Numerical Simulation of Microflows by a DOM With Streaming and Collision Processes

Inspired from the idea of developing lattice Boltzmann method (LBM), a discrete ordinate method (DOM) with streaming and collision processes is presented for simulation of microflows in this work. The current method is quite different from the conventional discrete ordinate method (DOM), unified gas kinetic scheme (UGKS) and discrete unified gas kinetic scheme (DUGKS), in which the finite volume method (FVM) or the finite difference method (FDM) is usually utilized to discretize the discrete velocity Boltzmann equation (DVBE). Due to the application of FVM or FDM, the evaluation of the flux of distribution function at the cell interface becomes an essential step for these approaches. Besides that, for the UGKS and DUGKS, not only the flux of distribution functions but also the conservative variables at the cell interface are needed to be computed. These processes require a lot of computational efforts. In contrast, for the developed method, it only needs interpolations within the cell to perform the streaming process. Thus, the computational efficiency can be improved accordingly. To compare the accuracy and efficiency of present scheme with those of DSMC and/or UGKS, several numerical examples including the Couette flow, pressure driven Poiseuille flow and thermal transpiration flow are simulated. Numerical results showed that the solution accuracy of current scheme is comparable to that of DSMC and UGKS. However, as far as the computational efficiency is concerned, the present scheme is more efficient than UGKS.