A Gradient Accuracy Study for the Adjoint-Based Navier-Stokes Design Method

A continuous adjoint method for Aerodynamic Shape Optimization (ASO) using the compressible Reynolds-Averaged Navier-Stokes (RANS) equations and the Baldwin-Lomax turbulence model was implemented and tested. The resulting implementation was used to determine the accuracy in the calculation of aerodynamic gradient information for use in ASO problems. For completeness, the formulation and discretization of the Navier-Stokes equations and the resulting adjoint equations are discussed. However, the reader is referred to previous work for details of the derivations. The accuracy of the resulting derivative information is investigated by direct comparison with finite-difference gradients. In the process, shortcomings of the finite difference method for the calculation of derivative information are pointed out and discussed. The advantages of the use of an adjoint method become apparent because of the strict requirements that the finite difference method imposes on the level of flow solver convergence and the sensitivity of the value of the gradients with respect to the choice of step size. Design examples for both inverse and drag minimization problems are presented. A parallel implementation using a domain decomposition approach and the MPI (Message Passing Interface) standard is used to reduce the computational cost of automatic design involving viscous flows.