Calculation of a three-dimensional locally elliptic flow with a zonal equation method
The Navier-Stokes equatons are elliptic or time hyperbolic, but parabolizing assumptions can be made under certain conditions leading to various boundary-layer and space-marching formulations that can greatly accelerate the solution time. A zonal equation method is presented which uses zones where ellipticity is high for solution by Navier-Stokes methods, and zones where parabolizing assumptions are valid for solution by space-marching techniques. The concept of localized ellipticity is explored and evaluated.