A Numerical Method for Simulation of Microflows by Solving Directly Kinetic Equations with WENO Schemes

• Published in: Journal of scientific computing Vol. 57; no. 1; pp. 42 - 73
• Main Authors: Kudryavtsev, A. N., Shershnev, A. A.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.10.2013; Springer Nature B.V
• Subjects: Algorithms; Boundary conditions; Computation; Computational Mathematics and Numerical Analysis; Direct simulation Monte Carlo method; Equilibrium; Gas flow; Gases; Kinetic equations; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Microchannels; Numerical methods; Rarefied gas dynamics; Rarefied gases; Shock capturing; Shock wave propagation; Simulation; Theoretical; Unsteady flow; Velocity; Viscosity; Finite-difference scheme; Kinetic models; Transitional regime; Gas microflows
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-013-9694-z

A numerical method for simulation of transitional-regime gas flows in microdevices is presented. The method is based on solving relaxation-type kinetic equations using high-order shock capturing weighted essentially non-oscillatory (WENO) schemes in the coordinate space and the discrete ordinate techniques in the velocity space. In contrast to the direct simulation Monte Carlo (DSMC) method, this approach is not subject to statistical scattering and is equally efficient when simulating both steady and unsteady flows. The presented numerical method is used to simulate some classical problems of rarefied gas dynamics as well as some microflows of practical interest, namely shock wave propagation in a microchannel and steady and unsteady flows in a supersonic micronozzle. Computational results are compared with Navier–Stokes and DSMC solutions.