Penetration of gold rods into SiC powder targets at velocities of 1 to 3 km/s are investigated using mesoscale simulations. The range of impact velocities is chosen to coincide with previous penetration experiments and represents a new regime over which to test the applicability of mesoscale simulations of granular materials. Both 2D and 3D geometries of the combined penetrator and powder system are considered. Analysis of the penetration depth histories at various impact velocities shows the penetrator undergoes an initial transient period of rapid deceleration within the first several microseconds before converging to a steady state characterized by jumps in the penetration velocity on the order of a few hundred meters per second. Steady-state penetration velocities obtained from 2D and 3D simulations agree well with one another, but lie below those computed using hydrodynamic theory, which indicates a non-zero strength for the simulated powders over this range of impact velocities. For comparable initial powder densities, 3D simulations predict steady-state penetration velocities in good agreement with those measured in penetration experiments on pre-compacted SiC powder specimens.