  We describe the construction of an N-body simulation that mimics the true
velocity and mass-density fields in a box of side 256\hmpc about the Local
Group , and the production of mock catalogs that mimic in detail current
catalogs of redshifts and peculiar velocities. Our main purpose is to provide a
tool for developing and testing reconstruction methods, but the different
components of the method can be used on their own in other applications. The
initial conditions are based on the IRAS 1.2Jy redshift survey, assuming that
galaxies trace mass and \Omega=1. A density field smoothed is recovered from
the redshift survey, using quasi-linear theory and a power-preserving filter.
The corresponding potential field is traced back to the linear regime using the
Zel'dovich-Bernoulli equation. Small-scale power is added by means of
constrained realization to mimic fluctuations on galactic scales. The
gravitating system is evolved forward in time with a PM code of 2\hmpc
resolution. The result reproduces the real dynamical structures on large scales
and the statistical properties of the structure down to galactic scales.
"Galaxies" are identified via a linear biasing scheme (b=1.35) and they are
divided into "spirals" and "ellipticals" to obey Dressler's morphology-density
relation. The galaxies are assigned internal-velocity parameters and absolute
magnitudes scattered about an assumed mean Tully-Fisher relation. They are then
"observed" as magnitude-limited samples, trying to mimic the selection criteria
of the data sets constituting the Mark III catalog of peculiar velocities.
Artificial IRAS 1.2Jy redshift surveys are also compiled. The simulations and
mock catalogs will be made available electronically as bench marks for testing
reconstruction methods.
