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problem was 0.536 using a grid composed by 100×30 cellules (close to the present medium mesh). For the optimization run using the finer grid FDC grows to 0.676. For the multigrid optimization run, FDC is even better and equals 0.691. These results demonstrate once more the strong link between the fitness function evaluation accuracy and the convergence rate of the GA. Figure 50 shows geometries of optimal individuals obtained, respectively, by using the finest grid and the multigrid strategy to evaluate the fitness function. The two geometries are very close to each other, almost within plotting accuracy. The corresponding values of the drag coefficient are also very similar: CD=7.32×10-4 for the multigrid optimal individual (a posteriori evaluated on the finest mesh) and CD=7.64×10-4 for the fine grid one. Figure 51 shows iso-Mach lines, and wall pressure and Mach number distributions for the two solutions: once again, they are almost superposed. In summary, the proposed multigrid strategy allows improving GA convergence, and avoids a posteriori solution refinement via a gradient-based method. Moreover, computational cost for a single fitness evaluation just slightly increases with respect to a single medium grid evaluation. The resulting solution is very close to that obtained by computing the fitness function on a very fine mesh for all individuals; nevertheless, CPU time required by a single fitness evaluation using the multigrid strategy is about 1/8 with respect to a fine grid evaluation. Since a whole optimization run requires about 800 evaluations, the gain in total CPU time is dramatic. 114PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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