DNS have become a viable tool for determining the basic physics of transition. Here, the full Navier-Stokes equations are solved directly by numerical methods, such as finite difference, finite element, finite volume, or spectral methods. Transition is a spatially evolving process, and the spatial DNS approach is widely applicable and the closest formulation to mimicking experiments. Temporal simulations, by contrast, use periodic boundary conditions in the chordwise direction which introduces several concerns if one is modeling complex geometries, 3-D boundary layers, receptivity, control, and breakdown. The basic idea of the spatial simulation is to disturb an established basic flow by forced, time-dependent perturbations. Then the reaction of this flow, that is, the temporal and spatial development of the perturbations, is determined by the numerical solution of the complete Navier-Stokes equations. Considerations associated with this method include:
- Investigators are developing advanced, highly accurate algorithms, and the time and memory savings reported have thus far been encouraging.
- One must impose a nonintrusive downstream boundary condition. If some sort of reasonable treatment is done ahead of the boundary, upstream wave reflections can be avoided.
- Both NPSE (see below) and DNS are hampered by our current inability to connect the freestream and boundary-layer response. A physical upstream or inflow condition must be specified. A goal of our Center is to bridge this gap through our receptivity studies.