Moment equations and gas-kinetic scheme application to numerical simulation of gas flows in micro scale devices

Abstract

This study is devoted to the comparison of continuous and kinetic approaches for two-dimensional numerical simulation of the gas flow transition regime. Regularized 13-moment Grad’s set of equations (R13) is used as continuum mathematical model and Unified Gas-Kinetic Scheme (UGKS) is used as kinetic method. The variant of explicit high resolution Godunov scheme with linear flow parameter reconstruction is chosen for numerical solution of the R13 set of equations. Five so-called kinetic boundary conditions are taken as a base of mathematical model of isothermal solid wall. The complete set of the wall boundary conditions is obtained by an approximation of the selected subset of the R13 bulk equations. The resulted set of nonlinear equations for the wall is solved with Newton’s numerical method. Our implementation of the UGKS follows in the basic details, and allows calculating continuous and rarefied flows in geometrically complex regions. Except well-known test cases, some complex shape micro device gas flows are used as examples of application of both approaches for various gas flow regimes (from continuous to moderately rarefied).