We evaluate a parallel Schur preconditioner for large systems of equations arising from a finite element discretization of the Navier-Stokes equations with streamline diffusion. The performance of the method is assessed on a biomedical problem involving oscillatory flow in a human abdominal bifurcation. Fast access to flow conditions in this location might support physicians in quicker decision making concerning potential interventions. We demonstrate scaling to 8 processors with more than 50% efficiency as well as a significant relaxation of memory requirements. We found an acceleration by up to a factor 9.5 compared to a direct sparse parallel solver at stopping criteria ensuring results similar to a validated reference solution.