The Lees-Edwards boundary conditions are described in chapter 8.2 of "Computer Simulation of Liquids" by M. P. Allen and D. J. Tildesley, Oxford Science Publications, as well as "Multiparticle collision dynamics simulations of viscoelastic fluids: Shear-thinning Gaussian dumbbells" by Bartosz Kowalik and Roland G. Winkler, The Journal of Chemical Physics 138, 104903 (2013), DOI:10.1063/1.4792196.

In this software, it is assumed that the primary simulation volume is replicated along all three of the x, y, and z axes of the Cartesian coordinate system. Images (including the primary simulation volume) that are adjacent to one another along the y direction are moving such that the image at larger y coordinate values has a relative velocity along the x direction of \( \Delta v_x = \dot{\gamma} L_y \) with respect to the other image at lower y, where \( \dot{\gamma} \) is the shear rate, and \( L_y \) is the size of the primary simulation volume along the y axis.