Abstract: It is interesting for designer how to reduce drag of transonic wing which meets design lift requirement. Based on adjoint equation theory and using Euler equations, an optimization design method of transonic wing with drag reduction and constant lift coefficient is developed. According to the cost function given, three dimensional adjoint equations and their boundary conditions in physical space are dreived, and a numerical method is developed to solve the three dimensional adjoint equations. The sensitivity derivation of objective function with respect to design variables can be obtained by using grid perturbation method, and the quasi-Newtonian algorithms are used. Some numerical tests are made for the drag reduction with constant lift coefficient. The test results show that shock strength on wing surface will become much weaker than that of initial wing, thus drag may be reduced effectively.

Key words: optimization design, drag reduction, adjoint equation, Euler equation, sensitivity derivative