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.
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