Simulation of Gas Flows in Micro Devices by Solving the Boltzmann Kinetic Equation Yu.A. Anikin a,b , O.I. Dodulad a,b , Yu.Yu. Kloss a,b,* , D.V. Martynov a,b , P.V. Shuvalov a,b , F.G. Tcheremissine a,c a Moscow Institute of Physics and Technology b National Research Centre ”Kurchatov Institute” c Dorodnicyn Computing Centre of RAS * Academician Kurchatov sq. 1, Moscow, Russia, 123182, Fax: 007 (499) 196-9516, kl@lokip.ru ABSTRACT The paper presents results of gas flow simulations in microdevices using the numerical method based on solving the Boltzmann kinetic equation. Slightly disturbed from equlibrium as well as supersonic flows are considered. The modeling was performed by using the problem solving environment developed by the authors of this paper. This problem solving environment is based on a finite-difference method and uses fixed rectangular velocity (momentum) space and spatial unstructured grids. The collision integral is calculated by the conservative projection method. Keywords: modeling of gas flows, micro/nano channels, Knudsen compressor, Boltzmann equation, problem solving environment 1 INTRODUCTION At the present time due to development of micro devices in various application areas, interest in gas flows modeling in micro- and nanochannels has increased significantly. Traditional approach of gas modeling is solving Navier-Stocks equations. However, this approach is relevant only if the mean free path of molecules is small compared to specific size of flows, whereas the rarefied gas effects are not important. Boltzmann Kinetic Equation represents a good approach to gas flows modeling in microdevices. The equation’s type is integro-differential, therefore, many researchers prefer to use alternative methods with less computational complexity. One of these is Direct Monte- Carlo Method [1]. This method is successfully used in supersonic aerodynamics. However, it turned out to be not very efficient for simulating slightly disturbed flows due to statistical noise. The other prevalent approaches are based on using model kinetic equations: the complex collision integral is replaced by relaxation forms [2]. Nevertheless, the reliability of the results obtained by these methods is dubious. Nowadays the rapid growth of modern computation systems power made it possible to solve the Boltzmann equation directly without any simplifications. We use a finite-difference method that uses fixed velocity (momentum) space and spatial grids [3]. The collision integral is evaluated by conservative projection method. It ensures the preservation of mass, momentum and energy conservation laws in molecular collisons. It also turns the collision integral of the Maxwellian distribution function into zero. This is especially important for slow flows distinctive for micro and nano devices. The approach is also valid in case of Boltzmann equation for gas mixtures, and can be applied to the generalized Boltzmann equation for gases with internal degrees of freedom [4]. In the next section the problem solving environment developed by our group is described. In section 3 the results of modeling of gas flows induced by temperature fields are analyzed. Three types of the gases are considered: monoatomic gas, gas with internal degrees of freedom and gas mixture. Section 4 presents simulation of the supersonic flow – interaction of a shock wave with periodic grid barrier in the transitional flow regime. 2 PROBLEM SOLVING ENVIRONMENT The essence of the program solving environment (PSE) is Solver – computer program that carries out numerical simulation of gas. The core of the Solver is conservative projection method. The process of computation presents an iterative process of distribution function evolution. Further, gas macroparameters are calculated and periodically recorded. Later on, the results are visualized by relevant software. The interaction of Solver with other components of the PSE is shown in Figure 1. The method of solving the Boltzmann equation uses the splitting scheme: the advection equation and the homogeneous relaxation equation are alternately solved. Consequently, the Solver consists of separate modules: modules for advection equation and modules for collision integral. The modules for collision integral enable the usage of various intermolecular potentials, such as Lennard-Jones potential, and simulation of multicomponent gas mixtures. UnstructSolv advection module is used for complex geometry modeling and is based on the method of finite volumes for unstructured grids. Generating unstructured grids is performed by the program package GMSH. NSTI-Nanotech 2012, www.nsti.org, ISBN 978-1-4665-6275-2 Vol. 2, 2012 617