Investigation of gradient computation based on discrete adjoint method

Viscous discrete adjoint equations and the corresponding solving method are studied and discussed based on PMB3D, i.e., a parallelized in-house CFD code for multi-block structured grid. Firstly, the discrete adjoint gradient strategy is briefly introduced. Secondly, we fully describe the variation derivation and the contribution of inviscid, artificial viscosity, and viscous parts to the discrete adjoint equations. Thirdly, the implementation of the inviscid part and the viscous boundary conditions are studied, and the simplification methods for variation derivation are discussed. Two typical simulations are respectively carried out on a wide-body aircraft and an external compression supersonic inlet to analyze the influences of these simplification methods on the solution precision. Finally, parallel solution, time integration, and convergence acceleration are discussed and validated. Numerical simulation demonstrates that the present discrete adjoint gradient strategy and equations contribute to a convenient programming and modularization. Moreover, the precision of the gradient solution is qualified for aerodynamic optimization design. The present study can be recognized as a useful reference for further study on discrete adjoint method.