Due to the steadily increasing number of computing cores of current hardware, advancements in the scalability of CFD solvers is an important research area. Time parallel methods are becoming popular because they handle more unknowns by including multiple time steps in the system, offering an extra dimension for parallelization. However, parallelizing across the time dimension presents unique challenges due to its one-way causal nature. Various strategies have been developed to address this. A notable approach is the multigrid waveform relaxation [2], which integrates well with domain decomposition based PDE solvers. This method has been effectively adapted for splitting based approaches, which require efficient preconditioners for time-parallel pressure-Poisson and convection-diffusion problems, see [3] and [1]. Instead, we propose a multigrid waveform relaxation applied to a monolithic solver for the unsteady Oseen equations, using an additive cell-wise Vanka preconditioner as a spatial smoother. The stability across various Reynolds numbers and the number of blocked time steps is investigated. Also the enhancement in strong scalability by optimizing interprocess communication is shown. Lastly, we present data demonstrating performance improvements in benchmark cases for a fully linearized system based on Newton’s method, showcasing the potential of our approach in practical applications. REFERENCES [1] J. Dünnebacke et al. Increased space-parallelism via time-simultaneous Newton- multigrid methods for nonstationary nonlinear PDE problems. Int. J. High Perform. Comput. Appl., vol. 35, no. 3, 2021. [2] J. Janssen and S. Vandewalle. Multigrid waveform relaxation on spatial finite element meshes: The discrete-time case. SIAM J. Sci. Comput., vol. 17, no. 1, pp. 133–155, 1996. [3] C. Lohmann and S. Turek. On the Design of Global-in-Time Newton-Multigrid- Pressure Schur Complement Solvers for Incompressible Flow Problems. J. Math. Fluid Mech. 25, 64 (2023).