Lees–Edwards Boundary Conditions for Lattice Boltzmann

Lees–Edwards boundary conditions (LEbc) for Molecular Dynamics simulations(1) are an extension of the well known periodic boundary conditions and allow the simulation of bulk systems in a simple shear flow. We show how the idea of LEbc can be implemented in isothermal lattice Boltzmann simulations and how LEbc can be used to overcome the problem of a maximum shear rate that is limited to less then 1/Ly (with Ly the transverse system size) in traditional lattice Boltzmann implementations of shear flow. The only previous Lattice Boltzmann implementation of LEbc(2) requires a specific fourth order equilibrium distribution. In this paper we show how LEbc can be implemented with the usual quadratic equilibrium distributions.