Numerical simulation of shock wave propagation in microchannels using continuum and kinetic approaches

Numerical simulations of shock wave propagation in microchannels and microtubes (viscous shock tube problem) have been performed using three different approaches: the Navier-Stokes equations with the velocity slip and temperature jump boundary conditions, the statistical Direct Simulation Monte Carlo method for the Boltzmann equation, and the model kinetic Bhatnagar-Gross-Krook equation with the Shakhov equilibrium distribution function. Effects of flow rarefaction and dissipation are investigated and the results obtained with different approaches are compared. A parametric study of the problem for different Knudsen numbers and initial shock strengths is carried out using the Navier-Stokes computations.