Numerical solution and boundary conditions for boundary layer like flows

The numerical solution of Navier-Stokes equations requires a large amount of computer time and storage, particularly for three-dimensional high Reynolds number flows. One way of reducing the computer time and storage requirements is to use approximate equations. Consideration is given here to parabolized Navier-Stokes equations that are derived from the Navier-Stokes equations by neglecting the diffusion effects in the flow direction (in agreement with boundary layer theory). Solving these equations by marching techniques along the main direction results in considerable savings in both storage and computer time, provided that the solution is acceptable after a single marching sweep.