Well-posed spatial marching of high-amplitude perturbations in viscous shear flows

摘要

The Parabolized Stability Equations (PSE) have been widely applied in the computation of perturbations in pre-transitional boundary layers. The formulation of the PSE nonetheless has several limitations which, depending on the setting, may undermine the stability and accuracy of the approach. In this work, we present a new marching scheme which overcomes two key deficiencies of the PSE. We derive an accurate and numerically stable marching formulation for viscous flows based on a reconstruction of the local solution in terms of downstream traveling modes. In addition, we present a method for the accurate and stable capturing of high-amplitude perturbations by computing the base flow in a streamwise marching procedure.