Numerical solution of unsteady, compressible, reduced NavierStokes equations
Abstract
The limits of applicability of the Reduced NavierStokes (RNS) equations are explored. Some steady flows with large separation and unsteady flows with vortex shedding are investigated with unsteady, compressible RNS equations. The line relaxation procedure previously developed to solve the steady RNS equations is extended to solve the unsteady equations. A modification of the standard line relaxation procedure that is more stable and efficient is presented. The five point coupled strongly implicit procedure, employed in the study of the stream function vorticity form of the full NS equation, is modified to solve a nine point finite difference scheme. The usefulness of the RNS approximation in the study of steady flows with large separation and unsteady flows with vortex shedding is demonstrated by comparing some RNS solutions with available full NS calculations. The shock capturing capability of the RNS procedure is demonstrated for a model problem. A hysteresis effect leading to different steady and unsteady solutions for the same conditions is observed from the numerical studies of the flow past a finite flat plate at incidence.
 Publication:

Ph.D. Thesis
 Pub Date:
 1988
 Bibcode:
 1988PhDT........17R
 Keywords:

 Compressible Flow;
 NavierStokes Equation;
 Steady Flow;
 Unsteady Flow;
 Vortex Shedding;
 Finite Difference Theory;
 Hysteresis;
 Relaxation Method (Mathematics);
 Fluid Mechanics and Heat Transfer