1. The location of the farfieldboundary at 16chords from the midchord of the airfoil is found to provide a suitable compromisebetween accuracy -within a fractionof a percent - and cost of the computation. A more elaborate far field model may be employed to attenuate further the effects of the truncation of the domain. Alternatively, the far field boundary could be extended even further from the airfoil, at the expense of the resolution in the far wake. The finest grid used so far has 257 x 257 nodes with an outer boundary extended 16 chords away from the midchord of the airfoil. The calculation with the time step dt = 0.05 is presented in Figure 17. Twenty multigrid W-cycles in pseudotime (using 7 grid levels) were sufficient to reduce the maximum continuity residual to the 10V5 level on each time step during the limitingcycle asshown in Figure 18. The following mean flow quantities were computed: St= 0.5199, Cl, = 1.1696, Cl,in = 0.6748, and Cd, = 0.4536, Cd,i, = 0.3331. The computational results agree well, apart from the lower value ofthe predicted Cd,i, with those obtainedby Miyake et al. [9]using a 128x 128grid. The method in [9] employs an explicit, up to a second order accurate time discretization scheme, rational Runge-Kutta discretization in pseudotime and a multigrid convcrgence acceleration, developed by Jameson [l].
2. This formulationhas the advantage that the time step is determined solely by the physical time scales of the problem, while a fast rate of convergence of the iteration is achieved by using multigrid acceleration. The scheme is very efficient and requires less than lo-* sec. CPU time per time step, per mesh point on an IBM RISC6000-580 processor.
3. Support forthiswork was provided through by the Officeof Naval Research through Grant N00014-93-1-0079,under the supervision of Dr. E.P. Rood.
4. Solution of the Euler equations for two dimensional transonic flow by a multigrid method