  In this work we present cosmological N-body simulations of the Local Universe
with initial conditions constrained by the Two-Micron Redshift Survey (2MRS)
within a cubic volume of 180 Mpc/h side-length centred at the Local Group. We
use a self-consistent Bayesian based approach to explore the joint parameter
space of primordial density fluctuations and peculiar velocity fields, which
are compatible with the 2MRS galaxy distribution after cosmic evolution. This
method (the KIGEN-code) includes the novel ALPT (Augmented Lagrangian
Perturbation Theory) structure formation model which combines second order LPT
(2LPT) on large scales with the spherical collapse model on small scales.
Furthermore we describe coherent flows with 2LPT and include a dispersion term
to model fingers-of-god (fogs). These implementations are crucial to avoid
artificial filamentary structures, which appear when using a structure
formation model with 2LPT and data with compressed fogs. We assume LCDM
cosmology throughout our method. The recovered initial Gaussian fields are used
to perform a set of 25 constrained simulations. Statistically this ensemble of
simulations is in agreement with a reference set of 25 simulations based on
randomly seeded Gaussian fluctuations in terms of matter statistics,
power-spectra and mass functions. Considering the entire volume, we obtain
correlation coefficients of about 98.3% for the comparison between the
simulated density fields and the galaxy density field in log-space with
Gaussian smoothing scales of r_S=3.5 Mpc/h (74% for r_S=1.4 Mpc/h). The cross
power-spectra show correlations with the galaxy distribution which weaken
towards smaller length scales until they vanish at scales of 2.2-3.0 Mpc/h. The
simulations we present provide a fully nonlinear density and velocity field
with a high level of correlation with the observed galaxy distribution at
scales of a few Mpc.
