Stability of Parallel Flows of Second-Order Liquids

The Orr-Sommerfeld equation, modified to include viscoelastic terms, is solved using a finite-difference method. Combined Couette-Poiseuille flow and flat-plate boundary-layer flow are considered, and it is shown that, for second-order liquids, the influence of the viscoelasticity is always stabilizing. The present numerical scheme, which is based on central differences, does not involve a filtering or a suppressing process and, consequently, is thought to be an improvement over the previously used methods, all of which are based on forward differences.