ИСТИНА

Now technologies related to the development of micro-electro-mechanical systems (MEMS) for a wide range of applications are actively developing. The collision frequency of molecules decreases with the decreasing of linear scale of the flow. So the nonequilibrium of the flow increases. For sufficiently rarefied flow, where Knudsen number (the ratio of the mean free path of molecules to the characteristic linear scale of the problem) increases to 10-1, the classical Navier-Stokes equations turn out to be inapplicable for a correct description of the gas flow. A natural alternative here is the kinetic approach based on the solution of Boltzmann equation or kinetic model equations (Bhatnagar-Gross-Krook equation, the Shakhov equation, etc.), as well as direct simulation Monte Carlo method (DSMC). The main difficulty of their application for moderately rarefied gas is the high demand for computational resources. Another way is extended gas dynamics. It is Barnett equations and their modifications obtained from the Boltzmann kinetic equation with Chapman-Enskog method, as well as Grad's moment equations. The mesoscale approach is a new trend in the numerical modeling of gas flows. This approach allows taking into account the processes occurring in the medium at the macro-scale level and at the macro-scale one. Lattice Boltzmann method (LBM) and gas-kinetic schemes present this way. LBM was proposed at the end of the twentieth century as an alternative of Navier-Stokes equations numerical solution for the modeling of subsonic fluid and gas flows. At the moment, this method has become widely used for engineering applications. The main advantage of this alternative to the Navier-Stokes equations is a significantly higher calculation speed, which is extremely important for engineering applications. Recently, a number of papers have appeared on the development of this approach for essentially non-equilibrium flows. This study is devoted to the development and implementation of non-isothermal LBM for nonequilibrium flows and for the problems of rarefied gas dynamics in particular. The numerical results of this LBM implementation for Knudsen pump and other micro-pump flows will be presented. LBM numerical results have been analyzed by the comparison with the results of other approaches (moment method and UGKS).