I developed an approach for rapid development of the adjoint to the Reynolds-Averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. Automatic differentiation is used to construct the partial derivatives in the adjoint formulation. The resulting adjoint is computationally efficient and highly accurate. The assembly of each partial derivatives in the adjoint formulation are discussed. In addition, a coloring acceleration technique is presented to improve the adjoint efficiency. This figure shows the Euler and RANS stencils in the CFD solver for the coloring.
A RANS aerodynamic shape optimization of ONERA M6 wing is shown here to show the effectiveness of this approach. The results are compared with experimental data.
The RANS optimized results are compared with Euler solver and adjoint.