ИСТИНА

This study is devoted to the numerical modeling of two-dimensional micro nozzle gas flow in transition regime with different mathematical models. Regularized 13-moment set of equations (R13) ([1]) and Navier-Stokes equations are used as continuum approaches. The kinetic equation results are used for further analysis of continuum approach data. The variant of explicit high resolution Godunov scheme with linear flow parameter reconstruction is chosen for numerical solution of the R13 and Navier-Stokes sets of equations ([2,3]). Five so-called kinetic boundary conditions are taken as a base of mathematical model of isothermal solid wall ([4]). The complete set of the wall boundary conditions is obtained by an approximation of the selected sub-set of the R13 bulk equations. The resulted set of nonlinear equations for the wall is solved with Newton’s numerical method ([2]). Some well-known test cases and some complex shape micro device gas flows have been already used as examples of application of approaches for various gas flow regimes (from continuous to moderately rarefied). The applicability of the R13 set of equations for mathematical modeling of transition gas flow regime in micro scale devices was confirmed due to comparison with kinetic model and other numerical results. There is a good coincidence of the results of both approaches when the Knudsen number is smaller than 0.5 (Kn<0.5). We will publish the first moment equations application to nozzle flows here. REFERNCES 1. Struchtrup H. and Torrilhon M. “Regularization of Grad’s 13-moment-equations: Derivation and linear analysis”, Phys. Fluids, 2003, 15, pp. 2668–2680. 2. Ivanov I.E., Kryukov I.A., and Timokhin M.Yu. “Application of Moment Equations to the Mathematical Simulation of Gas Microflows”, Comp. Math. and Math. Phys., 2013, 53, 10, pp. 1534–1550. 3. Kudryavtsev A.N., Shershnev A.A. “A numerical method for simulation of microflows by solving directly kinetic equations with WENO schemes”, J. of Scientific Computing, 2013, 57, 1, pp 42–73. 4. Struchtrup H. and Torrilhon M. “Boundary conditions for regularized 13-moment-equations for micro-channel-flows”, J. Comput. Phys., 2008, 227, pp. 1982–2011.