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We present local simulations that verify the linear streaming instabilitythat arises from aerodynamic coupling between solids and gas in protoplanetarydisks. This robust instability creates enhancements in the particle density inorder 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 analyticgrowth rates found by Youdin & Goodman (2005) using grid hydrodynamics tosimulate the gas and, alternatively, particle and grid representations of thesolids. Since the analytic derivation approximates particles as a fluid, thiswork corroborates the streaming instability when solids are treated asparticles. The idealized physical conditions -- axisymmetry, uniform particlesize, and the neglect of vertical stratification and collisions -- provide arigorous, well-defined test of any numerical algorithm for coupled particle-gasdynamics in protoplanetary disks. We describe a numerical particle-meshimplementation of the drag force, which is crucial for resolving the coupledoscillations. Finally we comment on the balance of energy and angular momentumin two-component disks with frictional coupling. A companion paper details thenon-linear evolution of the streaming instability into saturated turbulencewith dense particle clumps.Comment: Accepted for publication in ApJ (14 pages

Protoplanetary Disk Turbulence Driven by the Streaming Instability: Linear Evolution and Numerical Methods