Accurate, stable, explicit solution of the parabolized Navier-Stokes equations
Abstract
A stable, accurate and efficient implementation of MacCormack's explicit algorithm for the Parabolized Navier-Stokes (PNS) equations is demonstrated. The familiar problem of decoding the conservative axial flux factor is solved, resulting in accurate, smooth dependent variable profiles through the viscous layer sonic line. Source terms due to transformation of the parabolized governing functions into the computational plane and the resultant metric differencing have been identified and eliminated through inclusion of the appropriate geometric conservation law terms. Test cases computed include two- and three-dimensional supersonic and hypersonic flow at laminar and turbulent Reynolds numbers. The computed results demonstrate very good agreement with experiment and solutions of the full Navier-Stokes equations. Computational times required for the MacCormack explicit PNS code are approximately equal to those of existing implicit PNS solvers. The explicit PNS code proved to be sufficiently robust to allow initializing the computation from free stream conditions. In addition, little or no added damping is required once the initial starting transients have been reduced.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- December 1987
- Bibcode:
- 1987PhDT........20G
- Keywords:
-
- Algorithms;
- Navier-Stokes Equation;
- Parabolic Differential Equations;
- Solutions;
- Axial Flow;
- Conservation Laws;
- Damping;
- Free Flow;
- Geometry;
- Laminar Flow;
- Reynolds Number;
- Surges;
- Three Dimensional Flow;
- Turbulent Flow;
- Two Dimensional Flow;
- Fluid Mechanics and Heat Transfer