Study On Numerical Simulation Of 3-D N-S Equations And The Stability Of The Plane Boundary Layer

In the paper, nonlinear incompressible N-S equations are numerically solved by combining the higher accuracy compact finite differences of non-uniform meshes with the fourier spectral expansion. Third-order mixed explicit implicit scheme is employed for the time discretization. According to this numercial method and hydrodynamic stability theory, the nonlinear evolution of vortexes in the boundary layer and the nonlinear evolution of two-dimensional disturbance waves in the boundary layer with two dimensional localized roughnesses are studyed.The evolution of vortexes in the boundary layer are numerically simulated. Results show, during the nonlinear evolving of the vortexes, stagger high and low speed stripe structures increase gradually in the spanwise and streamwise direction, presenting symmetry stripe structure and the phenomena of the strong ejection and sweeping. The distribution of Reynolds stress and the forming of high shear layer are in reasonable agreement with other relevant articles.The evolution of the small and finite amplitude disturbance waves is simulated in the laminar boundary layer, and is according with the results of the linear theory. However, the amplification of finite amplitude disturbance waves changes a lots in the lower reaches because of the nonlinear effects.Flow of the boundary layer with two-dimensional localized roughness at the wall is simulated by distributing one or two of two-dimensional localized suction or two dimensional local blowing at the slippery wall, and the basic flow is tested to be steady. On the basis of this, the nonlinear evolution of the T-S waves are studied. All of two-dimensional T-S waves' amplitude grows greater in two dimensional basic flows induced by two dimensional blowing localized roughness at the wall than at the slippery wall. On the contrary, all of two-dimensional T-S waves' amplitude grows smaller in two dimensional basic flows induced by two dimensional suction localized roughness at the wall than at the slippery wall. The results of numerical simulation have shown that the flow instability depends, besides the strong nonlinear interaction, on the change of basic flow's stability.