# Stability of force-driven shear flows in nonequilibrium molecular simulations with periodic boundaries

## TL;DR

This paper investigates the stability of force-driven shear flows in nonequilibrium molecular simulations with periodic boundaries, revealing that such flows can be linearly unstable at much lower Reynolds numbers than traditional flows, impacting simulation methods.

## Contribution

It derives a critical Reynolds number expression for these flows and highlights how periodic boundaries fundamentally alter flow stability compared to aperiodic conditions.

## Key findings

- Flows in periodic domains are unstable at Reynolds numbers two orders of magnitude lower than in aperiodic flows.
- The derived critical Reynolds number depends on the geometric aspect ratio of the simulation domain.
- Implications for shear rheology simulations and nonequilibrium method design are discussed.

## Abstract

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.