Abstract: For the viscous aerodynamic inverse design with specified pressure distribution, in view of the fact that the pressure variation caused by wall perturbation is dominantly owing to its potential effect, an approximate adjoint equation is proposed to calculate the object function gradient with respect to the design variables. A viscous flow field of fine mesh is interpolated into the coarse mesh and the new mesh is treated as the solution of the viscous body force model. In this case, a simple source term replaces a complex viscous term in the original adjoint equations. The time cost by the approximate adjoint equations can be decreased to one tenth of the viscous equations because of the drastically reduced grid points of the coarse mesh and much faster convergence. The results of typical cases indicate that the sensitivity derivative gained by the approximate method has good accuracy and the inverse design can be completed efficiently with reduced total computational time.

Key words: viscous flow, body force model, adjoint equations, inverse design, sensitivity derivative