  The shock interaction and evolution of nova ejecta with a wind from a red
giant star in a symbiotic binary system are investigated via three-dimensional
hydrodynamics simulations. We specifically model the March 2010 outburst of the
symbiotic recurrent nova V407~Cygni from the quiescent phase to its eruption
phase. The circumstellar density enhancement due to wind-white dwarf
interaction is studied in detail. It is found that the density-enhancement
efficiency depends on the ratio of the orbital speed to the red giant wind
speed. Unlike another recurrent nova, RS~Ophiuchi, we do not observe a strong
disk-like density enhancement, but instead observe an aspherical density
distribution with $\sim 20\%$ higher density in the equatorial plane than at
the poles. To model the 2010 outburst, we consider several physical parameters,
including the red giant mass loss rate, nova eruption energy, and ejecta mass.
A detailed study of the shock interaction and evolution reveals that the
interaction of shocks with the red giant wind generates strong Rayleigh-Taylor
instabilities. In addition, the presence of the companion and circumstellar
density enhancement greatly alter the shock evolution during the nova phase.
The ejecta speed after sweeping out most of the circumstellar medium decreases
to $\sim 100-300$ km-s$^{-1}$, depending on model, which is consistent with the
observed extended redward emission in [N~II] lines in April 2011.
