh refinement and multigrid methods
 Shock preserving algorithms
 Multitimescales
 Matrix solvers and FFT methods
 Monte Carlo methods, Markov chains
 Code validation (!)
