Several finite differences schemes for the parabolized Navier-Stokes (PNS) equations are introduced. These schemes are investigated for accuracy and robustness by solving the PNS equations over a 10% thick parabolic arc airfoil in a Mach 2 flowfield. Each scheme varies in the manner in which the finite difference equations are modeled in the subsonic sublayer region. Departure solutions associated with grid refinement are discussed and investigated using an innovative numerical eigenvalue technique for single sweep schemes. Eigenvalue/vector histories of departure solutions are presented to verify the technique. A global iteration scheme is given that requires no more than one to two iterations for convergence for the airfoil flowfield and can be used to overcome the problems associated with departure solutions.
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- Computational Fluid Dynamics;
- Finite Difference Theory;
- Navier-Stokes Equation;
- Parabolic Differential Equations;
- Fluid Mechanics and Heat Transfer