  We present local simulations that verify the linear streaming instability
that arises from aerodynamic coupling between solids and gas in protoplanetary
disks. This robust instability creates enhancements in the particle density in
order to tap the free energy of the relative drift between solids and gas,
generated by the radial pressure gradient of the disk. We confirm the analytic
growth rates found by Youdin & Goodman (2005) using grid hydrodynamics to
simulate the gas and, alternatively, particle and grid representations of the
solids. Since the analytic derivation approximates particles as a fluid, this
work corroborates the streaming instability when solids are treated as
particles. The idealized physical conditions -- axisymmetry, uniform particle
size, and the neglect of vertical stratification and collisions -- provide a
rigorous, well-defined test of any numerical algorithm for coupled particle-gas
dynamics in protoplanetary disks. We describe a numerical particle-mesh
implementation of the drag force, which is crucial for resolving the coupled
oscillations. Finally we comment on the balance of energy and angular momentum
in two-component disks with frictional coupling. A companion paper details the
non-linear evolution of the streaming instability into saturated turbulence
with dense particle clumps.
