Stabilisation of Discrete Adjoint Solvers through Improved Primal Timestepping

One major challenge in applying the adjoint method to large industrial cases is the lack of robustness of the flow and adjoint solvers. Discrete adjoints transpose the Jacobian of the system of discretised equations exactly, and hence inherit the linear stability from the primal flow solver. Typically the linear stability properties of the iterative scheme of the flow solver is very well understood, hence this is an attractive property. When the flow solver does not converge fully due to either numerical or physical instabilities, the discrete adjoint is bound to diverge and force the gradient-based optimisation to stop prematurely.