Characteristics Analysis of the Parabolized Stability Equations

Some mathematical details of the parabolized stability equations (PSE) [4] are investigated. In particular, the sources of (unwanted) ellipticity in these equations are identified and suggestions are made for their suppression. Both the compressible and incompressible equations in primitive-variable formulation are discussed. Remarks are also made on the velocity-vorticity formulation. A slight modification to the PSEs usually method of treatment of streamwise derivatives higher than first is proposed. Also, an expression is derived for limiting the streamwise gradient of the pressure shape function.