  Using 3D radiation-hydrodynamic simulations and analytic theory, we study the
orbital evolution of asymptotic-giant-branch (AGB) binary systems for various
initial orbital separations and mass ratios, and thus different initial
accretion modes. The time evolution of binary separations and orbital periods
are calculated directly from the averaged mass loss rate, accretion rate and
angular momentum loss rate. We separately consider spin-orbit synchronized and
zero spin AGB cases. We find that the the angular momentum carried away by the
mass loss together with the mass transfer can effectively shrink the orbit when
accretion occurs via wind-Roche-lobe overflow. In contrast, the larger fraction
of mass lost in Bondi-Hoyle-Lyttleton accreting systems acts to enlarge the
orbit. Synchronized binaries tend to experience stronger orbital period decay
in close binaries. We also find that orbital period decay is faster when we
account for the nonlinear evolution of the accretion mode as the binary starts
to tighten. This can increase the fraction of binaries that result in common
envelope, luminous red novae, Type Ia supernovae and planetary nebulae with
tight central binaries. The results also imply that planets in the the
habitable zone around white dwarfs are unlikely to be found.
