Unified gas-kinetic scheme for microchannel and nanochannel flows

A Unified Gas-Kinetic Scheme (UGKS) is devised for micro and nano channel flow simulations. The principle underlying the scheme is a partial-differential-equation-based modeling in which the gas evolution is modeled with the help of kinetic equation, instead of solving the partial differential equation directly. Elastic collision and inelastic collision have both been taken into consideration in the presented scheme where the inelastic collision is modeled by a Landau-Teller-Jeans-type relaxation term. In this study, two dimensional channel flows are selected as our test cases. First, a thermal conduction case with a wide range of Knudsen number is carried out using the present scheme with different kinetic model equations in order to show the validity of the present scheme and to compare the accuracies of different model equations. Then, a series of pressure driven micro and nano channel flows whose working medium are nitrogen gas are used to validate the proposed scheme. In these cases, the results in both the stream direction and the radial direction agree well with the results predicted by the direct simulation Monte Carlo method, and UGKS results are smoother and without statistical fluctuation. When the density of working gas is high, the non-ideal effect should be taken into consideration. So, at the end of this paper, the presented scheme is also modified using the Enskog theory for non-ideal gas. Based on the gas evolution modeling process which automatically covers the whole scale mechanisms, the cell size and time step of UGKS are not limited by the molecular free path and collision time. Due to the advantages of cell size, time step, and accuracy (no statistical fluctuation), the UGKS is expected to be a practical method for the simulation of micro and nano channel flows.