- More study has been performed on the grid convergence. In all the previous cases, as part of the physical model, min-mod limiter was used. With this limiter, poor convergence of the L2 norm residual was observed. To see the effect of the limiter on the convergence, new runs with Van Albada limiter were performed for three different pressure ratios Pe/P0i=0.71, 0.7850 and 0.82. Results were obtained for the coarse, fine, and superfine grids that were created by the algebraic grid generation program described in last week's meeting.
- With the Van Albada limiter, much better convergence of the L2 norm residual has been observed for all the cases (figures 1 through 3). This shows the effect of the limiter, thus the choice of the physical modeling parameters, on the convergence.
- Figure 4 shows the mach number convergence history for coarse, fine, and superfine grids with Van Albada limiter at x/yt=2.245 and y/yt-0.445 (Pe/P0i=0.82).
- Figure 5 and 6 show nozzle efficiency results for different grids and limiters. Figure 7 shows P0/P0i results at two different locations (one upstream of the shock and the other at the exit) for different grids and min-mod limiter. Figure 8 shows the same variables (of figure 7) obtained with the Van Albada limiter.
- In figure 10 and 11 shock profiles obtained with all the grids and limiters are shown for Pe/P0i=0.71 and 0.82 respectively. At both pressure ratios, the min-mod results obtained with the old fine and the old coarse grids are in close agreement with the min-mod results of the new fine and the new coarse grid results.
- Now I'm in the process of calculating the error distribution by using the results obtained with the Van Albada limiter.
Figure 1. L2 norm residual convergence history for coarse, fine,
and superfine grids with Van Albada limiter (Pe/P0i=0.71)
Figure 2. L2 norm residual convergence history for coarse, fine, and
superfine grids with Van Albada limiter (Pe/P0i=0.7850).
Figure 3. L2 norm residual convergence history for coarse, fine, and
superfine grids with Van Albada limiter (Pe/P0i=0.82).
Figure 4. Mach number convergence history for coarse, fine, and superfine
grids with Van Albada limiter at x/yt=2.245 and y/yt-0.445 (Pe/P0i=0.82).
Figure 5. Nozzle efficiencies at Pe/P0i=0.71, 0.7850, and 0.82
for coarse, fine, and superfine grids with Van Albada limiter.
Figure 6. Nozzle efficiencies at Pe/P0i=0.71, 0.7850, and 0.82
for all grids and limiters used .
Figure 7. P0/P0i ratios at Pe/P0i=0.71, 0.7850, and 0.82 for coarse, fine, and superfine grids with min-mod limiter. Squares are for the point at x/yt=-1.065 and y/yt=0.418 (upstream of the shock). Circles stands for the point where x/yt=8.65 and y/yt=0.603 (at the exit).
Figure 8. P0/P0i ratios at Pe/P0i=0.71, 0.7850, and 0.82 for
coarse, fine, and superfine grids with Van Albada limiter. Squares are
for the point at x/yt=-1.065 and y/yt=0.418 (upstream of the shock). Circles
stands for the point where x/yt=8.65 and y/yt=0.603 (at the exit).
Figure 9. Shock profiles for coarse, fine, and superfine grids at Pe/P0i=0.71,
0.7850 and 0.82 with Van Albada limiter.
Figure 10. Shock profiles at Pe/P0i=0.71 for all the grids and limiters
used.
Figure 11. Shock profiles at Pe/P0i=0.82 for all the grids and limiters
used.
Figure 12. Total pressure change across the shock (P02/P01 ratio, P02
upstream of the shock, P01 downstream of the shock) at j=44 line of the
superfine grid for Pe/P0i=0.71, 0.7850, and 0.82. Shock locations are also
given with circles. Red symbols stand for the results obtained with min-mod
limiter and the blue symbols for the results obtained with Van Albada limiter.
Figure 13. Pressure distribution at a j=constant line of the coarse,
fine, and superfine grid for Pe/P0i=0.71. Solid lines are for the results
obtained with Van Albada limiter and dashed-dotted lines stand for the
min-mod limiter results.