A New Relaxation Time Model for Lattice Boltzmann Simulation of Nano Couette Flows in Wide Range of Flow Regimes

Abstract

The standard LBM with the relaxation time is only able to simulate the flow features in continuum and slip regimes. In the present paper, a new relaxation time formulation considering the rarefaction effect on the viscosity for the lattice Boltzmann simulation of shear driven flows is presented in order to cover wide range of the flow regimes. The results show that in spite of the standard Lattice Boltzmann Method, LBM, the presented relaxation time equation is able to predict flow features in wide range of flow regimes including slip, transition and to some extend free molecular flow regimes. The velocity profiles, slip length and shear stress agree very well with DSMC (Direct Simulation Monte Carlo) and linear Boltzmann results.

Keywords

• Lattice Boltzmann method; Micro and nano- Couette; Transitional regime; Knudsen number; Relaxation time; Rarefaction.