Time-parallel solution of the unsteady Reynolds-averaged Navier-Stokes equations based on a multiple-shooting approach

This research investigates the potential of a parallel-in-time formulation of the Unsteady Reynolds-Averaged Navier-Stokes Equations when applied to incompressible periodic ducted flows facing turbulent flow conditions. The parallelisation within the time dimension is achieved by relying on a multiple-shooting-based scheme that decomposes the time window of interest into multiple temporal subdomains promising Newton-like convergence. Various aspects are assessed by means of numerical studies that include the impact of the chosen number of shooting nodes, the imposed initial conditions therein, the overall numerical robustness as well as the performance of the underlying parallelisation framework. The general capability of the realised parallel-in-time method to provide fast approximations of unsteady turbulent flow fields is demonstrated and its potential computational benefits over a conventional solution procedure are discussed based on the required computational ressources observed in this research.