The adjoint based design optimisation is carried out, in which the sensitivity of the objective function to the design variables can be written as

where

*I*is the objective,**the design variable vector,***D***the flow property vector,***W***the residual,***R***the mesh vector,***X***the moving mesh operator,***T***the adjoint vectors.***L*In the above formulation, the solution of the flow adjoint problem eliminates the first term on the right hand side. This resolves the difficulty associated with the calculation of for large number of design variables.

Furthermore the solution of the mesh adjoint problem eliminates the second term on the right hand side, resolving the difficulty in calculating for large mesh and large number of design variables.