  Our previous linear analysis presents a new instability driven by dust
coagulation in protoplanetary disks. The coagulation instability has the
potential to concentrate dust grains into rings and assist dust coagulation and
planetesimal formation. In this series of papers, we perform numerical
simulations and investigate nonlinear outcome of coagulation instability. In
this paper (Paper I), we first conduct local simulations to demonstrate the
existence of coagulation instability. Linear growth observed in the simulations
is in good agreement with the previous linear analysis. We next conduct
radially global simulations to demonstrate that coagulation instability
develops during the inside-out disk evolution due to dust growth. To isolate
the various effects on dust concentration and growth, we neglect effects of
backreaction to a gas disk and dust fragmentation in Paper I. This simplified
simulation shows that either of backreaction or fragmentation is not
prerequisite for local dust concentration via the instability. In most runs
with weak turbulence, dust concentration via coagulation instability overcomes
dust depletion due to radial drift, leading to the formation of multiple dust
rings. The nonlinear development of coagulation instability also accelerates
dust growth, and the dimensionless stopping time $\tau_{\mathrm{s}}$ reaches
unity even at outer radii (>10 au). Therefore, coagulation instability is one
promising process to retain dust grains and to accelerate dust growth beyond
the drift barrier.
