  We analyze the hydrodynamic stability of force-driven parallel shear flows in
nonequilibrium molecular simulations with three-dimensional periodic boundary
conditions. We show that flows simulated in this way can be linearly unstable,
and we derive an expression for the critical Reynolds number as a function of
the geometric aspect ratio of the simulation domain. Approximate periodic
extensions of Couette and Poiseuille flows are unstable at Reynolds numbers two
orders of magnitude smaller than their aperiodic equivalents because the
periodic boundaries impose fundamentally different constraints on the flow.
This instability has important implications for simulating shear rheology and
for designing nonequilibrium simulation methods that are compatible with
periodic boundary conditions.
