The Hamburg Research Training Group (RTG 2583) "Modeling, Simulation and Optimization with Fluid Dynamic Applications" combines recent technologies from applied mathematics with relevant data-driven applications from climate research and meteorology, the engineering sciences and medicine. The RTG 2583 is a collaboration between the University of Hamburg (UHH) and the Hamburg University of Technology (TUHH). Partner institutions are the Hamburg University Hospital Eppendorf (UKE) and the Max Planck Institute for Meteorology (MPI-M). The RTG 2583 provides a holistic and application-oriented training to young scientists in the mathematical disciplines modeling, simulation and optimization (MSO). Education and research follow the RTG’s leitmotif "Mathematics drives applications while being inspired by applications", where tailored MSO training concepts for simulation-based fluid dynamic applications are applied. Collaborations in the RTG address relevant research problems from Hamburg-specific application areas, including climate research and meteorology, aircraft and ship design and medicine.