Marching with the parabolized Navier-Stokes equations
Abstract
Marching techniques for the parabolized Navier-Stokes equations are considered. It is shown that with the full pressure interaction and prescribed edge pressure these equations are weakly elliptic in subsonic zones. A minimum marching step size proportional to the total thickness of the subsonic layer, exists. For step sizes approaching zero the solutions are unstable. This departure effect reflects the ill-posedness of this weakly elliptic problem step sizes less than the minimum marching step size. However, for thin subsonic boundary layers, stable and accurate solutions are possible. Moreover, by appropriate forward differencing of the axial pressure gradient a global iteration procedure, requiring only the storage of the pressure term, has been demonstrated for a separated flow problem. By further allowing for the edge pressure to adjust to the displacement effect the global procedure can be stabilized for all step sizes.
- Publication:
-
Israel Journal of Technology
- Pub Date:
- 1980
- Bibcode:
- 1980IsJT...18...21R
- Keywords:
-
- Computational Fluid Dynamics;
- Flow Equations;
- Navier-Stokes Equation;
- Parabolic Differential Equations;
- Spatial Marching;
- Boundary Layer Separation;
- Digital Techniques;
- Finite Difference Theory;
- Flat Plates;
- Flow Stability;
- Mach Number;
- Stability Derivatives;
- Subsonic Flow;
- Supersonic Flow;
- Wall Flow;
- Fluid Mechanics and Heat Transfer