Automatic Differentiation Adjoint of the Reynolds-Averaged Navier–Stokes Equations with a Turbulence Model

This paper presents an approach for the rapid implementation of an adjoint solver for the Reynolds-Averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. Automatic differen-tiation is used to construct the partial derivatives required in the adjoint formulation. The resulting adjoint implementation is computationally efficient and highly accurate. The assembly of each par-tial derivative in the adjoint formulation is discussed. In addition, a coloring acceleration technique is presented to improve the adjoint efficiency. The RANS adjoint is verified with complex-step method using a flow over a bump case. The RANS-based aerodynamic shape optimization of an ONERA M6 wing is also presented to demonstrate the aerodynamic shape optimization capability. The drag coef-ficient is reduced by 19 % when subject to a lift coefficient constraint. The results are compared with Euler-based aerodynamic shape optimization and previous work. Finally, the effects of the frozen-turbulence assumption on the accuracy and computational cost are assessed. I