Why
simulate structure formation ?
- to understand the
effects of non-linear 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 low-energy 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
- tdyn~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)
- "semi-analytic 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 high-resolution cosmological simulations of different dark
energy cosmologies, including also non-standard theories of gravity (e.g. MG) and coupled
dark matter-dark energy cosmologies, and to comparing them to the standard ΛCDM model allows us to
explore the viability of these theories
LSS as environment for galaxies :
The basis of (dark matter) n-body simulation. Basic concepts of numerical simulations, continuous and discrete
simulations.Discretization of ordinary differential equations, integration schemes
of different order. N-body problems.
- dynamics in a expanding universe
- symplectic integrators
- multi-scale dynamics
- Multigrid Poisson solver
- Cosmological initial conditions
- Zoom simulations
Accounting for baryons :
- Multi-scale hydro-dynamics
- 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
Navier-Stokes equations,for example on a refining/moving mesh,and
sub-grid techniques that allow multi-physics.
-
Lattice methods
- Adaptive mesh refinement and multi-grid methods
- Shock preserving algorithms
- Multi-timescales
- Matrix solvers and FFT methods
- Monte Carlo methods, Markov chains
- Code validation (!)
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