A novel modified lattice Boltzmann method for simulation of gas flows in wide range of Knudsen number

To cover a wide range of the flow regimes, a new relaxation time formulation by considering the rarefaction effect and the effective dynamic viscosity has been obtained. By using the modified lattice Boltzmann method (LBM), pressure driven flow through micro and nano channels has been modeled for wide range of Knudsen number, Kn, covering the slip, transition and to some extent the free molecular regimes. The results agree very well with existing empirical and numerical data. The velocity profile was predicted as well as the volumetric flow rate and for the first time, the well known Knudsen minimum effect has been captured about Kn = 1.