Parabolized Navier-Stokes Algorithm for Solving Supersonic Flows with Upstream Influences

Abstract

A new parabolized Navier ‐Stokes (PNS) algorithm has been developed to efe ciently compute supersonic e ows with embedded regions that produce upstream effects. Innovative techniques are used to automatically detect and measure the extent of the embedded regions. Within the embedded regions, the PNS equations are globally iterated to duplicate the results that would be obtained with the complete Navier ‐Stokes (NS) equations. Once an embedded region is computed, the algorithm returns to the standard space-marching PNS mode until the next embedded region is encountered. This procedure has been successfully incorporated into NASA’ s upwind PNS code and it has been validated by its application to several two-dimensional test cases. All of these test cases include embedded regions that produce signie cant upstream effects. The present numerical results arein excellent agreement with previous NS computations and experimental data. In addition, these calculations demonstrate the signie cant reduction in computer time and storage that can be achieved by the use of this approach.