On the prescribed inlet boundary condition with no buffer zone for the subsonic compressible laminar boundary layer with hybrid application of equations

In the computation of compressible Navier-Stokes equations for viscous flows, if a uniform boundary condition is enforced at the inlet of computational domain without buffer zone, the thickness of boundary layer is underestimated while the inner-layer velocity is overestimated since the pressure is artificially added due to the growth of shear velocity at the surface of a flat plate. This results in unstable and inaccurate numerical solutions, and to solve this problem, a novel hybrid method is proposed to obtain an aligned prescribed inlet boundary condition. With a solution of perturbed velocity potential equation for compressible flow and the consideration of displacement thickness of laminar boundary layer at the earlier stage, the whole domain is solved rapidly to prescribe the modified velocity profile at the inlet boundary as a next step for the main solution of full Navier-Stokes equations. For faster convergence and better numerical stability, 2D-NSCBC(two-dimensional Navier-Stokes characteristics boundary condition) is applied in the solution of full Navier-Stokes equations. The results overall give a complete success for Ma < 0.9 at least, and are even improved remarkably for the numerical stability with adoption of specified velocity despite of considerable error in the transonic flow regime above the critical Mach number 0.9. With the present method, we succeeded to remove the whole buffer zone for the inlet boundary condition of subsonic compressible flow.