Numerical solution of Couette problem for monoatomic gas flow in slip regime

In this work, an approach for numerical modeling of a monatomic gas flow between two parallel plates using a finite-volume scheme is presented. Two systems of closed transport equations are derived to describe the flow. The first system addresses the classical Couette flow problem, incorporating a time component to implement the relaxation method. The second system further includes a normal velocity component, which is zero in the classical formulation. A comparative analysis of the advantages and disadvantages of both models is carried out. The simulation results show that the first formulation demonstrates better agreement with data obtained by the direct simulation Monte Carlo method. Several test cases are considered for this formulation, including different degrees of wall heating, as well as subsonic and supersonic plate velocity. The simulations for all test cases are conducted for gas in the slip regime, allowing for an assessment of the impact of slip boundary conditions on the profiles of flow parameters. It is found that for the considered test cases, the influence of boundary conditions in the main flow region is insignificant; however, near the walls, the values of macroscopic parameters differ significantly. The velocity slip and temperature jump increase substantially with the increase of Mach number and decrease of the momentum accommodation coefficient. Comparison with the results from statistical modeling shows good accuracy of the proposed approach.