Numerical simulation of transition in boundary layers

Different implications of employment of the temporal or spatial model in direct numerical simulations of transition based on the complete Navier-Stokes equations are outlined, and it is noted that in situations where approximations are not justified, the temporal model cannot be employed. The discussion is then concentrated on developing numerical methods for solving the Navier-Stokes equations based on the spatial model that are applicable for realistic situations for which the temporal model would not be valid. It is concluded that in the future numerical simulations based on the spatial approach will replace, to a large extent, the temporal simulations.