A novel shape optimization method using knot insertion algorithm in B-spline and its application to transonic airfoil design

A new method using the cubic B-spline curves with nominal uniform knot set to parameterize the geometry is proposed to deal with shape optimization problems. In the method, the control points of the B-spline curves are set to be the design variables in the optimization scheme. A knot insertion algorithm has been introduced in order to keep the geometry unchanged whilst increasing the number of control points at the final optimization stage. The super-reduced idea and the mesh refinement are also employed to deal with the equality constraint and speed up the optimization process. The method is applied to two problems. The first is a 2-dimensional Poisson problem, and the second is an airfoil design problem. In both applications, the results show that the new method is much more efficient when compared with the traditional methods. In the airfoil design problem, the drag of the airfoil has been reduced significantly with much less function calls.