First, download the configuration files from here, then go to the DASimpleFoam folder, and run the commends mentioned in the overview section.
For most of the cases, the adjoint matches the reference values by 14 significant digits.
Shape variable
dCD/dFFD variable 0 variable 1 variable 2 Forward AD Reference 0.009260839088106553 0.01047989656042717 0.02535943905573043 JacobianFree Adjoint 0.009260839088106503 0.01047989656042720 0.02535943905573065
dCL/dFFD variable 0 variable 1 variable 2 Forward AD Reference 0.2419525437248771 0.2002145064954005 0.2802869444676860 JacobianFree Adjoint 0.2419525437248756 0.2002145064953999 0.2802869444676880
dCM/dFFD variable 0 variable 1 variable 2 Forward AD Reference -0.2192473028507383 -0.2264587861502322 -0.2456468063599592 JacobianFree Adjoint -0.2192473028507387 -0.2264587861502318 -0.2456468063599599
Angle of attack
dCD/dAOA variable 0 Forward AD Reference 0.001315555355365731 JacobianFree Adjoint 0.001315555355365766
dCL/dAOA variable 0 Forward AD Reference 0.09954288373144168 JacobianFree Adjoint 0.09954288373144177
dCM/dAOA variable 0 Forward AD Reference -0.001699253810007804 JacobianFree Adjoint -0.001699253810007761