Compressible laminar boundary-layer flows with statistical Bhatnagar-Gross-Krook approaches

In this work, we study the well-known, fundamental viscous fluid problem of compressible, laminar boundarylayer flow over a flat plate. The paper investigates the modeling of such flows using the Bhatnagar-Gross-Krook and ellipsoidal statistical Bhatnagar-Gross-Krook model kinetic equations for the supersonic flow of argon gas over a flat plate in the semirarefied regime. The Bhatnagar-Gross-Krook and ellipsoidal statistical Bhatnagar-Gross-Krook solutions are compared with the exact, well-known direct simulation Monte Carlo method as well as the theoretical solution of the boundary-layer equations that include velocity slip and temperature jump boundary conditions for adiabatic and isothermal wall boundary conditions. It is found that the solutions obtained by the statistical Bhatnagar-Gross-Krook and ellipsoidal statistical Bhatnagar-Gross-Krook methods agree well with the theoretical and the benchmark direct simulation Monte Carlo solutions. Both approaches capture the shock wave appearing at the leading edge of the flat plate, but the ellipsoidal statistical Bhatnagar-Gross-Krook approach is shown to be in better agreement with the benchmark direct simulation Monte Carlo method solutions as well as the theoretical results. In addition, the statistical Bhatnagar-Gross-Krook and ellipsoidal statistical Bhatnagar-Gross-Krook methods are shown to be numerically more efficient than the direct simulation Monte Carlo method.