Abstract
Several numerical schemes are proposed for the solution of Nonequilibrium Langevin Dynamics (NELD), and the strong rate of convergence for each scheme is analyzed. The schemes considered here employ specialised periodic boundary conditions that deform with the flow, namely Lees-Edwards and Kraynik-Reinelt boundary conditions and their generalisations. We show that care must be taken when implementing standard stochastic integration schemes with these boundary conditions in order to avoid a breakdown in the strong order of convergence.