Propagation of a Shock Wave through a Viscous Heat-Conducting Gas in a Long Microchannel

The problem of unsteady gas flow in a channel between parallel plates initiated by the initial discontinuity of the pressure and density (Riemann problem) in the channel cross-section at the high pressure drops and moderately low Knudsen numbers is solved numerically on the basis of the full system of Navier—Stokes equations. The finite-difference scheme of the second order with respect to the spatial variables and time is used. The effect of the gas viscosity and thermal conductivity on the velocity of the shock wave and the nature of flow behind it is studied under the conditions of long channel and low gas density in the low-pressure section. The numerical solution obtained is compared with the available experimental and computational data.