In this paper, a cross-section of numerical algorithm development at NLR for end-user applications in aerospace is presented. Aerospace is characterized by high safety requirements and standards, complex development programs and operational processes, and challenging multi-physics phenomena. An example is the certification or qualification of civil and military aircraft, helicopters, Unmanned (Combat) Aerial Vehicles (UCAV), or Expendable Launch Vehicles (ELV). This application requires numerical algorithms that have a high level of physical fidelity, a high level of accuracy, short total turn-around times, and low cost. Three applications driving numerical algorithm development at NLR are presented: the simulation of nozzle buffet loads, for qualified space launchers, the simulation of non-linear flutter properties, for qualified fighter configurations, and the simulation of blade-vortex interaction, for the development of environmentally friendly helicopters.