This talk presents a parallel-in-time formulation for the unsteady Reynolds-Averaged Navier-Stokes equations applied to incompressible periodic ducted flows under turbulent conditions. The method is based on a multiple-shooting approach, in which the time domain is decomposed into temporal subdomains, enabling the forward solution to be computed in parallel. The implementation relies on the open-source CFD framework OpenFOAM, using a finite-volume URANS solver based on the PIMPLE algorithm.

A key feature of the approach is that the flow solver is treated largely as a black box. Consequently, no fundamental modification of the underlying solver structure is required, making the method non-intrusive and potentially transferable to other CFD solvers. At the same time, the efficiency of the framework depends on the coordination of repeated solver calls, the exchange of data between shooting nodes, and the availability of suitable linearized solution procedures. We present numerical studies addressing the influence of shooting nodes, initial conditions, and parallel performance, and provide insight into the use of this framework for primal and adjoint computations in optimal shape design problems.