Adjoint-based optimization allows for the optimization of complex problems with an arbitrary number of design variables. The design is traditionally optimized in a nested fashion, where the flow, adjoint, and design problems are converged separately. This can be a time-consuming process, depending on the number of iterations required to reach an optimum design. One way to substantially reduce the computational cost of design optimization is the one-shot approach. Here, the flow and adjoint feasibility are achieved simultaneously with optimality. This requires a problem-specific pre-conditioning approach, which has thus-far limited the application of the method. Within SU2, the method has only been used for external compressible Euler flow problems. The current work aims to generalize the applicability of the SU2 one-shot method. In particular, we demonstrate the application to incompressible, internal flow problems. This would allow for the application of one-shot optimization to the optimization of for example mixers or turbomachinery components.