SIMULATION TECHNIQUES FOR SPATIALLY EVOLVING INSTABILITIES IN COMPRESSIBLE FLOW OVER A FLAT-PLATE

In this paper we present numerical techniques suitable for a direct nu merical simulation in the spatial setting. We demonstrate the applicat ion to the simulation of compressible flat plate flow instabilities. W e compare second and fourth order accurate spatial discretization sche mes in combination with explicit multistage time stepping for the simu lation of the 2D Navier-Stokes equations. We consider Mach numbers 0.5 and 4.5. In the vicinity of the outflow boundary, an efficient buffer domain treatment is introduced, which is suitable in conjunction with an explicit time integration scheme. This treatment requires only a s hort buffer domain to damp wave reflections at the outflow boundary. R esults for the instability of Tollmien-Schlichting (T-S) waves are com pared with two instability theories, linear stability theory (LST) and linear parabolized stability equations (PSE). The growth rates of T-S waves for parallel base flow at both Mach numbers compare well with L ST results. Moreover, the growth rates of TS waves for nonparallel bas e flow compare well with results obtained by solving the PSE at Mach n umber 0.5. The second order discretization scheme requires, however, c onsiderably higher grid resolution than the fourth order method to ach ieve accurate results. High amplitude disturbances were also considere d to activate nonlinear terms. The nonlinearity strongly affects the f orm of the T-S waves and the growth rate of the disturbances. The resu lts obtained here support the use of these numerical techniques in flo w simulations with increasing complexity such as flat plate flow simul ations up to the turbulent regime and with separation regions in 3D. T he results also encourage the use of perturbations derived from the co mpressible PSE as inlet perturbations for nonparallel flow. (C) 1997 E lsevier Science Ltd.