Multi-objective genetic algorithms are implemented to optimize airfoil shape for obtaining greater laminar range and weaker shock wave drag simultaneously by using a shock control bump. Non dominated solutions of this two-objective optimization problem indicate that aerodynamic performances of airfoils trade-off between delay of profile's transition location and increased intensity of shock wave due the bump installed at upper surface of airfoil.

The effects of grid aspect ratio on the efficiency of implicit multigrid method have been analysed theoretically. The results indicate that the algorithm affects convergence on highly stretched or non unifirm grids. The improvement ways are introduced, and the validations are also been discussed. Finally the comparison of convergence between the original model and the improved one is presented.